Infomotions, Inc.Metaphysics / Aristotle



Author: Aristotle
Title: Metaphysics
Publisher: Eris Etext Project
Tag(s): substance; western philosophy
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                                     350 BC

                                  METAPHYSICS

                                  by Aristotle

                            translated by W. D. Ross

                                Book I

                                   1

    ALL men by nature desire to know. An indication of this is the
delight we take in our senses; for even apart from their usefulness
they are loved for themselves; and above all others the sense of
sight. For not only with a view to action, but even when we are not
going to do anything, we prefer seeing (one might say) to everything
else. The reason is that this, most of all the senses, makes us know
and brings to light many differences between things.

    By nature animals are born with the faculty of sensation, and from
sensation memory is produced in some of them, though not in others.
And therefore the former are more intelligent and apt at learning than
those which cannot remember; those which are incapable of hearing
sounds are intelligent though they cannot be taught, e.g. the bee, and
any other race of animals that may be like it; and those which besides
memory have this sense of hearing can be taught.

    The animals other than man live by appearances and memories, and
have but little of connected experience; but the human race lives also
by art and reasonings. Now from memory experience is produced in
men; for the several memories of the same thing produce finally the
capacity for a single experience. And experience seems pretty much
like science and art, but really science and art come to men through
experience; for 'experience made art', as Polus says, 'but
inexperience luck.' Now art arises when from many notions gained by
experience one universal judgement about a class of objects is
produced. For to have a judgement that when Callias was ill of this
disease this did him good, and similarly in the case of Socrates and
in many individual cases, is a matter of experience; but to judge that
it has done good to all persons of a certain constitution, marked
off in one class, when they were ill of this disease, e.g. to
phlegmatic or bilious people when burning with fevers-this is a matter
of art.

    With a view to action experience seems in no respect inferior to
art, and men of experience succeed even better than those who have
theory without experience. (The reason is that experience is knowledge
of individuals, art of universals, and actions and productions are all
concerned with the individual; for the physician does not cure man,
except in an incidental way, but Callias or Socrates or some other
called by some such individual name, who happens to be a man. If,
then, a man has the theory without the experience, and recognizes
the universal but does not know the individual included in this, he
will often fail to cure; for it is the individual that is to be
cured.) But yet we think that knowledge and understanding belong to
art rather than to experience, and we suppose artists to be wiser than
men of experience (which implies that Wisdom depends in all cases
rather on knowledge); and this because the former know the cause,
but the latter do not. For men of experience know that the thing is
so, but do not know why, while the others know the 'why' and the
cause. Hence we think also that the masterworkers in each craft are
more honourable and know in a truer sense and are wiser than the
manual workers, because they know the causes of the things that are
done (we think the manual workers are like certain lifeless things
which act indeed, but act without knowing what they do, as fire
burns,-but while the lifeless things perform each of their functions
by a natural tendency, the labourers perform them through habit); thus
we view them as being wiser not in virtue of being able to act, but of
having the theory for themselves and knowing the causes. And in
general it is a sign of the man who knows and of the man who does
not know, that the former can teach, and therefore we think art more
truly knowledge than experience is; for artists can teach, and men
of mere experience cannot.

    Again, we do not regard any of the senses as Wisdom; yet surely
these give the most authoritative knowledge of particulars. But they
do not tell us the 'why' of anything-e.g. why fire is hot; they only
say that it is hot.

    At first he who invented any art whatever that went beyond the
common perceptions of man was naturally admired by men, not only
because there was something useful in the inventions, but because he
was thought wise and superior to the rest. But as more arts were
invented, and some were directed to the necessities of life, others to
recreation, the inventors of the latter were naturally always regarded
as wiser than the inventors of the former, because their branches of
knowledge did not aim at utility. Hence when all such inventions
were already established, the sciences which do not aim at giving
pleasure or at the necessities of life were discovered, and first in
the places where men first began to have leisure. This is why the
mathematical arts were founded in Egypt; for there the priestly
caste was allowed to be at leisure.

    We have said in the Ethics what the difference is between art
and science and the other kindred faculties; but the point of our
present discussion is this, that all men suppose what is called Wisdom
to deal with the first causes and the principles of things; so that,
as has been said before, the man of experience is thought to be
wiser than the possessors of any sense-perception whatever, the artist
wiser than the men of experience, the masterworker than the
mechanic, and the theoretical kinds of knowledge to be more of the
nature of Wisdom than the productive. Clearly then Wisdom is knowledge
about certain principles and causes.

                                   2

    Since we are seeking this knowledge, we must inquire of what
kind are the causes and the principles, the knowledge of which is
Wisdom. If one were to take the notions we have about the wise man,
this might perhaps make the answer more evident. We suppose first,
then, that the wise man knows all things, as far as possible, although
he has not knowledge of each of them in detail; secondly, that he
who can learn things that are difficult, and not easy for man to know,
is wise (sense-perception is common to all, and therefore easy and
no mark of Wisdom); again, that he who is more exact and more
capable of teaching the causes is wiser, in every branch of knowledge;
and that of the sciences, also, that which is desirable on its own
account and for the sake of knowing it is more of the nature of Wisdom
than that which is desirable on account of its results, and the
superior science is more of the nature of Wisdom than the ancillary;
for the wise man must not be ordered but must order, and he must not
obey another, but the less wise must obey him.

    Such and so many are the notions, then, which we have about Wisdom
and the wise. Now of these characteristics that of knowing all
things must belong to him who has in the highest degree universal
knowledge; for he knows in a sense all the instances that fall under
the universal. And these things, the most universal, are on the
whole the hardest for men to know; for they are farthest from the
senses. And the most exact of the sciences are those which deal most
with first principles; for those which involve fewer principles are
more exact than those which involve additional principles, e.g.
arithmetic than geometry. But the science which investigates causes is
also instructive, in a higher degree, for the people who instruct us
are those who tell the causes of each thing. And understanding and
knowledge pursued for their own sake are found most in the knowledge
of that which is most knowable (for he who chooses to know for the
sake of knowing will choose most readily that which is most truly
knowledge, and such is the knowledge of that which is most
knowable); and the first principles and the causes are most
knowable; for by reason of these, and from these, all other things
come to be known, and not these by means of the things subordinate
to them. And the science which knows to what end each thing must be
done is the most authoritative of the sciences, and more authoritative
than any ancillary science; and this end is the good of that thing,
and in general the supreme good in the whole of nature. Judged by
all the tests we have mentioned, then, the name in question falls to
the same science; this must be a science that investigates the first
principles and causes; for the good, i.e. the end, is one of the
causes.

    That it is not a science of production is clear even from the
history of the earliest philosophers. For it is owing to their
wonder that men both now begin and at first began to philosophize;
they wondered originally at the obvious difficulties, then advanced
little by little and stated difficulties about the greater matters,
e.g. about the phenomena of the moon and those of the sun and of the
stars, and about the genesis of the universe. And a man who is puzzled
and wonders thinks himself ignorant (whence even the lover of myth
is in a sense a lover of Wisdom, for the myth is composed of wonders);
therefore since they philosophized order to escape from ignorance,
evidently they were pursuing science in order to know, and not for any
utilitarian end. And this is confirmed by the facts; for it was when
almost all the necessities of life and the things that make for
comfort and recreation had been secured, that such knowledge began
to be sought. Evidently then we do not seek it for the sake of any
other advantage; but as the man is free, we say, who exists for his
own sake and not for another's, so we pursue this as the only free
science, for it alone exists for its own sake.

    Hence also the possession of it might be justly regarded as beyond
human power; for in many ways human nature is in bondage, so that
according to Simonides 'God alone can have this privilege', and it
is unfitting that man should not be content to seek the knowledge that
is suited to him. If, then, there is something in what the poets
say, and jealousy is natural to the divine power, it would probably
occur in this case above all, and all who excelled in this knowledge
would be unfortunate. But the divine power cannot be jealous (nay,
according to the proverb, 'bards tell a lie'), nor should any other
science be thought more honourable than one of this sort. For the most
divine science is also most honourable; and this science alone must
be, in two ways, most divine. For the science which it would be most
meet for God to have is a divine science, and so is any science that
deals with divine objects; and this science alone has both these
qualities; for (1) God is thought to be among the causes of all things
and to be a first principle, and (2) such a science either God alone
can have, or God above all others. All the sciences, indeed, are
more necessary than this, but none is better.

    Yet the acquisition of it must in a sense end in something which
is the opposite of our original inquiries. For all men begin, as we
said, by wondering that things are as they are, as they do about
self-moving marionettes, or about the solstices or the
incommensurability of the diagonal of a square with the side; for it
seems wonderful to all who have not yet seen the reason, that there is
a thing which cannot be measured even by the smallest unit. But we
must end in the contrary and, according to the proverb, the better
state, as is the case in these instances too when men learn the cause;
for there is nothing which would surprise a geometer so much as if the
diagonal turned out to be commensurable.

    We have stated, then, what is the nature of the science we are
searching for, and what is the mark which our search and our whole
investigation must reach.

                                   3

    Evidently we have to acquire knowledge of the original causes (for
we say we know each thing only when we think we recognize its first
cause), and causes are spoken of in four senses. In one of these we
mean the substance, i.e. the essence (for the 'why' is reducible
finally to the definition, and the ultimate 'why' is a cause and
principle); in another the matter or substratum, in a third the source
of the change, and in a fourth the cause opposed to this, the
purpose and the good (for this is the end of all generation and
change). We have studied these causes sufficiently in our work on
nature, but yet let us call to our aid those who have attacked the
investigation of being and philosophized about reality before us.
For obviously they too speak of certain principles and causes; to go
over their views, then, will be of profit to the present inquiry,
for we shall either find another kind of cause, or be more convinced
of the correctness of those which we now maintain.

    Of the first philosophers, then, most thought the principles which
were of the nature of matter were the only principles of all things.
That of which all things that are consist, the first from which they
come to be, the last into which they are resolved (the substance
remaining, but changing in its modifications), this they say is the
element and this the principle of things, and therefore they think
nothing is either generated or destroyed, since this sort of entity is
always conserved, as we say Socrates neither comes to be absolutely
when he comes to be beautiful or musical, nor ceases to be when
loses these characteristics, because the substratum, Socrates
himself remains. just so they say nothing else comes to be or ceases
to be; for there must be some entity-either one or more than
one-from which all other things come to be, it being conserved.

    Yet they do not all agree as to the number and the nature of these
principles. Thales, the founder of this type of philosophy, says the
principle is water (for which reason he declared that the earth
rests on water), getting the notion perhaps from seeing that the
nutriment of all things is moist, and that heat itself is generated
from the moist and kept alive by it (and that from which they come
to be is a principle of all things). He got his notion from this fact,
and from the fact that the seeds of all things have a moist nature,
and that water is the origin of the nature of moist things.

    Some think that even the ancients who lived long before the
present generation, and first framed accounts of the gods, had a
similar view of nature; for they made Ocean and Tethys the parents
of creation, and described the oath of the gods as being by water,
to which they give the name of Styx; for what is oldest is most
honourable, and the most honourable thing is that by which one swears.
It may perhaps be uncertain whether this opinion about nature is
primitive and ancient, but Thales at any rate is said to have declared
himself thus about the first cause. Hippo no one would think fit to
include among these thinkers, because of the paltriness of his
thought.

    Anaximenes and Diogenes make air prior to water, and the most
primary of the simple bodies, while Hippasus of Metapontium and
Heraclitus of Ephesus say this of fire, and Empedocles says it of
the four elements (adding a fourth-earth-to those which have been
named); for these, he says, always remain and do not come to be,
except that they come to be more or fewer, being aggregated into one
and segregated out of one.

    Anaxagoras of Clazomenae, who, though older than Empedocles, was
later in his philosophical activity, says the principles are
infinite in number; for he says almost all the things that are made of
parts like themselves, in the manner of water or fire, are generated
and destroyed in this way, only by aggregation and segregation, and
are not in any other sense generated or destroyed, but remain
eternally.

    From these facts one might think that the only cause is the
so-called material cause; but as men thus advanced, the very facts
opened the way for them and joined in forcing them to investigate
the subject. However true it may be that all generation and
destruction proceed from some one or (for that matter) from more
elements, why does this happen and what is the cause? For at least the
substratum itself does not make itself change; e.g. neither the wood
nor the bronze causes the change of either of them, nor does the
wood manufacture a bed and the bronze a statue, but something else
is the cause of the change. And to seek this is to seek the second
cause, as we should say,-that from which comes the beginning of the
movement. Now those who at the very beginning set themselves to this
kind of inquiry, and said the substratum was one, were not at all
dissatisfied with themselves; but some at least of those who
maintain it to be one-as though defeated by this search for the second
cause-say the one and nature as a whole is unchangeable not only in
respect of generation and destruction (for this is a primitive belief,
and all agreed in it), but also of all other change; and this view
is peculiar to them. Of those who said the universe was one, then none
succeeded in discovering a cause of this sort, except perhaps
Parmenides, and he only inasmuch as he supposes that there is not only
one but also in some sense two causes. But for those who make more
elements it is more possible to state the second cause, e.g. for those
who make hot and cold, or fire and earth, the elements; for they treat
fire as having a nature which fits it to move things, and water and
earth and such things they treat in the contrary way.

    When these men and the principles of this kind had had their
day, as the latter were found inadequate to generate the nature of
things men were again forced by the truth itself, as we said, to
inquire into the next kind of cause. For it is not likely either
that fire or earth or any such element should be the reason why things
manifest goodness and, beauty both in their being and in their
coming to be, or that those thinkers should have supposed it was;
nor again could it be right to entrust so great a matter to
spontaneity and chance. When one man said, then, that reason was
present-as in animals, so throughout nature-as the cause of order
and of all arrangement, he seemed like a sober man in contrast with
the random talk of his predecessors. We know that Anaxagoras certainly
adopted these views, but Hermotimus of Clazomenae is credited with
expressing them earlier. Those who thought thus stated that there is a
principle of things which is at the same time the cause of beauty, and
that sort of cause from which things acquire movement.

                                   4

    One might suspect that Hesiod was the first to look for such a
thing-or some one else who put love or desire among existing things as
a principle, as Parmenides, too, does; for he, in constructing the
genesis of the universe, says:-

          Love first of all the Gods she planned.

    And Hesiod says:-

          First of all things was chaos made, and then

          Broad-breasted earth...

          And love, 'mid all the gods pre-eminent,

  which implies that among existing things there must be from the
first a cause which will move things and bring them together. How
these thinkers should be arranged with regard to priority of discovery
let us be allowed to decide later; but since the contraries of the
various forms of good were also perceived to be present in
nature-not only order and the beautiful, but also disorder and the
ugly, and bad things in greater number than good, and ignoble things
than beautiful-therefore another thinker introduced friendship and
strife, each of the two the cause of one of these two sets of
qualities. For if we were to follow out the view of Empedocles, and
interpret it according to its meaning and not to its lisping
expression, we should find that friendship is the cause of good
things, and strife of bad. Therefore, if we said that Empedocles in
a sense both mentions, and is the first to mention, the bad and the
good as principles, we should perhaps be right, since the cause of all
goods is the good itself.

    These thinkers, as we say, evidently grasped, and to this
extent, two of the causes which we distinguished in our work on
nature-the matter and the source of the movement-vaguely, however, and
with no clearness, but as untrained men behave in fights; for they
go round their opponents and often strike fine blows, but they do
not fight on scientific principles, and so too these thinkers do not
seem to know what they say; for it is evident that, as a rule, they
make no use of their causes except to a small extent. For Anaxagoras
uses reason as a deus ex machina for the making of the world, and when
he is at a loss to tell from what cause something necessarily is, then
he drags reason in, but in all other cases ascribes events to anything
rather than to reason. And Empedocles, though he uses the causes to
a greater extent than this, neither does so sufficiently nor attains
consistency in their use. At least, in many cases he makes love
segregate things, and strife aggregate them. For whenever the universe
is dissolved into its elements by strife, fire is aggregated into one,
and so is each of the other elements; but whenever again under the
influence of love they come together into one, the parts must again be
segregated out of each element.

    Empedocles, then, in contrast with his precessors, was the first
to introduce the dividing of this cause, not positing one source of
movement, but different and contrary sources. Again, he was the
first to speak of four material elements; yet he does not use four,
but treats them as two only; he treats fire by itself, and its
opposite-earth, air, and water-as one kind of thing. We may learn this
by study of his verses.

    This philosopher then, as we say, has spoken of the principles
in this way, and made them of this number. Leucippus and his associate
Democritus say that the full and the empty are the elements, calling
the one being and the other non-being-the full and solid being
being, the empty non-being (whence they say being no more is than
non-being, because the solid no more is than the empty); and they make
these the material causes of things. And as those who make the
underlying substance one generate all other things by its
modifications, supposing the rare and the dense to be the sources of
the modifications, in the same way these philosophers say the
differences in the elements are the causes of all other qualities.
These differences, they say, are three-shape and order and position.
For they say the real is differentiated only by 'rhythm and
'inter-contact' and 'turning'; and of these rhythm is shape,
inter-contact is order, and turning is position; for A differs from
N in shape, AN from NA in order, M from W in position. The question of
movement-whence or how it is to belong to things-these thinkers,
like the others, lazily neglected.

    Regarding the two causes, then, as we say, the inquiry seems to
have been pushed thus far by the early philosophers.

                                   5

    Contemporaneously with these philosophers and before them, the
so-called Pythagoreans, who were the first to take up mathematics, not
only advanced this study, but also having been brought up in it they
thought its principles were the principles of all things. Since of
these principles numbers are by nature the first, and in numbers
they seemed to see many resemblances to the things that exist and come
into being-more than in fire and earth and water (such and such a
modification of numbers being justice, another being soul and
reason, another being opportunity-and similarly almost all other
things being numerically expressible); since, again, they saw that the
modifications and the ratios of the musical scales were expressible in
numbers;-since, then, all other things seemed in their whole nature to
be modelled on numbers, and numbers seemed to be the first things in
the whole of nature, they supposed the elements of numbers to be the
elements of all things, and the whole heaven to be a musical scale and
a number. And all the properties of numbers and scales which they
could show to agree with the attributes and parts and the whole
arrangement of the heavens, they collected and fitted into their
scheme; and if there was a gap anywhere, they readily made additions
so as to make their whole theory coherent. E.g. as the number 10 is
thought to be perfect and to comprise the whole nature of numbers,
they say that the bodies which move through the heavens are ten, but
as the visible bodies are only nine, to meet this they invent a
tenth--the 'counter-earth'. We have discussed these matters more
exactly elsewhere.

    But the object of our review is that we may learn from these
philosophers also what they suppose to be the principles and how these
fall under the causes we have named. Evidently, then, these thinkers
also consider that number is the principle both as matter for things
and as forming both their modifications and their permanent states,
and hold that the elements of number are the even and the odd, and
that of these the latter is limited, and the former unlimited; and
that the One proceeds from both of these (for it is both even and
odd), and number from the One; and that the whole heaven, as has
been said, is numbers.

    Other members of this same school say there are ten principles,
which they arrange in two columns of cognates-limit and unlimited, odd
and even, one and plurality, right and left, male and female,
resting and moving, straight and curved, light and darkness, good
and bad, square and oblong. In this way Alcmaeon of Croton seems
also to have conceived the matter, and either he got this view from
them or they got it from him; for he expressed himself similarly to
them. For he says most human affairs go in pairs, meaning not definite
contrarieties such as the Pythagoreans speak of, but any chance
contrarieties, e.g. white and black, sweet and bitter, good and bad,
great and small. He threw out indefinite suggestions about the other
contrarieties, but the Pythagoreans declared both how many and which
their contraricties are.

    From both these schools, then, we can learn this much, that the
contraries are the principles of things; and how many these principles
are and which they are, we can learn from one of the two schools.
But how these principles can be brought together under the causes we
have named has not been clearly and articulately stated by them;
they seem, however, to range the elements under the head of matter;
for out of these as immanent parts they say substance is composed
and moulded.

    From these facts we may sufficiently perceive the meaning of the
ancients who said the elements of nature were more than one; but there
are some who spoke of the universe as if it were one entity, though
they were not all alike either in the excellence of their statement or
in its conformity to the facts of nature. The discussion of them is in
no way appropriate to our present investigation of causes, for. they
do not, like some of the natural philosophers, assume being to be
one and yet generate it out of the one as out of matter, but they
speak in another way; those others add change, since they generate the
universe, but these thinkers say the universe is unchangeable. Yet
this much is germane to the present inquiry: Parmenides seems to
fasten on that which is one in definition, Melissus on that which is
one in matter, for which reason the former says that it is limited,
the latter that it is unlimited; while Xenophanes, the first of
these partisans of the One (for Parmenides is said to have been his
pupil), gave no clear statement, nor does he seem to have grasped
the nature of either of these causes, but with reference to the
whole material universe he says the One is God. Now these thinkers, as
we said, must be neglected for the purposes of the present inquiry-two
of them entirely, as being a little too naive, viz. Xenophanes and
Melissus; but Parmenides seems in places to speak with more insight.
For, claiming that, besides the existent, nothing non-existent exists,
he thinks that of necessity one thing exists, viz. the existent and
nothing else (on this we have spoken more clearly in our work on
nature), but being forced to follow the observed facts, and
supposing the existence of that which is one in definition, but more
than one according to our sensations, he now posits two causes and two
principles, calling them hot and cold, i.e. fire and earth; and of
these he ranges the hot with the existent, and the other with the
non-existent.

    From what has been said, then, and from the wise men who have
now sat in council with us, we have got thus much-on the one hand from
the earliest philosophers, who regard the first principle as corporeal
(for water and fire and such things are bodies), and of whom some
suppose that there is one corporeal principle, others that there are
more than one, but both put these under the head of matter; and on the
other hand from some who posit both this cause and besides this the
source of movement, which we have got from some as single and from
others as twofold.

    Down to the Italian school, then, and apart from it,
philosophers have treated these subjects rather obscurely, except
that, as we said, they have in fact used two kinds of cause, and one
of these-the source of movement-some treat as one and others as two.
But the Pythagoreans have said in the same way that there are two
principles, but added this much, which is peculiar to them, that
they thought that finitude and infinity were not attributes of certain
other things, e.g. of fire or earth or anything else of this kind, but
that infinity itself and unity itself were the substance of the things
of which they are predicated. This is why number was the substance
of all things. On this subject, then, they expressed themselves
thus; and regarding the question of essence they began to make
statements and definitions, but treated the matter too simply. For
they both defined superficially and thought that the first subject
of which a given definition was predicable was the substance of the
thing defined, as if one supposed that 'double' and '2' were the same,
because 2 is the first thing of which 'double' is predicable. But
surely to be double and to be 2 are not the same; if they are, one
thing will be many-a consequence which they actually drew. From the
earlier philosophers, then, and from their successors we can learn
thus much.

                                   6

    After the systems we have named came the philosophy of Plato,
which in most respects followed these thinkers, but had
pecullarities that distinguished it from the philosophy of the
Italians. For, having in his youth first become familiar with Cratylus
and with the Heraclitean doctrines (that all sensible things are
ever in a state of flux and there is no knowledge about them), these
views he held even in later years. Socrates, however, was busying
himself about ethical matters and neglecting the world of nature as
a whole but seeking the universal in these ethical matters, and
fixed thought for the first time on definitions; Plato accepted his
teaching, but held that the problem applied not to sensible things but
to entities of another kind-for this reason, that the common
definition could not be a definition of any sensible thing, as they
were always changing. Things of this other sort, then, he called
Ideas, and sensible things, he said, were all named after these, and
in virtue of a relation to these; for the many existed by
participation in the Ideas that have the same name as they. Only the
name 'participation' was new; for the Pythagoreans say that things
exist by 'imitation' of numbers, and Plato says they exist by
participation, changing the name. But what the participation or the
imitation of the Forms could be they left an open question.

    Further, besides sensible things and Forms he says there are the
objects of mathematics, which occupy an intermediate position,
differing from sensible things in being eternal and unchangeable, from
Forms in that there are many alike, while the Form itself is in each
case unique.

    Since the Forms were the causes of all other things, he thought
their elements were the elements of all things. As matter, the great
and the small were principles; as essential reality, the One; for from
the great and the small, by participation in the One, come the
Numbers.

    But he agreed with the Pythagoreans in saying that the One is
substance and not a predicate of something else; and in saying that
the Numbers are the causes of the reality of other things he agreed
with them; but positing a dyad and constructing the infinite out of
great and small, instead of treating the infinite as one, is
peculiar to him; and so is his view that the Numbers exist apart
from sensible things, while they say that the things themselves are
Numbers, and do not place the objects of mathematics between Forms and
sensible things. His divergence from the Pythagoreans in making the
One and the Numbers separate from things, and his introduction of
the Forms, were due to his inquiries in the region of definitions (for
the earlier thinkers had no tincture of dialectic), and his making the
other entity besides the One a dyad was due to the belief that the
numbers, except those which were prime, could be neatly produced out
of the dyad as out of some plastic material. Yet what happens is the
contrary; the theory is not a reasonable one. For they make many
things out of the matter, and the form generates only once, but what
we observe is that one table is made from one matter, while the man
who applies the form, though he is one, makes many tables. And the
relation of the male to the female is similar; for the latter is
impregnated by one copulation, but the male impregnates many
females; yet these are analogues of those first principles.

    Plato, then, declared himself thus on the points in question; it
is evident from what has been said that he has used only two causes,
that of the essence and the material cause (for the Forms are the
causes of the essence of all other things, and the One is the cause of
the essence of the Forms); and it is evident what the underlying
matter is, of which the Forms are predicated in the case of sensible
things, and the One in the case of Forms, viz. that this is a dyad,
the great and the small. Further, he has assigned the cause of good
and that of evil to the elements, one to each of the two, as we say
some of his predecessors sought to do, e.g. Empedocles and Anaxagoras.

                                   7

    Our review of those who have spoken about first principles and
reality and of the way in which they have spoken, has been concise and
summary; but yet we have learnt this much from them, that of those who
speak about 'principle' and 'cause' no one has mentioned any principle
except those which have been distinguished in our work on nature,
but all evidently have some inkling of them, though only vaguely.
For some speak of the first principle as matter, whether they
suppose one or more first principles, and whether they suppose this to
be a body or to be incorporeal; e.g. Plato spoke of the great and
the small, the Italians of the infinite, Empedocles of fire, earth,
water, and air, Anaxagoras of the infinity of things composed of
similar parts. These, then, have all had a notion of this kind of
cause, and so have all who speak of air or fire or water, or something
denser than fire and rarer than air; for some have said the prime
element is of this kind.

    These thinkers grasped this cause only; but certain others have
mentioned the source of movement, e.g. those who make friendship and
strife, or reason, or love, a principle.

    The essence, i.e. the substantial reality, no one has expressed
distinctly. It is hinted at chiefly by those who believe in the Forms;
for they do not suppose either that the Forms are the matter of
sensible things, and the One the matter of the Forms, or that they are
the source of movement (for they say these are causes rather of
immobility and of being at rest), but they furnish the Forms as the
essence of every other thing, and the One as the essence of the Forms.

    That for whose sake actions and changes and movements take
place, they assert to be a cause in a way, but not in this way, i.e.
not in the way in which it is its nature to be a cause. For those
who speak of reason or friendship class these causes as goods; they do
not speak, however, as if anything that exists either existed or
came into being for the sake of these, but as if movements started
from these. In the same way those who say the One or the existent is
the good, say that it is the cause of substance, but not that
substance either is or comes to be for the sake of this. Therefore
it turns out that in a sense they both say and do not say the good
is a cause; for they do not call it a cause qua good but only
incidentally.

    All these thinkers then, as they cannot pitch on another cause,
seem to testify that we have determined rightly both how many and of
what sort the causes are. Besides this it is plain that when the
causes are being looked for, either all four must be sought thus or
they must be sought in one of these four ways. Let us next discuss the
possible difficulties with regard to the way in which each of these
thinkers has spoken, and with regard to his situation relatively to
the first principles.

                                   8

    Those, then, who say the universe is one and posit one kind of
thing as matter, and as corporeal matter which has spatial
magnitude, evidently go astray in many ways. For they posit the
elements of bodies only, not of incorporeal things, though there are
also incorporeal things. And in trying to state the causes of
generation and destruction, and in giving a physical account of all
things, they do away with the cause of movement. Further, they err
in not positing the substance, i.e. the essence, as the cause of
anything, and besides this in lightly calling any of the simple bodies
except earth the first principle, without inquiring how they are
produced out of one anothers-I mean fire, water, earth, and air. For
some things are produced out of each other by combination, others by
separation, and this makes the greatest difference to their priority
and posteriority. For (1) in a way the property of being most
elementary of all would seem to belong to the first thing from which
they are produced by combination, and this property would belong to
the most fine-grained and subtle of bodies. For this reason those
who make fire the principle would be most in agreement with this
argument. But each of the other thinkers agrees that the element of
corporeal things is of this sort. At least none of those who named one
element claimed that earth was the element, evidently because of the
coarseness of its grain. (Of the other three elements each has found
some judge on its side; for some maintain that fire, others that
water, others that air is the element. Yet why, after all, do they not
name earth also, as most men do? For people say all things are earth
Hesiod says earth was produced first of corporeal things; so primitive
and popular has the opinion been.) According to this argument, then,
no one would be right who either says the first principle is any of
the elements other than fire, or supposes it to be denser than air but
rarer than water. But (2) if that which is later in generation is
prior in nature, and that which is concocted and compounded is later
in generation, the contrary of what we have been saying must be
true,-water must be prior to air, and earth to water.

    So much, then, for those who posit one cause such as we mentioned;
but the same is true if one supposes more of these, as Empedocles says
matter of things is four bodies. For he too is confronted by
consequences some of which are the same as have been mentioned,
while others are peculiar to him. For we see these bodies produced
from one another, which implies that the same body does not always
remain fire or earth (we have spoken about this in our works on
nature); and regarding the cause of movement and the question
whether we must posit one or two, he must be thought to have spoken
neither correctly nor altogether plausibly. And in general, change
of quality is necessarily done away with for those who speak thus, for
on their view cold will not come from hot nor hot from cold. For if it
did there would be something that accepted the contraries
themselves, and there would be some one entity that became fire and
water, which Empedocles denies.

    As regards Anaxagoras, if one were to suppose that he said there
were two elements, the supposition would accord thoroughly with an
argument which Anaxagoras himself did not state articulately, but
which he must have accepted if any one had led him on to it. True,
to say that in the beginning all things were mixed is absurd both on
other grounds and because it follows that they must have existed
before in an unmixed form, and because nature does not allow any
chance thing to be mixed with any chance thing, and also because on
this view modifications and accidents could be separated from
substances (for the same things which are mixed can be separated); yet
if one were to follow him up, piecing together what he means, he would
perhaps be seen to be somewhat modern in his views. For when nothing
was separated out, evidently nothing could be truly asserted of the
substance that then existed. I mean, e.g. that it was neither white
nor black, nor grey nor any other colour, but of necessity colourless;
for if it had been coloured, it would have had one of these colours.
And similarly, by this same argument, it was flavourless, nor had it
any similar attribute; for it could not be either of any quality or of
any size, nor could it be any definite kind of thing. For if it
were, one of the particular forms would have belonged to it, and
this is impossible, since all were mixed together; for the
particular form would necessarily have been already separated out, but
he all were mixed except reason, and this alone was unmixed and
pure. From this it follows, then, that he must say the principles
are the One (for this is simple and unmixed) and the Other, which is
of such a nature as we suppose the indefinite to be before it is
defined and partakes of some form. Therefore, while expressing himself
neither rightly nor clearly, he means something like what the later
thinkers say and what is now more clearly seen to be the case.

    But these thinkers are, after all, at home only in arguments about
generation and destruction and movement; for it is practically only of
this sort of substance that they seek the principles and the causes.
But those who extend their vision to all things that exist, and of
existing things suppose some to be perceptible and others not
perceptible, evidently study both classes, which is all the more
reason why one should devote some time to seeing what is good in their
views and what bad from the standpoint of the inquiry we have now
before us.

    The 'Pythagoreans' treat of principles and elements stranger
than those of the physical philosophers (the reason is that they got
the principles from non-sensible things, for the objects of
mathematics, except those of astronomy, are of the class of things
without movement); yet their discussions and investigations are all
about nature; for they generate the heavens, and with regard to
their parts and attributes and functions they observe the phenomena,
and use up the principles and the causes in explaining these, which
implies that they agree with the others, the physical philosophers,
that the real is just all that which is perceptible and contained by
the so-called 'heavens'. But the causes and the principles which
they mention are, as we said, sufficient to act as steps even up to
the higher realms of reality, and are more suited to these than to
theories about nature. They do not tell us at all, however, how
there can be movement if limit and unlimited and odd and even are
the only things assumed, or how without movement and change there
can be generation and destruction, or the bodies that move through the
heavens can do what they do.

    Further, if one either granted them that spatial magnitude
consists of these elements, or this were proved, still how would
some bodies be light and others have weight? To judge from what they
assume and maintain they are speaking no more of mathematical bodies
than of perceptible; hence they have said nothing whatever about
fire or earth or the other bodies of this sort, I suppose because they
have nothing to say which applies peculiarly to perceptible things.

    Further, how are we to combine the beliefs that the attributes
of number, and number itself, are causes of what exists and happens in
the heavens both from the beginning and now, and that there is no
other number than this number out of which the world is composed? When
in one particular region they place opinion and opportunity, and, a
little above or below, injustice and decision or mixture, and
allege, as proof, that each of these is a number, and that there
happens to be already in this place a plurality of the extended bodies
composed of numbers, because these attributes of number attach to
the various places,-this being so, is this number, which we must
suppose each of these abstractions to be, the same number which is
exhibited in the material universe, or is it another than this?
Plato says it is different; yet even he thinks that both these
bodies and their causes are numbers, but that the intelligible numbers
are causes, while the others are sensible.

                                   9

    Let us leave the Pythagoreans for the present; for it is enough to
have touched on them as much as we have done. But as for those who
posit the Ideas as causes, firstly, in seeking to grasp the causes
of the things around us, they introduced others equal in number to
these, as if a man who wanted to count things thought he would not
be able to do it while they were few, but tried to count them when
he had added to their number. For the Forms are practically equal
to-or not fewer than-the things, in trying to explain which these
thinkers proceeded from them to the Forms. For to each thing there
answers an entity which has the same name and exists apart from the
substances, and so also in the case of all other groups there is a one
over many, whether the many are in this world or are eternal.

    Further, of the ways in which we prove that the Forms exist,
none is convincing; for from some no inference necessarily follows,
and from some arise Forms even of things of which we think there are
no Forms. For according to the arguments from the existence of the
sciences there will be Forms of all things of which there are sciences
and according to the 'one over many' argument there will be Forms even
of negations, and according to the argument that there is an object
for thought even when the thing has perished, there will be Forms of
perishable things; for we have an image of these. Further, of the more
accurate arguments, some lead to Ideas of relations, of which we say
there is no independent class, and others introduce the 'third man'.

    And in general the arguments for the Forms destroy the things
for whose existence we are more zealous than for the existence of
the Ideas; for it follows that not the dyad but number is first,
i.e. that the relative is prior to the absolute,-besides all the other
points on which certain people by following out the opinions held
about the Ideas have come into conflict with the principles of the
theory.

    Further, according to the assumption on which our belief in the
Ideas rests, there will be Forms not only of substances but also of
many other things (for the concept is single not only in the case of
substances but also in the other cases, and there are sciences not
only of substance but also of other things, and a thousand other
such difficulties confront them). But according to the necessities
of the case and the opinions held about the Forms, if Forms can be
shared in there must be Ideas of substances only. For they are not
shared in incidentally, but a thing must share in its Form as in
something not predicated of a subject (by 'being shared in
incidentally' I mean that e.g. if a thing shares in 'double itself',
it shares also in 'eternal', but incidentally; for 'eternal' happens
to be predicable of the 'double'). Therefore the Forms will be
substance; but the same terms indicate substance in this and in the
ideal world (or what will be the meaning of saying that there is
something apart from the particulars-the one over many?). And if the
Ideas and the particulars that share in them have the same form, there
will be something common to these; for why should '2' be one and the
same in the perishable 2's or in those which are many but eternal, and
not the same in the '2' itself' as in the particular 2? But if they
have not the same form, they must have only the name in common, and it
is as if one were to call both Callias and a wooden image a 'man',
without observing any community between them.

    Above all one might discuss the question what on earth the Forms
contribute to sensible things, either to those that are eternal or
to those that come into being and cease to be. For they cause
neither movement nor any change in them. But again they help in no
wise either towards the knowledge of the other things (for they are
not even the substance of these, else they would have been in them),
or towards their being, if they are not in the particulars which share
in them; though if they were, they might be thought to be causes, as
white causes whiteness in a white object by entering into its
composition. But this argument, which first Anaxagoras and later
Eudoxus and certain others used, is very easily upset; for it is not
difficult to collect many insuperable objections to such a view.

    But, further, all other things cannot come from the Forms in any
of the usual senses of 'from'. And to say that they are patterns and
the other things share in them is to use empty words and poetical
metaphors. For what is it that works, looking to the Ideas? And
anything can either be, or become, like another without being copied
from it, so that whether Socrates or not a man Socrates like might
come to be; and evidently this might be so even if Socrates were
eternal. And there will be several patterns of the same thing, and
therefore several Forms; e.g. 'animal' and 'two-footed' and also
'man himself' will be Forms of man. Again, the Forms are patterns
not only sensible things, but of Forms themselves also; i.e. the
genus, as genus of various species, will be so; therefore the same
thing will be pattern and copy.

    Again, it would seem impossible that the substance and that of
which it is the substance should exist apart; how, therefore, could
the Ideas, being the substances of things, exist apart? In the Phaedo'
the case is stated in this way-that the Forms are causes both of being
and of becoming; yet when the Forms exist, still the things that share
in them do not come into being, unless there is something to originate
movement; and many other things come into being (e.g. a house or a
ring) of which we say there are no Forms. Clearly, therefore, even the
other things can both be and come into being owing to such causes as
produce the things just mentioned.

    Again, if the Forms are numbers, how can they be causes? Is it
because existing things are other numbers, e.g. one number is man,
another is Socrates, another Callias? Why then are the one set of
numbers causes of the other set? It will not make any difference
even if the former are eternal and the latter are not. But if it is
because things in this sensible world (e.g. harmony) are ratios of
numbers, evidently the things between which they are ratios are some
one class of things. If, then, this--the matter--is some definite
thing, evidently the numbers themselves too will be ratios of
something to something else. E.g. if Callias is a numerical ratio
between fire and earth and water and air, his Idea also will be a
number of certain other underlying things; and man himself, whether it
is a number in a sense or not, will still be a numerical ratio of
certain things and not a number proper, nor will it be a of number
merely because it is a numerical ratio.

    Again, from many numbers one number is produced, but how can one
Form come from many Forms? And if the number comes not from the many
numbers themselves but from the units in them, e.g. in 10,000, how
is it with the units? If they are specifically alike, numerous
absurdities will follow, and also if they are not alike (neither the
units in one number being themselves like one another nor those in
other numbers being all like to all); for in what will they differ, as
they are without quality? This is not a plausible view, nor is it
consistent with our thought on the matter.

    Further, they must set up a second kind of number (with which
arithmetic deals), and all the objects which are called 'intermediate'
by some thinkers; and how do these exist or from what principles do
they proceed? Or why must they be intermediate between the things in
this sensible world and the things-themselves?

    Further, the units in must each come from a prior but this is
impossible.

    Further, why is a number, when taken all together, one?

    Again, besides what has been said, if the units are diverse the
Platonists should have spoken like those who say there are four, or
two, elements; for each of these thinkers gives the name of element
not to that which is common, e.g. to body, but to fire and earth,
whether there is something common to them, viz. body, or not. But in
fact the Platonists speak as if the One were homogeneous like fire
or water; and if this is so, the numbers will not be substances.
Evidently, if there is a One itself and this is a first principle,
'one' is being used in more than one sense; for otherwise the theory
is impossible.

    When we wish to reduce substances to their principles, we state
that lines come from the short and long (i.e. from a kind of small and
great), and the plane from the broad and narrow, and body from the
deep and shallow. Yet how then can either the plane contain a line, or
the solid a line or a plane? For the broad and narrow is a different
class from the deep and shallow. Therefore, just as number is not
present in these, because the many and few are different from these,
evidently no other of the higher classes will be present in the lower.
But again the broad is not a genus which includes the deep, for then
the solid would have been a species of plane. Further, from what
principle will the presence of the points in the line be derived?
Plato even used to object to this class of things as being a
geometrical fiction. He gave the name of principle of the line-and
this he often posited-to the indivisible lines. Yet these must have
a limit; therefore the argument from which the existence of the line
follows proves also the existence of the point.

    In general, though philosophy seeks the cause of perceptible
things, we have given this up (for we say nothing of the cause from
which change takes its start), but while we fancy we are stating the
substance of perceptible things, we assert the existence of a second
class of substances, while our account of the way in which they are
the substances of perceptible things is empty talk; for 'sharing',
as we said before, means nothing.

    Nor have the Forms any connexion with what we see to be the
cause in the case of the arts, that for whose sake both all mind and
the whole of nature are operative,-with this cause which we assert
to be one of the first principles; but mathematics has come to be
identical with philosophy for modern thinkers, though they say that it
should be studied for the sake of other things. Further, one might
suppose that the substance which according to them underlies as matter
is too mathematical, and is a predicate and differentia of the
substance, ie. of the matter, rather than matter itself; i.e. the
great and the small are like the rare and the dense which the physical
philosophers speak of, calling these the primary differentiae of the
substratum; for these are a kind of excess and defect. And regarding
movement, if the great and the small are to he movement, evidently the
Forms will be moved; but if they are not to be movement, whence did
movement come? The whole study of nature has been annihilated.

    And what is thought to be easy-to show that all things are
one-is not done; for what is proved by the method of setting out
instances is not that all things are one but that there is a One
itself,-if we grant all the assumptions. And not even this follows, if
we do not grant that the universal is a genus; and this in some
cases it cannot be.

    Nor can it be explained either how the lines and planes and solids
that come after the numbers exist or can exist, or what significance
they have; for these can neither be Forms (for they are not
numbers), nor the intermediates (for those are the objects of
mathematics), nor the perishable things. This is evidently a
distinct fourth class.

    In general, if we search for the elements of existing things
without distinguishing the many senses in which things are said to
exist, we cannot find them, especially if the search for the
elements of which things are made is conducted in this manner. For
it is surely impossible to discover what 'acting' or 'being acted on',
or 'the straight', is made of, but if elements can be discovered at
all, it is only the elements of substances; therefore either to seek
the elements of all existing things or to think one has them is
incorrect.

    And how could we learn the elements of all things? Evidently we
cannot start by knowing anything before. For as he who is learning
geometry, though he may know other things before, knows none of the
things with which the science deals and about which he is to learn, so
is it in all other cases. Therefore if there is a science of all
things, such as some assert to exist, he who is learning this will
know nothing before. Yet all learning is by means of premisses which
are (either all or some of them) known before,-whether the learning be
by demonstration or by definitions; for the elements of the definition
must be known before and be familiar; and learning by induction
proceeds similarly. But again, if the science were actually innate, it
were strange that we are unaware of our possession of the greatest
of sciences.

    Again, how is one to come to know what all things are made of, and
how is this to be made evident? This also affords a difficulty; for
there might be a conflict of opinion, as there is about certain
syllables; some say za is made out of s and d and a, while others
say it is a distinct sound and none of those that are familiar.

    Further, how could we know the objects of sense without having the
sense in question? Yet we ought to, if the elements of which all
things consist, as complex sounds consist of the clements proper to
sound, are the same.

                                  10

    It is evident, then, even from what we have said before, that
all men seem to seek the causes named in the Physics, and that we
cannot name any beyond these; but they seek these vaguely; and
though in a sense they have all been described before, in a sense they
have not been described at all. For the earliest philosophy is, on all
subjects, like one who lisps, since it is young and in its beginnings.
For even Empedocles says bone exists by virtue of the ratio in it. Now
this is the essence and the substance of the thing. But it is
similarly necessary that flesh and each of the other tissues should be
the ratio of its elements, or that not one of them should; for it is
on account of this that both flesh and bone and everything else will
exist, and not on account of the matter, which he names,-fire and
earth and water and air. But while he would necessarily have agreed if
another had said this, he has not said it clearly.

    On these questions our views have been expressed before; but let
us return to enumerate the difficulties that might be raised on
these same points; for perhaps we may get from them some help
towards our later difficulties.

                                Book II

                                   1

    THE investigation of the truth is in one way hard, in another
easy. An indication of this is found in the fact that no one is able
to attain the truth adequately, while, on the other hand, we do not
collectively fail, but every one says something true about the
nature of things, and while individually we contribute little or
nothing to the truth, by the union of all a considerable amount is
amassed. Therefore, since the truth seems to be like the proverbial
door, which no one can fail to hit, in this respect it must be easy,
but the fact that we can have a whole truth and not the particular
part we aim at shows the difficulty of it.

    Perhaps, too, as difficulties are of two kinds, the cause of the
present difficulty is not in the facts but in us. For as the eyes of
bats are to the blaze of day, so is the reason in our soul to the
things which are by nature most evident of all.

    It is just that we should be grateful, not only to those with
whose views we may agree, but also to those who have expressed more
superficial views; for these also contributed something, by developing
before us the powers of thought. It is true that if there had been
no Timotheus we should have been without much of our lyric poetry; but
if there had been no Phrynis there would have been no Timotheus. The
same holds good of those who have expressed views about the truth; for
from some thinkers we have inherited certain opinions, while the
others have been responsible for the appearance of the former.

    It is right also that philosophy should be called knowledge of the
truth. For the end of theoretical knowledge is truth, while that of
practical knowledge is action (for even if they consider how things
are, practical men do not study the eternal, but what is relative
and in the present). Now we do not know a truth without its cause; and
a thing has a quality in a higher degree than other things if in
virtue of it the similar quality belongs to the other things as well
(e.g. fire is the hottest of things; for it is the cause of the heat
of all other things); so that that causes derivative truths to be true
is most true. Hence the principles of eternal things must be always
most true (for they are not merely sometimes true, nor is there any
cause of their being, but they themselves are the cause of the being
of other things), so that as each thing is in respect of being, so
is it in respect of truth.

                                   2

    But evidently there is a first principle, and the causes of things
are neither an infinite series nor infinitely various in kind. For
neither can one thing proceed from another, as from matter, ad
infinitum (e.g. flesh from earth, earth from air, air from fire, and
so on without stopping), nor can the sources of movement form an
endless series (man for instance being acted on by air, air by the
sun, the sun by Strife, and so on without limit). Similarly the
final causes cannot go on ad infinitum,-walking being for the sake
of health, this for the sake of happiness, happiness for the sake of
something else, and so one thing always for the sake of another. And
the case of the essence is similar. For in the case of
intermediates, which have a last term and a term prior to them, the
prior must be the cause of the later terms. For if we had to say which
of the three is the cause, we should say the first; surely not the
last, for the final term is the cause of none; nor even the
intermediate, for it is the cause only of one. (It makes no difference
whether there is one intermediate or more, nor whether they are
infinite or finite in number.) But of series which are infinite in
this way, and of the infinite in general, all the parts down to that
now present are alike intermediates; so that if there is no first
there is no cause at all.

    Nor can there be an infinite process downwards, with a beginning
in the upward direction, so that water should proceed from fire, earth
from water, and so always some other kind should be produced. For
one thing comes from another in two ways-not in the sense in which
'from' means 'after' (as we say 'from the Isthmian games come the
Olympian'), but either (i) as the man comes from the boy, by the boy's
changing, or (ii) as air comes from water. By 'as the man comes from
the boy' we mean 'as that which has come to be from that which is
coming to be' or 'as that which is finished from that which is being
achieved' (for as becoming is between being and not being, so that
which is becoming is always between that which is and that which is
not; for the learner is a man of science in the making, and this is
what is meant when we say that from a learner a man of science is
being made); on the other hand, coming from another thing as water
comes from air implies the destruction of the other thing. This is why
changes of the former kind are not reversible, and the boy does not
come from the man (for it is not that which comes to be something that
comes to be as a result of coming to be, but that which exists after
the coming to be; for it is thus that the day, too, comes from the
morning-in the sense that it comes after the morning; which is the
reason why the morning cannot come from the day); but changes of the
other kind are reversible. But in both cases it is impossible that the
number of terms should be infinite. For terms of the former kind,
being intermediates, must have an end, and terms of the latter kind
change back into one another, for the destruction of either is the
generation of the other.

    At the same time it is impossible that the first cause, being
eternal, should be destroyed; for since the process of becoming is not
infinite in the upward direction, that which is the first thing by
whose destruction something came to be must be non-eternal.

    Further, the final cause is an end, and that sort of end which
is not for the sake of something else, but for whose sake everything
else is; so that if there is to be a last term of this sort, the
process will not be infinite; but if there is no such term, there will
be no final cause, but those who maintain the infinite series
eliminate the Good without knowing it (yet no one would try to do
anything if he were not going to come to a limit); nor would there
be reason in the world; the reasonable man, at least, always acts
for a purpose, and this is a limit; for the end is a limit.

    But the essence, also, cannot be reduced to another definition
which is fuller in expression. For the original definition is always
more of a definition, and not the later one; and in a series in
which the first term has not the required character, the next has
not it either. Further, those who speak thus destroy science; for it
is not possible to have this till one comes to the unanalysable terms.
And knowledge becomes impossible; for how can one apprehend things
that are infinite in this way? For this is not like the case of the
line, to whose divisibility there is no stop, but which we cannot
think if we do not make a stop (for which reason one who is tracing
the infinitely divisible line cannot be counting the possibilities
of section), but the whole line also must be apprehended by
something in us that does not move from part to part.-Again, nothing
infinite can exist; and if it could, at least the notion of infinity
is not infinite.

    But if the kinds of causes had been infinite in number, then
also knowledge would have been impossible; for we think we know,
only when we have ascertained the causes, that but that which is
infinite by addition cannot be gone through in a finite time.

                                   3

    The effect which lectures produce on a hearer depends on his
habits; for we demand the language we are accustomed to, and that
which is different from this seems not in keeping but somewhat
unintelligible and foreign because of its unwontedness. For it is
the customary that is intelligible. The force of habit is shown by the
laws, in which the legendary and childish elements prevail over our
knowledge about them, owing to habit. Thus some people do not listen
to a speaker unless he speaks mathematically, others unless he gives
instances, while others expect him to cite a poet as witness. And some
want to have everything done accurately, while others are annoyed by
accuracy, either because they cannot follow the connexion of thought
or because they regard it as pettifoggery. For accuracy has
something of this character, so that as in trade so in argument some
people think it mean. Hence one must be already trained to know how to
take each sort of argument, since it is absurd to seek at the same
time knowledge and the way of attaining knowledge; and it is not
easy to get even one of the two.

    The minute accuracy of mathematics is not to be demanded in all
cases, but only in the case of things which have no matter. Hence
method is not that of natural science; for presumably the whole of
nature has matter. Hence we must inquire first what nature is: for
thus we shall also see what natural science treats of (and whether
it belongs to one science or to more to investigate the causes and the
principles of things).

                                Book III

                                   1

    WE must, with a view to the science which we are seeking, first
recount the subjects that should be first discussed. These include
both the other opinions that some have held on the first principles,
and any point besides these that happens to have been overlooked.
For those who wish to get clear of difficulties it is advantageous
to discuss the difficulties well; for the subsequent free play of
thought implies the solution of the previous difficulties, and it is
not possible to untie a knot of which one does not know. But the
difficulty of our thinking points to a 'knot' in the object; for in so
far as our thought is in difficulties, it is in like case with those
who are bound; for in either case it is impossible to go forward.
Hence one should have surveyed all the difficulties beforehand, both
for the purposes we have stated and because people who inquire without
first stating the difficulties are like those who do not know where
they have to go; besides, a man does not otherwise know even whether
he has at any given time found what he is looking for or not; for
the end is not clear to such a man, while to him who has first
discussed the difficulties it is clear. Further, he who has heard
all the contending arguments, as if they were the parties to a case,
must be in a better position for judging.

    The first problem concerns the subject which we discussed in our
prefatory remarks. It is this-(1) whether the investigation of the
causes belongs to one or to more sciences, and (2) whether such a
science should survey only the first principles of substance, or
also the principles on which all men base their proofs, e.g. whether
it is possible at the same time to assert and deny one and the same
thing or not, and all other such questions; and (3) if the science
in question deals with substance, whether one science deals with all
substances, or more than one, and if more, whether all are akin, or
some of them must be called forms of Wisdom and the others something
else. And (4) this itself is also one of the things that must be
discussed-whether sensible substances alone should be said to exist or
others also besides them, and whether these others are of one kind
or there are several classes of substances, as is supposed by those
who believe both in Forms and in mathematical objects intermediate
between these and sensible things. Into these questions, then, as we
say, we must inquire, and also (5) whether our investigation is
concerned only with substances or also with the essential attributes
of substances. Further, with regard to the same and other and like and
unlike and contrariety, and with regard to prior and posterior and all
other such terms about which the dialecticians try to inquire,
starting their investigation from probable premises only,-whose
business is it to inquire into all these? Further, we must discuss the
essential attributes of these themselves; and we must ask not only
what each of these is, but also whether one thing always has one
contrary. Again (6), are the principles and elements of things the
genera, or the parts present in each thing, into which it is
divided; and (7) if they are the genera, are they the genera that
are predicated proximately of the individuals, or the highest
genera, e.g. is animal or man the first principle and the more
independent of the individual instance? And (8) we must inquire and
discuss especially whether there is, besides the matter, any thing
that is a cause in itself or not, and whether this can exist apart
or not, and whether it is one or more in number, and whether there
is something apart from the concrete thing (by the concrete thing I
mean the matter with something already predicated of it), or there
is nothing apart, or there is something in some cases though not in
others, and what sort of cases these are. Again (9) we ask whether the
principles are limited in number or in kind, both those in the
definitions and those in the substratum; and (10) whether the
principles of perishable and of imperishable things are the same or
different; and whether they are all imperishable or those of
perishable things are perishable. Further (11) there is the question
which is hardest of all and most perplexing, whether unity and
being, as the Pythagoreans and Plato said, are not attributes of
something else but the substance of existing things, or this is not
the case, but the substratum is something else,-as Empedocles says,
love; as some one else says, fire; while another says water or air.
Again (12) we ask whether the principles are universal or like
individual things, and (13) whether they exist potentially or
actually, and further, whether they are potential or actual in any
other sense than in reference to movement; for these questions also
would present much difficulty. Further (14), are numbers and lines and
figures and points a kind of substance or not, and if they are
substances are they separate from sensible things or present in
them? With regard to all these matters not only is it hard to get
possession of the truth, but it is not easy even to think out the
difficulties well.

                                   2

    (1) First then with regard to what we mentioned first, does it
belong to one or to more sciences to investigate all the kinds of
causes? How could it belong to one science to recognize the principles
if these are not contrary?

    Further, there are many things to which not all the principles
pertain. For how can a principle of change or the nature of the good
exist for unchangeable things, since everything that in itself and
by its own nature is good is an end, and a cause in the sense that for
its sake the other things both come to be and are, and since an end or
purpose is the end of some action, and all actions imply change? So in
the case of unchangeable things this principle could not exist, nor
could there be a good itself. This is why in mathematics nothing is
proved by means of this kind of cause, nor is there any
demonstration of this kind-'because it is better, or worse'; indeed no
one even mentions anything of the kind. And so for this reason some of
the Sophists, e.g. Aristippus, used to ridicule mathematics; for in
the arts (he maintained), even in the industrial arts, e.g. in
carpentry and cobbling, the reason always given is 'because it is
better, or worse,' but the mathematical sciences take no account of
goods and evils.

    But if there are several sciences of the causes, and a different
science for each different principle, which of these sciences should
be said to be that which we seek, or which of the people who possess
them has the most scientific knowledge of the object in question?
The same thing may have all the kinds of causes, e.g. the moving cause
of a house is the art or the builder, the final cause is the
function it fulfils, the matter is earth and stones, and the form is
the definition. To judge from our previous discussion of the
question which of the sciences should be called Wisdom, there is
reason for applying the name to each of them. For inasmuch as it is
most architectonic and authoritative and the other sciences, like
slavewomen, may not even contradict it, the science of the end and
of the good is of the nature of Wisdom (for the other things are for
the sake of the end). But inasmuch as it was described' as dealing
with the first causes and that which is in the highest sense object of
knowledge, the science of substance must be of the nature of Wisdom.
For since men may know the same thing in many ways, we say that he who
recognizes what a thing is by its being so and so knows more fully
than he who recognizes it by its not being so and so, and in the
former class itself one knows more fully than another, and he knows
most fully who knows what a thing is, not he who knows its quantity or
quality or what it can by nature do or have done to it. And further in
all cases also we think that the knowledge of each even of the
things of which demonstration is possible is present only when we know
what the thing is, e.g. what squaring a rectangle is, viz. that it
is the finding of a mean; and similarly in all other cases. And we
know about becomings and actions and about every change when we know
the source of the movement; and this is other than and opposed to
the end. Therefore it would seem to belong to different sciences to
investigate these causes severally.

    But (2), taking the starting-points of demonstration as well as
the causes, it is a disputable question whether they are the object of
one science or of more (by the starting-points of demonstration I mean
the common beliefs, on which all men base their proofs); e.g. that
everything must be either affirmed or denied, and that a thing
cannot at the same time be and not be, and all other such
premisses:-the question is whether the same science deals with them as
with substance, or a different science, and if it is not one
science, which of the two must be identified with that which we now
seek.-It is not reasonable that these topics should be the object of
one science; for why should it be peculiarly appropriate to geometry
or to any other science to understand these matters? If then it
belongs to every science alike, and cannot belong to all, it is not
peculiar to the science which investigates substances, any more than
to any other science, to know about these topics.-And, at the same
time, in what way can there be a science of the first principles?
For we are aware even now what each of them in fact is (at least
even other sciences use them as familiar); but if there is a
demonstrative science which deals with them, there will have to be
an underlying kind, and some of them must be demonstrable attributes
and others must be axioms (for it is impossible that there should be
demonstration about all of them); for the demonstration must start
from certain premisses and be about a certain subject and prove
certain attributes. Therefore it follows that all attributes that
are proved must belong to a single class; for all demonstrative
sciences use the axioms.

    But if the science of substance and the science which deals with
the axioms are different, which of them is by nature more
authoritative and prior? The axioms are most universal and are
principles of all things. And if it is not the business of the
philosopher, to whom else will it belong to inquire what is true and
what is untrue about them?

    (3) In general, do all substances fall under one science or
under more than one? If the latter, to what sort of substance is the
present science to be assigned?-On the other hand, it is not
reasonable that one science should deal with all. For then there would
be one demonstrative science dealing with all attributes. For ever
demonstrative science investigates with regard to some subject its
essential attributes, starting from the common beliefs. Therefore to
investigate the essential attributes of one class of things,
starting from one set of beliefs, is the business of one science.
For the subject belongs to one science, and the premisses belong to
one, whether to the same or to another; so that the attributes do so
too, whether they are investigated by these sciences or by one
compounded out of them.

    (5) Further, does our investigation deal with substances alone
or also with their attributes? I mean for instance, if the solid is
a substance and so are lines and planes, is it the business of the
same science to know these and to know the attributes of each of these
classes (the attributes about which the mathematical sciences offer
proofs), or of a different science? If of the same, the science of
substance also must be a demonstrative science, but it is thought that
there is no demonstration of the essence of things. And if of another,
what will be the science that investigates the attributes of
substance? This is a very difficult question.

    (4) Further, must we say that sensible substances alone exist,
or that there are others besides these? And are substances of one kind
or are there in fact several kinds of substances, as those say who
assert the existence both of the Forms and of the intermediates,
with which they say the mathematical sciences deal?-The sense in which
we say the Forms are both causes and self-dependent substances has
been explained in our first remarks about them; while the theory
presents difficulties in many ways, the most paradoxical thing of
all is the statement that there are certain things besides those in
the material universe, and that these are the same as sensible
things except that they are eternal while the latter are perishable.
For they say there is a man-himself and a horse-itself and
health-itself, with no further qualification,-a procedure like that of
the people who said there are gods, but in human form. For they were
positing nothing but eternal men, nor are the Platonists making the
Forms anything other than eternal sensible things.

    Further, if we are to posit besides the Forms and the sensibles
the intermediates between them, we shall have many difficulties. For
clearly on the same principle there will be lines besides the
lines-themselves and the sensible lines, and so with each of the other
classes of things; so that since astronomy is one of these
mathematical sciences there will also be a heaven besides the sensible
heaven, and a sun and a moon (and so with the other heavenly bodies)
besides the sensible. Yet how are we to believe in these things? It is
not reasonable even to suppose such a body immovable, but to suppose
it moving is quite impossible.-And similarly with the things of
which optics and mathematical harmonics treat; for these also cannot
exist apart from the sensible things, for the same reasons. For if
there are sensible things and sensations intermediate between Form and
individual, evidently there will also be animals intermediate
between animals-themselves and the perishable animals.-We might also
raise the question, with reference to which kind of existing things we
must look for these sciences of intermediates. If geometry is to
differ from mensuration only in this, that the latter deals with
things that we perceive, and the former with things that are not
perceptible, evidently there will also be a science other than
medicine, intermediate between medical-science-itself and this
individual medical science, and so with each of the other sciences.
Yet how is this possible? There would have to be also healthy things
besides the perceptible healthy things and the healthy-itself.--And at
the same time not even this is true, that mensuration deals with
perceptible and perishable magnitudes; for then it would have perished
when they perished.

    But on the other hand astronomy cannot be dealing with perceptible
magnitudes nor with this heaven above us. For neither are
perceptible lines such lines as the geometer speaks of (for no
perceptible thing is straight or round in the way in which he
defines 'straight' and 'round'; for a hoop touches a straight edge not
at a point, but as Protagoras used to say it did, in his refutation of
the geometers), nor are the movements and spiral orbits in the heavens
like those of which astronomy treats, nor have geometrical points
the same nature as the actual stars.-Now there are some who say that
these so-called intermediates between the Forms and the perceptible
things exist, not apart from the perceptible things, however, but in
these; the impossible results of this view would take too long to
enumerate, but it is enough to consider even such points as the
following:-It is not reasonable that this should be so only in the
case of these intermediates, but clearly the Forms also might be in
the perceptible things; for both statements are parts of the same
theory. Further, it follows from this theory that there are two solids
in the same place, and that the intermediates are not immovable, since
they are in the moving perceptible things. And in general to what
purpose would one suppose them to exist indeed, but to exist in
perceptible things? For the same paradoxical results will follow which
we have already mentioned; there will be a heaven besides the
heaven, only it will be not apart but in the same place; which is
still more impossible.

                                   3

    (6) Apart from the great difficulty of stating the case truly with
regard to these matters, it is very hard to say, with regard to the
first principles, whether it is the genera that should be taken as
elements and principles, or rather the primary constituents of a
thing; e.g. it is the primary parts of which articulate sounds consist
that are thought to be elements and principles of articulate sound,
not the common genus-articulate sound; and we give the name of
'elements' to those geometrical propositions, the proofs of which
are implied in the proofs of the others, either of all or of most.
Further, both those who say there are several elements of corporeal
things and those who say there is one, say the parts of which bodies
are compounded and consist are principles; e.g. Empedocles says fire
and water and the rest are the constituent elements of things, but
does not describe these as genera of existing things. Besides this, if
we want to examine the nature of anything else, we examine the parts
of which, e.g. a bed consists and how they are put together, and
then we know its nature.

    To judge from these arguments, then, the principles of things
would not be the genera; but if we know each thing by its
definition, and the genera are the principles or starting-points of
definitions, the genera must also be the principles of definable
things. And if to get the knowledge of the species according to
which things are named is to get the knowledge of things, the genera
are at least starting-points of the species. And some also of those
who say unity or being, or the great and the small, are elements of
things, seem to treat them as genera.

    But, again, it is not possible to describe the principles in
both ways. For the formula of the essence is one; but definition by
genera will be different from that which states the constituent
parts of a thing.

    (7) Besides this, even if the genera are in the highest degree
principles, should one regard the first of the genera as principles,
or those which are predicated directly of the individuals? This also
admits of dispute. For if the universals are always more of the nature
of principles, evidently the uppermost of the genera are the
principles; for these are predicated of all things. There will,
then, be as many principles of things as there are primary genera,
so that both being and unity will be principles and substances; for
these are most of all predicated of all existing things. But it is not
possible that either unity or being should be a single genus of
things; for the differentiae of any genus must each of them both
have being and be one, but it is not possible for the genus taken
apart from its species (any more than for the species of the genus) to
be predicated of its proper differentiae; so that if unity or being is
a genus, no differentia will either have being or be one. But if unity
and being are not genera, neither will they be principles, if the
genera are the principles. Again, the intermediate kinds, in whose
nature the differentiae are included, will on this theory be genera,
down to the indivisible species; but as it is, some are thought to
be genera and others are not thought to be so. Besides this, the
differentiae are principles even more than the genera; and if these
also are principles, there comes to be practically an infinite
number of principles, especially if we suppose the highest genus to be
a principle.-But again, if unity is more of the nature of a principle,
and the indivisible is one, and everything indivisible is so either in
quantity or in species, and that which is so in species is the
prior, and genera are divisible into species for man is not the
genus of individual men), that which is predicated directly of the
individuals will have more unity.-Further, in the case of things in
which the distinction of prior and posterior is present, that which is
predicable of these things cannot be something apart from them (e.g.
if two is the first of numbers, there will not be a Number apart
from the kinds of numbers; and similarly there will not be a Figure
apart from the kinds of figures; and if the genera of these things
do not exist apart from the species, the genera of other things will
scarcely do so; for genera of these things are thought to exist if any
do). But among the individuals one is not prior and another posterior.
Further, where one thing is better and another worse, the better is
always prior; so that of these also no genus can exist. From these
considerations, then, the species predicated of individuals seem to be
principles rather than the genera. But again, it is not easy to say in
what sense these are to be taken as principles. For the principle or
cause must exist alongside of the things of which it is the principle,
and must be capable of existing in separation from them; but for
what reason should we suppose any such thing to exist alongside of the
individual, except that it is predicated universally and of all? But
if this is the reason, the things that are more universal must be
supposed to be more of the nature of principles; so that the highest
genera would be the principles.

                                   4

    (8) There is a difficulty connected with these, the hardest of all
and the most necessary to examine, and of this the discussion now
awaits us. If, on the one hand, there is nothing apart from individual
things, and the individuals are infinite in number, how then is it
possible to get knowledge of the infinite individuals? For all
things that we come to know, we come to know in so far as they have
some unity and identity, and in so far as some attribute belongs to
them universally.

    But if this is necessary, and there must be something apart from
the individuals, it will be necessary that the genera exist apart from
the individuals, either the lowest or the highest genera; but we found
by discussion just now that this is impossible.

    Further, if we admit in the fullest sense that something exists
apart from the concrete thing, whenever something is predicated of the
matter, must there, if there is something apart, be something apart
from each set of individuals, or from some and not from others, or
from none? (A) If there is nothing apart from individuals, there
will be no object of thought, but all things will be objects of sense,
and there will not be knowledge of anything, unless we say that
sensation is knowledge. Further, nothing will be eternal or unmovable;
for all perceptible things perish and are in movement. But if there is
nothing eternal, neither can there be a process of coming to be; for
there must be something that comes to be, i.e. from which something
comes to be, and the ultimate term in this series cannot have come
to be, since the series has a limit and since nothing can come to be
out of that which is not. Further, if generation and movement exist
there must also be a limit; for no movement is infinite, but every
movement has an end, and that which is incapable of completing its
coming to be cannot be in process of coming to be; and that which
has completed its coming to be must he as soon as it has come to be.
Further, since the matter exists, because it is ungenerated, it is a
fortiori reasonable that the substance or essence, that which the
matter is at any time coming to be, should exist; for if neither
essence nor matter is to be, nothing will be at all, and since this is
impossible there must be something besides the concrete thing, viz.
the shape or form.

    But again (B) if we are to suppose this, it is hard to say in
which cases we are to suppose it and in which not. For evidently it is
not possible to suppose it in all cases; we could not suppose that
there is a house besides the particular houses.-Besides this, will the
substance of all the individuals, e.g. of all men, be one? This is
paradoxical, for all the things whose substance is one are one. But
are the substances many and different? This also is unreasonable.-At
the same time, how does the matter become each of the individuals, and
how is the concrete thing these two elements?

    (9) Again, one might ask the following question also about the
first principles. If they are one in kind only, nothing will be
numerically one, not even unity-itself and being-itself; and how
will knowing exist, if there is not to be something common to a
whole set of individuals?

    But if there is a common element which is numerically one, and
each of the principles is one, and the principles are not as in the
case of perceptible things different for different things (e.g.
since this particular syllable is the same in kind whenever it occurs,
the elements it are also the same in kind; only in kind, for these
also, like the syllable, are numerically different in different
contexts),-if it is not like this but the principles of things are
numerically one, there will be nothing else besides the elements
(for there is no difference of meaning between 'numerically one' and
'individual'; for this is just what we mean by the individual-the
numerically one, and by the universal we mean that which is predicable
of the individuals). Therefore it will be just as if the elements of
articulate sound were limited in number; all the language in the world
would be confined to the ABC, since there could not be two or more
letters of the same kind.

    (10) One difficulty which is as great as any has been neglected
both by modern philosophers and by their predecessors-whether the
principles of perishable and those of imperishable things are the same
or different. If they are the same, how are some things perishable and
others imperishable, and for what reason? The school of Hesiod and all
the theologians thought only of what was plausible to themselves,
and had no regard to us. For, asserting the first principles to be
gods and born of gods, they say that the beings which did not taste of
nectar and ambrosia became mortal; and clearly they are using words
which are familiar to themselves, yet what they have said about the
very application of these causes is above our comprehension. For if
the gods taste of nectar and ambrosia for their pleasure, these are in
no wise the causes of their existence; and if they taste them to
maintain their existence, how can gods who need food be eternal?-But
into the subtleties of the mythologists it is not worth our while to
inquire seriously; those, however, who use the language of proof we
must cross-examine and ask why, after all, things which consist of the
same elements are, some of them, eternal in nature, while others
perish. Since these philosophers mention no cause, and it is
unreasonable that things should be as they say, evidently the
principles or causes of things cannot be the same. Even the man whom
one might suppose to speak most consistently-Empedocles, even he has
made the same mistake; for he maintains that strife is a principle
that causes destruction, but even strife would seem no less to produce
everything, except the One; for all things excepting God proceed
from strife. At least he says:-

          From which all that was and is and will be hereafter-

          Trees, and men and women, took their growth,

          And beasts and birds and water-nourished fish,

          And long-aged gods.

    The implication is evident even apart from these words; for if
strife had not been present in things, all things would have been one,
according to him; for when they have come together, 'then strife stood
outermost.' Hence it also follows on his theory that God most
blessed is less wise than all others; for he does not know all the
elements; for he has in him no strife, and knowledge is of the like by
the like. 'For by earth,' he says,

               we see earth, by water water,

           By ether godlike ether, by fire wasting fire,

           Love by love, and strife by gloomy strife.

  But-and this is the point we started from this at least is
evident, that on his theory it follows that strife is as much the
cause of existence as of destruction. And similarly love is not
specially the cause of existence; for in collecting things into the
One it destroys all other things. And at the same time Empedocles
mentions no cause of the change itself, except that things are so by
nature.

        But when strife at last waxed great in the limbs of the

          Sphere,

        And sprang to assert its rights as the time was fulfilled

        Which is fixed for them in turn by a mighty oath.

    This implies that change was necessary; but he shows no cause of
the necessity. But yet so far at least he alone speaks consistently;
for he does not make some things perishable and others imperishable,
but makes all perishable except the elements. The difficulty we are
speaking of now is, why some things are perishable and others are not,
if they consist of the same principles.

    Let this suffice as proof of the fact that the principles cannot
be the same. But if there are different principles, one difficulty
is whether these also will be imperishable or perishable. For if
they are perishable, evidently these also must consist of certain
elements (for all things that perish, perish by being resolved into
the elements of which they consist); so that it follows that prior
to the principles there are other principles. But this is
impossible, whether the process has a limit or proceeds to infinity.
Further, how will perishable things exist, if their principles are
to be annulled? But if the principles are imperishable, why will
things composed of some imperishable principles be perishable, while
those composed of the others are imperishable? This is not probable,
but is either impossible or needs much proof. Further, no one has even
tried to maintain different principles; they maintain the same
principles for all things. But they swallow the difficulty we stated
first as if they took it to be something trifling.

    (11) The inquiry that is both the hardest of all and the most
necessary for knowledge of the truth is whether being and unity are
the substances of things, and whether each of them, without being
anything else, is being or unity respectively, or we must inquire what
being and unity are, with the implication that they have some other
underlying nature. For some people think they are of the former,
others think they are of the latter character. Plato and the
Pythagoreans thought being and unity were nothing else, but this was
their nature, their essence being just unity and being. But the
natural philosophers take a different line; e.g. Empedocles-as
though reducing to something more intelligible-says what unity is; for
he would seem to say it is love: at least, this is for all things
the cause of their being one. Others say this unity and being, of
which things consist and have been made, is fire, and others say it is
air. A similar view is expressed by those who make the elements more
than one; for these also must say that unity and being are precisely
all the things which they say are principles.

    (A) If we do not suppose unity and being to be substances, it
follows that none of the other universals is a substance; for these
are most universal of all, and if there is no unity itself or
being-itself, there will scarcely be in any other case anything
apart from what are called the individuals. Further, if unity is not a
substance, evidently number also will not exist as an entity
separate from the individual things; for number is units, and the unit
is precisely a certain kind of one.

    But (B) if there is a unity-itself and a being itself, unity and
being must be their substance; for it is not something else that is
predicated universally of the things that are and are one, but just
unity and being. But if there is to be a being-itself and a
unity-itself, there is much difficulty in seeing how there will be
anything else besides these,-I mean, how things will be more than
one in number. For what is different from being does not exist, so
that it necessarily follows, according to the argument of
Parmenides, that all things that are are one and this is being.

    There are objections to both views. For whether unity is not a
substance or there is a unity-itself, number cannot be a substance. We
have already said why this result follows if unity is not a substance;
and if it is, the same difficulty arises as arose with regard to
being. For whence is there to be another one besides unity-itself?
It must be not-one; but all things are either one or many, and of
the many each is one.

    Further, if unity-itself is indivisible, according to Zeno's
postulate it will be nothing. For that which neither when added
makes a thing greater nor when subtracted makes it less, he asserts to
have no being, evidently assuming that whatever has being is a spatial
magnitude. And if it is a magnitude, it is corporeal; for the
corporeal has being in every dimension, while the other objects of
mathematics, e.g. a plane or a line, added in one way will increase
what they are added to, but in another way will not do so, and a point
or a unit does so in no way. But, since his theory is of a low
order, and an indivisible thing can exist in such a way as to have a
defence even against him (for the indivisible when added will make the
number, though not the size, greater),-yet how can a magnitude proceed
from one such indivisible or from many? It is like saying that the
line is made out of points.

    But even if ore supposes the case to be such that, as some say,
number proceeds from unity-itself and something else which is not one,
none the less we must inquire why and how the product will be
sometimes a number and sometimes a magnitude, if the not-one was
inequality and was the same principle in either case. For it is not
evident how magnitudes could proceed either from the one and this
principle, or from some number and this principle.

                                   5

    (14) A question connected with these is whether numbers and bodies
and planes and points are substances of a kind, or not. If they are
not, it baffles us to say what being is and what the substances of
things are. For modifications and movements and relations and
dispositions and ratios do not seem to indicate the substance of
anything; for all are predicated of a subject, and none is a 'this'.
And as to the things which might seem most of all to indicate
substance, water and earth and fire and air, of which composite bodies
consist, heat and cold and the like are modifications of these, not
substances, and the body which is thus modified alone persists as
something real and as a substance. But, on the other hand, the body is
surely less of a substance than the surface, and the surface than
the line, and the line than the unit and the point. For the body is
bounded by these; and they are thought to be capable of existing
without body, but body incapable of existing without these. This is
why, while most of the philosophers and the earlier among them thought
that substance and being were identical with body, and that all
other things were modifications of this, so that the first
principles of the bodies were the first principles of being, the
more recent and those who were held to be wiser thought numbers were
the first principles. As we said, then, if these are not substance,
there is no substance and no being at all; for the accidents of
these it cannot be right to call beings.

    But if this is admitted, that lines and points are substance
more than bodies, but we do not see to what sort of bodies these could
belong (for they cannot be in perceptible bodies), there can be no
substance.-Further, these are all evidently divisions of body,-one
in breadth, another in depth, another in length. Besides this, no sort
of shape is present in the solid more than any other; so that if the
Hermes is not in the stone, neither is the half of the cube in the
cube as something determinate; therefore the surface is not in it
either; for if any sort of surface were in it, the surface which marks
off the half of the cube would be in it too. And the same account
applies to the line and to the point and the unit. Therefore, if on
the one hand body is in the highest degree substance, and on the other
hand these things are so more than body, but these are not even
instances of substance, it baffles us to say what being is and what
the substance of things is.-For besides what has been said, the
questions of generation and instruction confront us with further
paradoxes. For if substance, not having existed before, now exists, or
having existed before, afterwards does not exist, this change is
thought to be accompanied by a process of becoming or perishing; but
points and lines and surfaces cannot be in process either of
becoming or of perishing, when they at one time exist and at another
do not. For when bodies come into contact or are divided, their
boundaries simultaneously become one in the one case when they
touch, and two in the other-when they are divided; so that when they
have been put together one boundary does not exist but has perished,
and when they have been divided the boundaries exist which before
did not exist (for it cannot be said that the point, which is
indivisible, was divided into two). And if the boundaries come into
being and cease to be, from what do they come into being? A similar
account may also be given of the 'now' in time; for this also cannot
be in process of coming into being or of ceasing to be, but yet
seems to be always different, which shows that it is not a
substance. And evidently the same is true of points and lines and
planes; for the same argument applies, since they are all alike either
limits or divisions.

                                   6

    In general one might raise the question why after all, besides
perceptible things and the intermediates, we have to look for
another class of things, i.e. the Forms which we posit. If it is for
this reason, because the objects of mathematics, while they differ
from the things in this world in some other respect, differ not at all
in that there are many of the same kind, so that their first
principles cannot be limited in number (just as the elements of all
the language in this sensible world are not limited in number, but
in kind, unless one takes the elements of this individual syllable
or of this individual articulate sound-whose elements will be
limited even in number; so is it also in the case of the
intermediates; for there also the members of the same kind are
infinite in number), so that if there are not-besides perceptible
and mathematical objects-others such as some maintain the Forms to be,
there will be no substance which is one in number, but only in kind,
nor will the first principles of things be determinate in number,
but only in kind:-if then this must be so, the Forms also must
therefore be held to exist. Even if those who support this view do not
express it articulately, still this is what they mean, and they must
be maintaining the Forms just because each of the Forms is a substance
and none is by accident.

    But if we are to suppose both that the Forms exist and that the
principles are one in number, not in kind, we have mentioned the
impossible results that necessarily follow.

    (13) Closely connected with this is the question whether the
elements exist potentially or in some other manner. If in some other
way, there will be something else prior to the first principles; for
the potency is prior to the actual cause, and it is not necessary
for everything potential to be actual.-But if the elements exist
potentially, it is possible that everything that is should not be. For
even that which is not yet is capable of being; for that which is
not comes to be, but nothing that is incapable of being comes to be.

    (12) We must not only raise these questions about the first
principles, but also ask whether they are universal or what we call
individuals. If they are universal, they will not be substances; for
everything that is common indicates not a 'this' but a 'such', but
substance is a 'this'. And if we are to be allowed to lay it down that
a common predicate is a 'this' and a single thing, Socrates will be
several animals-himself and 'man' and 'animal', if each of these
indicates a 'this' and a single thing.

    If, then, the principles are universals, these universal.
Therefore if there is to be results follow; if they are not universals
but of knowledge of the principles there must be the nature of
individuals, they will not be other principles prior to them, namely
those knowable; for the knowledge of anything is that are
universally predicated of them.

                                Book IV

                                   1

    THERE is a science which investigates being as being and the
attributes which belong to this in virtue of its own nature. Now
this is not the same as any of the so-called special sciences; for
none of these others treats universally of being as being. They cut
off a part of being and investigate the attribute of this part; this
is what the mathematical sciences for instance do. Now since we are
seeking the first principles and the highest causes, clearly there
must be some thing to which these belong in virtue of its own
nature. If then those who sought the elements of existing things
were seeking these same principles, it is necessary that the
elements must be elements of being not by accident but just because it
is being. Therefore it is of being as being that we also must grasp
the first causes.

                                    2

    There are many senses in which a thing may be said to 'be', but
all that 'is' is related to one central point, one definite kind of
thing, and is not said to 'be' by a mere ambiguity. Everything which
is healthy is related to health, one thing in the sense that it
preserves health, another in the sense that it produces it, another in
the sense that it is a symptom of health, another because it is
capable of it. And that which is medical is relative to the medical
art, one thing being called medical because it possesses it, another
because it is naturally adapted to it, another because it is a
function of the medical art. And we shall find other words used
similarly to these. So, too, there are many senses in which a thing is
said to be, but all refer to one starting-point; some things are
said to be because they are substances, others because they are
affections of substance, others because they are a process towards
substance, or destructions or privations or qualities of substance, or
productive or generative of substance, or of things which are relative
to substance, or negations of one of these thing of substance
itself. It is for this reason that we say even of non-being that it is
nonbeing. As, then, there is one science which deals with all
healthy things, the same applies in the other cases also. For not only
in the case of things which have one common notion does the
investigation belong to one science, but also in the case of things
which are related to one common nature; for even these in a sense have
one common notion. It is clear then that it is the work of one science
also to study the things that are, qua being.-But everywhere science
deals chiefly with that which is primary, and on which the other
things depend, and in virtue of which they get their names. If,
then, this is substance, it will be of substances that the philosopher
must grasp the principles and the causes.

    Now for each one class of things, as there is one perception, so
there is one science, as for instance grammar, being one science,
investigates all articulate sounds. Hence to investigate all the
species of being qua being is the work of a science which is
generically one, and to investigate the several species is the work of
the specific parts of the science.

    If, now, being and unity are the same and are one thing in the
sense that they are implied in one another as principle and cause are,
not in the sense that they are explained by the same definition
(though it makes no difference even if we suppose them to be like
that-in fact this would even strengthen our case); for 'one man' and
'man' are the same thing, and so are 'existent man' and 'man', and the
doubling of the words in 'one man and one existent man' does not
express anything different (it is clear that the two things are not
separated either in coming to be or in ceasing to be); and similarly
'one existent man' adds nothing to 'existent man', and that it is
obvious that the addition in these cases means the same thing, and
unity is nothing apart from being; and if, further, the substance of
each thing is one in no merely accidental way, and similarly is from
its very nature something that is:-all this being so, there must be
exactly as many species of being as of unity. And to investigate the
essence of these is the work of a science which is generically one-I
mean, for instance, the discussion of the same and the similar and the
other concepts of this sort; and nearly all contraries may be referred
to this origin; let us take them as having been investigated in the
'Selection of Contraries'.

    And there are as many parts of philosophy as there are kinds of
substance, so that there must necessarily be among them a first
philosophy and one which follows this. For being falls immediately
into genera; for which reason the sciences too will correspond to
these genera. For the philosopher is like the mathematician, as that
word is used; for mathematics also has parts, and there is a first and
a second science and other successive ones within the sphere of
mathematics.

    Now since it is the work of one science to investigate
opposites, and plurality is opposed to unity-and it belongs to one
science to investigate the negation and the privation because in
both cases we are really investigating the one thing of which the
negation or the privation is a negation or privation (for we either
say simply that that thing is not present, or that it is not present
in some particular class; in the latter case difference is present
over and above what is implied in negation; for negation means just
the absence of the thing in question, while in privation there is also
employed an underlying nature of which the privation is
asserted):-in view of all these facts, the contraries of the
concepts we named above, the other and the dissimilar and the unequal,
and everything else which is derived either from these or from
plurality and unity, must fall within the province of the science
above named. And contrariety is one of these concepts; for contrariety
is a kind of difference, and difference is a kind of otherness.
Therefore, since there are many senses in which a thing is said to
be one, these terms also will have many senses, but yet it belongs
to one science to know them all; for a term belongs to different
sciences not if it has different senses, but if it has not one meaning
and its definitions cannot be referred to one central meaning. And
since all things are referred to that which is primary, as for
instance all things which are called one are referred to the primary
one, we must say that this holds good also of the same and the other
and of contraries in general; so that after distinguishing the various
senses of each, we must then explain by reference to what is primary
in the case of each of the predicates in question, saying how they are
related to it; for some will be called what they are called because
they possess it, others because they produce it, and others in other
such ways.

    It is evident, then, that it belongs to one science to be able
to give an account of these concepts as well as of substance (this was
one of the questions in our book of problems), and that it is the
function of the philosopher to be able to investigate all things.
For if it is not the function of the philosopher, who is it who will
inquire whether Socrates and Socrates seated are the same thing, or
whether one thing has one contrary, or what contrariety is, or how
many meanings it has? And similarly with all other such questions.
Since, then, these are essential modifications of unity qua unity
and of being qua being, not qua numbers or lines or fire, it is
clear that it belongs to this science to investigate both the
essence of these concepts and their properties. And those who study
these properties err not by leaving the sphere of philosophy, but by
forgetting that substance, of which they have no correct idea, is
prior to these other things. For number qua number has peculiar
attributes, such as oddness and evenness, commensurability and
equality, excess and defect, and these belong to numbers either in
themselves or in relation to one another. And similarly the solid
and the motionless and that which is in motion and the weightless
and that which has weight have other peculiar properties. So too there
are certain properties peculiar to being as such, and it is about
these that the philosopher has to investigate the truth.-An indication
of this may be mentioned: dialecticians and sophists assume the same
guise as the philosopher, for sophistic is Wisdom which exists only in
semblance, and dialecticians embrace all things in their dialectic,
and being is common to all things; but evidently their dialectic
embraces these subjects because these are proper to philosophy.-For
sophistic and dialectic turn on the same class of things as
philosophy, but this differs from dialectic in the nature of the
faculty required and from sophistic in respect of the purpose of the
philosophic life. Dialectic is merely critical where philosophy claims
to know, and sophistic is what appears to be philosophy but is not.

    Again, in the list of contraries one of the two columns is
privative, and all contraries are reducible to being and non-being,
and to unity and plurality, as for instance rest belongs to unity
and movement to plurality. And nearly all thinkers agree that being
and substance are composed of contraries; at least all name contraries
as their first principles-some name odd and even, some hot and cold,
some limit and the unlimited, some love and strife. And all the others
as well are evidently reducible to unity and plurality (this reduction
we must take for granted), and the principles stated by other thinkers
fall entirely under these as their genera. It is obvious then from
these considerations too that it belongs to one science to examine
being qua being. For all things are either contraries or composed of
contraries, and unity and plurality are the starting-points of all
contraries. And these belong to one science, whether they have or have
not one single meaning. Probably the truth is that they have not;
yet even if 'one' has several meanings, the other meanings will be
related to the primary meaning (and similarly in the case of the
contraries), even if being or unity is not a universal and the same in
every instance or is not separable from the particular instances (as
in fact it probably is not; the unity is in some cases that of
common reference, in some cases that of serial succession). And for
this reason it does not belong to the geometer to inquire what is
contrariety or completeness or unity or being or the same or the
other, but only to presuppose these concepts and reason from this
starting-point.--Obviously then it is the work of one science to
examine being qua being, and the attributes which belong to it qua
being, and the same science will examine not only substances but
also their attributes, both those above named and the concepts 'prior'
and 'posterior', 'genus' and 'species', 'whole' and 'part', and the
others of this sort.

                                   3

    We must state whether it belongs to one or to different sciences
to inquire into the truths which are in mathematics called axioms, and
into substance. Evidently, the inquiry into these also belongs to
one science, and that the science of the philosopher; for these truths
hold good for everything that is, and not for some special genus apart
from others. And all men use them, because they are true of being
qua being and each genus has being. But men use them just so far as to
satisfy their purposes; that is, as far as the genus to which their
demonstrations refer extends. Therefore since these truths clearly
hold good for all things qua being (for this is what is common to
them), to him who studies being qua being belongs the inquiry into
these as well. And for this reason no one who is conducting a
special inquiry tries to say anything about their truth or
falsity,-neither the geometer nor the arithmetician. Some natural
philosophers indeed have done so, and their procedure was intelligible
enough; for they thought that they alone were inquiring about the
whole of nature and about being. But since there is one kind of
thinker who is above even the natural philosopher (for nature is
only one particular genus of being), the discussion of these truths
also will belong to him whose inquiry is universal and deals with
primary substance. Physics also is a kind of Wisdom, but it is not the
first kind.-And the attempts of some of those who discuss the terms on
which truth should be accepted, are due to a want of training in
logic; for they should know these things already when they come to a
special study, and not be inquiring into them while they are listening
to lectures on it.

    Evidently then it belongs to the philosopher, i.e. to him who is
studying the nature of all substance, to inquire also into the
principles of syllogism. But he who knows best about each genus must
be able to state the most certain principles of his subject, so that
he whose subject is existing things qua existing must be able to state
the most certain principles of all things. This is the philosopher,
and the most certain principle of all is that regarding which it is
impossible to be mistaken; for such a principle must be both the
best known (for all men may be mistaken about things which they do not
know), and non-hypothetical. For a principle which every one must have
who understands anything that is, is not a hypothesis; and that
which every one must know who knows anything, he must already have
when he comes to a special study. Evidently then such a principle is
the most certain of all; which principle this is, let us proceed to
say. It is, that the same attribute cannot at the same time belong and
not belong to the same subject and in the same respect; we must
presuppose, to guard against dialectical objections, any further
qualifications which might be added. This, then, is the most certain
of all principles, since it answers to the definition given above. For
it is impossible for any one to believe the same thing to be and not
to be, as some think Heraclitus says. For what a man says, he does not
necessarily believe; and if it is impossible that contrary
attributes should belong at the same time to the same subject (the
usual qualifications must be presupposed in this premiss too), and
if an opinion which contradicts another is contrary to it, obviously
it is impossible for the same man at the same time to believe the same
thing to be and not to be; for if a man were mistaken on this point he
would have contrary opinions at the same time. It is for this reason
that all who are carrying out a demonstration reduce it to this as
an ultimate belief; for this is naturally the starting-point even
for all the other axioms.

                                   4

    There are some who, as we said, both themselves assert that it
is possible for the same thing to be and not to be, and say that
people can judge this to be the case. And among others many writers
about nature use this language. But we have now posited that it is
impossible for anything at the same time to be and not to be, and by
this means have shown that this is the most indisputable of all
principles.-Some indeed demand that even this shall be demonstrated,
but this they do through want of education, for not to know of what
things one should demand demonstration, and of what one should not,
argues want of education. For it is impossible that there should be
demonstration of absolutely everything (there would be an infinite
regress, so that there would still be no demonstration); but if
there are things of which one should not demand demonstration, these
persons could not say what principle they maintain to be more
self-evident than the present one.

    We can, however, demonstrate negatively even that this view is
impossible, if our opponent will only say something; and if he says
nothing, it is absurd to seek to give an account of our views to one
who cannot give an account of anything, in so far as he cannot do
so. For such a man, as such, is from the start no better than a
vegetable. Now negative demonstration I distinguish from demonstration
proper, because in a demonstration one might be thought to be
begging the question, but if another person is responsible for the
assumption we shall have negative proof, not demonstration. The
starting-point for all such arguments is not the demand that our
opponent shall say that something either is or is not (for this one
might perhaps take to be a begging of the question), but that he shall
say something which is significant both for himself and for another;
for this is necessary, if he really is to say anything. For, if he
means nothing, such a man will not be capable of reasoning, either
with himself or with another. But if any one grants this,
demonstration will be possible; for we shall already have something
definite. The person responsible for the proof, however, is not he who
demonstrates but he who listens; for while disowning reason he listens
to reason. And again he who admits this has admitted that something is
true apart from demonstration (so that not everything will be 'so
and not so').

    First then this at least is obviously true, that the word 'be'
or 'not be' has a definite meaning, so that not everything will be 'so
and not so'. Again, if 'man' has one meaning, let this be
'two-footed animal'; by having one meaning I understand this:-if 'man'
means 'X', then if A is a man 'X' will be what 'being a man' means for
him. (It makes no difference even if one were to say a word has
several meanings, if only they are limited in number; for to each
definition there might be assigned a different word. For instance,
we might say that 'man' has not one meaning but several, one of
which would have one definition, viz. 'two-footed animal', while there
might be also several other definitions if only they were limited in
number; for a peculiar name might be assigned to each of the
definitions. If, however, they were not limited but one were to say
that the word has an infinite number of meanings, obviously
reasoning would be impossible; for not to have one meaning is to
have no meaning, and if words have no meaning our reasoning with one
another, and indeed with ourselves, has been annihilated; for it is
impossible to think of anything if we do not think of one thing; but
if this is possible, one name might be assigned to this thing.)

    Let it be assumed then, as was said at the beginning, that the
name has a meaning and has one meaning; it is impossible, then, that
'being a man' should mean precisely 'not being a man', if 'man' not
only signifies something about one subject but also has one
significance (for we do not identify 'having one significance' with
'signifying something about one subject', since on that assumption
even 'musical' and 'white' and 'man' would have had one
significance, so that all things would have been one; for they would
all have had the same significance).

    And it will not be possible to be and not to be the same thing,
except in virtue of an ambiguity, just as if one whom we call 'man',
others were to call 'not-man'; but the point in question is not
this, whether the same thing can at the same time be and not be a
man in name, but whether it can in fact. Now if 'man' and 'not-man'
mean nothing different, obviously 'not being a man' will mean
nothing different from 'being a man'; so that 'being a man' will be
'not being a man'; for they will be one. For being one means
this-being related as 'raiment' and 'dress' are, if their definition
is one. And if 'being a man' and 'being a not-man' are to be one, they
must mean one thing. But it was shown earlier' that they mean
different things.-Therefore, if it is true to say of anything that
it is a man, it must be a two-footed animal (for this was what 'man'
meant); and if this is necessary, it is impossible that the same thing
should not at that time be a two-footed animal; for this is what
'being necessary' means-that it is impossible for the thing not to be.
It is, then, impossible that it should be at the same time true to say
the same thing is a man and is not a man.

    The same account holds good with regard to 'not being a man',
for 'being a man' and 'being a not-man' mean different things, since
even 'being white' and 'being a man' are different; for the former
terms are much more different so that they must a fortiori mean
different things. And if any one says that 'white' means one and the
same thing as 'man', again we shall say the same as what was said
before, that it would follow that all things are one, and not only
opposites. But if this is impossible, then what we have maintained
will follow, if our opponent will only answer our question.

    And if, when one asks the question simply, he adds the
contradictories, he is not answering the question. For there is
nothing to prevent the same thing from being both a man and white
and countless other things: but still, if one asks whether it is or is
not true to say that this is a man, our opponent must give an answer
which means one thing, and not add that 'it is also white and
large'. For, besides other reasons, it is impossible to enumerate
its accidental attributes, which are infinite in number; let him,
then, enumerate either all or none. Similarly, therefore, even if
the same thing is a thousand times a man and a not-man, he must not,
in answering the question whether this is a man, add that it is also
at the same time a not-man, unless he is bound to add also all the
other accidents, all that the subject is or is not; and if he does
this, he is not observing the rules of argument.

    And in general those who say this do away with substance and
essence. For they must say that all attributes are accidents, and that
there is no such thing as 'being essentially a man' or 'an animal'.
For if there is to be any such thing as 'being essentially a man' this
will not be 'being a not-man' or 'not being a man' (yet these are
negations of it); for there was one thing which it meant, and this was
the substance of something. And denoting the substance of a thing
means that the essence of the thing is nothing else. But if its
being essentially a man is to be the same as either being
essentially a not-man or essentially not being a man, then its essence
will be something else. Therefore our opponents must say that there
cannot be such a definition of anything, but that all attributes are
accidental; for this is the distinction between substance and
accident-'white' is accidental to man, because though he is white,
whiteness is not his essence. But if all statements are accidental,
there will be nothing primary about which they are made, if the
accidental always implies predication about a subject. The
predication, then, must go on ad infinitum. But this is impossible;
for not even more than two terms can be combined in accidental
predication. For (1) an accident is not an accident of an accident,
unless it be because both are accidents of the same subject. I mean,
for instance, that the white is musical and the latter is white,
only because both are accidental to man. But (2) Socrates is
musical, not in this sense, that both terms are accidental to
something else. Since then some predicates are accidental in this
and some in that sense, (a) those which are accidental in the latter
sense, in which white is accidental to Socrates, cannot form an
infinite series in the upward direction; e.g. Socrates the white has
not yet another accident; for no unity can be got out of such a sum.
Nor again (b) will 'white' have another term accidental to it, e.g.
'musical'. For this is no more accidental to that than that is to
this; and at the same time we have drawn the distinction, that while
some predicates are accidental in this sense, others are so in the
sense in which 'musical' is accidental to Socrates; and the accident
is an accident of an accident not in cases of the latter kind, but
only in cases of the other kind, so that not all terms will be
accidental. There must, then, even so be something which denotes
substance. And if this is so, it has been shown that contradictories
cannot be predicated at the same time.

    Again, if all contradictory statements are true of the same
subject at the same time, evidently all things will be one. For the
same thing will be a trireme, a wall, and a man, if of everything it
is possible either to affirm or to deny anything (and this premiss
must be accepted by those who share the views of Protagoras). For if
any one thinks that the man is not a trireme, evidently he is not a
trireme; so that he also is a trireme, if, as they say,
contradictory statements are both true. And we thus get the doctrine
of Anaxagoras, that all things are mixed together; so that nothing
really exists. They seem, then, to be speaking of the indeterminate,
and, while fancying themselves to be speaking of being, they are
speaking about non-being; for it is that which exists potentially
and not in complete reality that is indeterminate. But they must
predicate of every subject the affirmation or the negation of every
attribute. For it is absurd if of each subject its own negation is
to be predicable, while the negation of something else which cannot be
predicated of it is not to be predicable of it; for instance, if it is
true to say of a man that he is not a man, evidently it is also true
to say that he is either a trireme or not a trireme. If, then, the
affirmative can be predicated, the negative must be predicable too;
and if the affirmative is not predicable, the negative, at least, will
be more predicable than the negative of the subject itself. If,
then, even the latter negative is predicable, the negative of
'trireme' will be also predicable; and, if this is predicable, the
affirmative will be so too.

    Those, then, who maintain this view are driven to this conclusion,
and to the further conclusion that it is not necessary either to
assert or to deny. For if it is true that a thing is a man and a
not-man, evidently also it will be neither a man nor a not-man. For to
the two assertions there answer two negations, and if the former is
treated as a single proposition compounded out of two, the latter also
is a single proposition opposite to the former.

    Again, either the theory is true in all cases, and a thing is both
white and not-white, and existent and non-existent, and all other
assertions and negations are similarly compatible or the theory is
true of some statements and not of others. And if not of all, the
exceptions will be contradictories of which admittedly only one is
true; but if of all, again either the negation will be true wherever
the assertion is, and the assertion true wherever the negation is,
or the negation will be true where the assertion is, but the assertion
not always true where the negation is. And (a) in the latter case
there will be something which fixedly is not, and this will be an
indisputable belief; and if non-being is something indisputable and
knowable, the opposite assertion will be more knowable. But (b) if
it is equally possible also to assert all that it is possible to deny,
one must either be saying what is true when one separates the
predicates (and says, for instance, that a thing is white, and again
that it is not-white), or not. And if (i) it is not true to apply
the predicates separately, our opponent is not saying what he
professes to say, and also nothing at all exists; but how could
non-existent things speak or walk, as he does? Also all things would
on this view be one, as has been already said, and man and God and
trireme and their contradictories will be the same. For if
contradictories can be predicated alike of each subject, one thing
will in no wise differ from another; for if it differ, this difference
will be something true and peculiar to it. And (ii) if one may with
truth apply the predicates separately, the above-mentioned result
follows none the less, and, further, it follows that all would then be
right and all would be in error, and our opponent himself confesses
himself to be in error.-And at the same time our discussion with him
is evidently about nothing at all; for he says nothing. For he says
neither 'yes' nor 'no', but 'yes and no'; and again he denies both
of these and says 'neither yes nor no'; for otherwise there would
already be something definite.

    Again if when the assertion is true, the negation is false, and
when this is true, the affirmation is false, it will not be possible
to assert and deny the same thing truly at the same time. But
perhaps they might say this was the very question at issue.

    Again, is he in error who judges either that the thing is so or
that it is not so, and is he right who judges both? If he is right,
what can they mean by saying that the nature of existing things is
of this kind? And if he is not right, but more right than he who
judges in the other way, being will already be of a definite nature,
and this will be true, and not at the same time also not true. But
if all are alike both wrong and right, one who is in this condition
will not be able either to speak or to say anything intelligible;
for he says at the same time both 'yes' and 'no.' And if he makes no
judgement but 'thinks' and 'does not think', indifferently, what
difference will there be between him and a vegetable?-Thus, then, it
is in the highest degree evident that neither any one of those who
maintain this view nor any one else is really in this position. For
why does a man walk to Megara and not stay at home, when he thinks
he ought to be walking there? Why does he not walk early some
morning into a well or over a precipice, if one happens to be in his
way? Why do we observe him guarding against this, evidently because he
does not think that falling in is alike good and not good?
Evidently, then, he judges one thing to be better and another worse.
And if this is so, he must also judge one thing to be a man and
another to be not-a-man, one thing to be sweet and another to be
not-sweet. For he does not aim at and judge all things alike, when,
thinking it desirable to drink water or to see a man, he proceeds to
aim at these things; yet he ought, if the same thing were alike a
man and not-a-man. But, as was said, there is no one who does not
obviously avoid some things and not others. Therefore, as it seems,
all men make unqualified judgements, if not about all things, still
about what is better and worse. And if this is not knowledge but
opinion, they should be all the more anxious about the truth, as a
sick man should be more anxious about his health than one who is
healthy; for he who has opinions is, in comparison with the man who
knows, not in a healthy state as far as the truth is concerned.

    Again, however much all things may be 'so and not so', still there
is a more and a less in the nature of things; for we should not say
that two and three are equally even, nor is he who thinks four
things are five equally wrong with him who thinks they are a thousand.
If then they are not equally wrong, obviously one is less wrong and
therefore more right. If then that which has more of any quality is
nearer the norm, there must be some truth to which the more true is
nearer. And even if there is not, still there is already something
better founded and liker the truth, and we shall have got rid of the
unqualified doctrine which would prevent us from determining
anything in our thought.

                                   5

    From the same opinion proceeds the doctrine of Protagoras, and
both doctrines must be alike true or alike untrue. For on the one
hand, if all opinions and appearances are true, all statements must be
at the same time true and false. For many men hold beliefs in which
they conflict with one another, and think those mistaken who have
not the same opinions as themselves; so that the same thing must
both be and not be. And on the other hand, if this is so, all opinions
must be true; for those who are mistaken and those who are right are
opposed to one another in their opinions; if, then, reality is such as
the view in question supposes, all will be right in their beliefs.

    Evidently, then, both doctrines proceed from the same way of
thinking. But the same method of discussion must not be used with
all opponents; for some need persuasion, and others compulsion.
Those who have been driven to this position by difficulties in their
thinking can easily be cured of their ignorance; for it is not their
expressed argument but their thought that one has to meet. But those
who argue for the sake of argument can be cured only by refuting the
argument as expressed in speech and in words.

    Those who really feel the difficulties have been led to this
opinion by observation of the sensible world. (1) They think that
contradictories or contraries are true at the same time, because
they see contraries coming into existence out of the same thing. If,
then, that which is not cannot come to be, the thing must have existed
before as both contraries alike, as Anaxagoras says all is mixed in
all, and Democritus too; for he says the void and the full exist alike
in every part, and yet one of these is being, and the other non-being.
To those, then, whose belief rests on these grounds, we shall say that
in a sense they speak rightly and in a sense they err. For 'that which
is' has two meanings, so that in some sense a thing can come to be out
of that which is not, while in some sense it cannot, and the same
thing can at the same time be in being and not in being-but not in the
same respect. For the same thing can be potentially at the same time
two contraries, but it cannot actually. And again we shall ask them to
believe that among existing things there is also another kind of
substance to which neither movement nor destruction nor generation
at all belongs.

    And (2) similarly some have inferred from observation of the
sensible world the truth of appearances. For they think that the truth
should not be determined by the large or small number of those who
hold a belief, and that the same thing is thought sweet by some when
they taste it, and bitter by others, so that if all were ill or all
were mad, and only two or three were well or sane, these would be
thought ill and mad, and not the others.

    And again, they say that many of the other animals receive
impressions contrary to ours; and that even to the senses of each
individual, things do not always seem the same. Which, then, of
these impressions are true and which are false is not obvious; for the
one set is no more true than the other, but both are alike. And this
is why Democritus, at any rate, says that either there is no truth
or to us at least it is not evident.

    And in general it is because these thinkers suppose knowledge to
be sensation, and this to be a physical alteration, that they say that
what appears to our senses must be true; for it is for these reasons
that both Empedocles and Democritus and, one may almost say, all the
others have fallen victims to opinions of this sort. For Empedocles
says that when men change their condition they change their knowledge;

    For wisdom increases in men according to what is before them.

    And elsewhere he says that:-

          So far as their nature changed, so far to them always

          Came changed thoughts into mind.

    And Parmenides also expresses himself in the same way:

          For as at each time the much-bent limbs are composed,

          So is the mind of men; for in each and all men

          'Tis one thing thinks-the substance of their limbs:

          For that of which there is more is thought.

    A saying of Anaxagoras to some of his friends is also
related,-that things would be for them such as they supposed them to
be. And they say that Homer also evidently had this opinion, because
he made Hector, when he was unconscious from the blow, lie 'thinking
other thoughts',-which implies that even those who are bereft of
thought have thoughts, though not the same thoughts. Evidently,
then, if both are forms of knowledge, the real things also are at
the same time 'both so and not so'. And it is in this direction that
the consequences are most difficult. For if those who have seen most
of such truth as is possible for us (and these are those who seek
and love it most)-if these have such opinions and express these
views about the truth, is it not natural that beginners in
philosophy should lose heart? For to seek the truth would be to follow
flying game.

    But the reason why these thinkers held this opinion is that
while they were inquiring into the truth of that which is, they
thought, 'that which is' was identical with the sensible world; in
this, however, there is largely present the nature of the
indeterminate-of that which exists in the peculiar sense which we have
explained; and therefore, while they speak plausibly, they do not
say what is true (for it is fitting to put the matter so rather than
as Epicharmus put it against Xenophanes). And again, because they
saw that all this world of nature is in movement and that about that
which changes no true statement can be made, they said that of course,
regarding that which everywhere in every respect is changing,
nothing could truly be affirmed. It was this belief that blossomed
into the most extreme of the views above mentioned, that of the
professed Heracliteans, such as was held by Cratylus, who finally
did not think it right to say anything but only moved his finger,
and criticized Heraclitus for saying that it is impossible to step
twice into the same river; for he thought one could not do it even
once.

    But we shall say in answer to this argument also that while
there is some justification for their thinking that the changing, when
it is changing, does not exist, yet it is after all disputable; for
that which is losing a quality has something of that which is being
lost, and of that which is coming to be, something must already be.
And in general if a thing is perishing, will be present something that
exists; and if a thing is coming to be, there must be something from
which it comes to be and something by which it is generated, and
this process cannot go on ad infinitum.-But, leaving these
arguments, let us insist on this, that it is not the same thing to
change in quantity and in quality. Grant that in quantity a thing is
not constant; still it is in respect of its form that we know each
thing.-And again, it would be fair to criticize those who hold this
view for asserting about the whole material universe what they saw
only in a minority even of sensible things. For only that region of
the sensible world which immediately surrounds us is always in process
of destruction and generation; but this is-so to speak-not even a
fraction of the whole, so that it would have been juster to acquit
this part of the world because of the other part, than to condemn
the other because of this.-And again, obviously we shall make to
them also the same reply that we made long ago; we must show them
and persuade them that there is something whose nature is
changeless. Indeed, those who say that things at the same time are and
are not, should in consequence say that all things are at rest
rather than that they are in movement; for there is nothing into which
they can change, since all attributes belong already to all subjects.

    Regarding the nature of truth, we must maintain that not
everything which appears is true; firstly, because even if
sensation-at least of the object peculiar to the sense in
question-is not false, still appearance is not the same as
sensation.-Again, it is fair to express surprise at our opponents'
raising the question whether magnitudes are as great, and colours
are of such a nature, as they appear to people at a distance, or as
they appear to those close at hand, and whether they are such as
they appear to the healthy or to the sick, and whether those things
are heavy which appear so to the weak or those which appear so to
the strong, and those things true which appear to the slee ing or to
the waking. For obviously they do not think these to be open
questions; no one, at least, if when he is in Libya he has fancied one
night that he is in Athens, starts for the concert hall.-And again
with regard to the future, as Plato says, surely the opinion of the
physician and that of the ignorant man are not equally weighty, for
instance, on the question whether a man will get well or not.-And
again, among sensations themselves the sensation of a foreign object
and that of the appropriate object, or that of a kindred object and
that of the object of the sense in question, are not equally
authoritative, but in the case of colour sight, not taste, has the
authority, and in the case of flavour taste, not sight; each of
which senses never says at the same time of the same object that it
simultaneously is 'so and not so'.-But not even at different times
does one sense disagree about the quality, but only about that to
which the quality belongs. I mean, for instance, that the same wine
might seem, if either it or one's body changed, at one time sweet
and at another time not sweet; but at least the sweet, such as it is
when it exists, has never yet changed, but one is always right about
it, and that which is to be sweet is of necessity of such and such a
nature. Yet all these views destroy this necessity, leaving nothing to
be of necessity, as they leave no essence of anything; for the
necessary cannot be in this way and also in that, so that if
anything is of necessity, it will not be 'both so and not so'.

    And, in general, if only the sensible exists, there would be
nothing if animate things were not; for there would be no faculty of
sense. Now the view that neither the sensible qualities nor the
sensations would exist is doubtless true (for they are affections of
the perceiver), but that the substrata which cause the sensation
should not exist even apart from sensation is impossible. For
sensation is surely not the sensation of itself, but there is
something beyond the sensation, which must be prior to the
sensation; for that which moves is prior in nature to that which is
moved, and if they are correlative terms, this is no less the case.

                                   6

    There are, both among those who have these convictions and among
those who merely profess these views, some who raise a difficulty by
asking, who is to be the judge of the healthy man, and in general
who is likely to judge rightly on each class of questions. But such
inquiries are like puzzling over the question whether we are now
asleep or awake. And all such questions have the same meaning. These
people demand that a reason shall be given for everything; for they
seek a starting-point, and they seek to get this by demonstration,
while it is obvious from their actions that they have no conviction.
But their mistake is what we have stated it to be; they seek a
reason for things for which no reason can be given; for the
starting-point of demonstration is not demonstration.

    These, then, might be easily persuaded of this truth, for it is
not difficult to grasp; but those who seek merely compulsion in
argument seek what is impossible; for they demand to be allowed to
contradict themselves-a claim which contradicts itself from the very
first.-But if not all things are relative, but some are self-existent,
not everything that appears will be true; for that which appears is
apparent to some one; so that he who says all things that appear are
true, makes all things relative. And, therefore, those who ask for
an irresistible argument, and at the same time demand to be called
to account for their views, must guard themselves by saying that the
truth is not that what appears exists, but that what appears exists
for him to whom it appears, and when, and to the sense to which, and
under the conditions under which it appears. And if they give an
account of their view, but do not give it in this way, they will
soon find themselves contradicting themselves. For it is possible that
the same thing may appear to be honey to the sight, but not to the
taste, and that, since we have two eyes, things may not appear the
same to each, if their sight is unlike. For to those who for the
reasons named some time ago say that what appears is true, and
therefore that all things are alike false and true, for things do
not appear either the same to all men or always the same to the same
man, but often have contrary appearances at the same time (for touch
says there are two objects when we cross our fingers, while sight says
there is one)-to these we shall say 'yes, but not to the same sense
and in the same part of it and under the same conditions and at the
same time', so that what appears will be with these qualifications
true. But perhaps for this reason those who argue thus not because
they feel a difficulty but for the sake of argument, should say that
this is not true, but true for this man. And as has been said
before, they must make everything relative-relative to opinion and
perception, so that nothing either has come to be or will be without
some one's first thinking so. But if things have come to be or will
be, evidently not all things will be relative to opinion.-Again, if
a thing is one, it is in relation to one thing or to a definite number
of things; and if the same thing is both half and equal, it is not
to the double that the equal is correlative. If, then, in relation
to that which thinks, man and that which is thought are the same,
man will not be that which thinks, but only that which is thought. And
if each thing is to be relative to that which thinks, that which
thinks will be relative to an infinity of specifically different
things.

    Let this, then, suffice to show (1) that the most indisputable
of all beliefs is that contradictory statements are not at the same
time true, and (2) what consequences follow from the assertion that
they are, and (3) why people do assert this. Now since it is
impossible that contradictories should be at the same time true of the
same thing, obviously contraries also cannot belong at the same time
to the same thing. For of contraries, one is a privation no less
than it is a contrary-and a privation of the essential nature; and
privation is the denial of a predicate to a determinate genus. If,
then, it is impossible to affirm and deny truly at the same time, it
is also impossible that contraries should belong to a subject at the
same time, unless both belong to it in particular relations, or one in
a particular relation and one without qualification.

                                   7

    But on the other hand there cannot be an intermediate between
contradictories, but of one subject we must either affirm or deny
any one predicate. This is clear, in the first place, if we define
what the true and the false are. To say of what is that it is not,
or of what is not that it is, is false, while to say of what is that
it is, and of what is not that it is not, is true; so that he who says
of anything that it is, or that it is not, will say either what is
true or what is false; but neither what is nor what is not is said
to be or not to be.-Again, the intermediate between the
contradictories will be so either in the way in which grey is
between black and white, or as that which is neither man nor horse
is between man and horse. (a) If it were of the latter kind, it
could not change into the extremes (for change is from not-good to
good, or from good to not-good), but as a matter of fact when there is
an intermediate it is always observed to change into the extremes. For
there is no change except to opposites and to their intermediates. (b)
But if it is really intermediate, in this way too there would have
to be a change to white, which was not from not-white; but as it is,
this is never seen.-Again, every object of understanding or reason the
understanding either affirms or denies-this is obvious from the
definition-whenever it says what is true or false. When it connects in
one way by assertion or negation, it says what is true, and when it
does so in another way, what is false.-Again, there must be an
intermediate between all contradictories, if one is not arguing merely
for the sake of argument; so that it will be possible for a man to say
what is neither true nor untrue, and there will be a middle between
that which is and that which is not, so that there will also be a kind
of change intermediate between generation and destruction.-Again, in
all classes in which the negation of an attribute involves the
assertion of its contrary, even in these there will be an
intermediate; for instance, in the sphere of numbers there will be
number which is neither odd nor not-odd. But this is impossible, as is
obvious from the definition.-Again, the process will go on ad
infinitum, and the number of realities will be not only half as
great again, but even greater. For again it will be possible to deny
this intermediate with reference both to its assertion and to its
negation, and this new term will be some definite thing; for its
essence is something different.-Again, when a man, on being asked
whether a thing is white, says 'no', he has denied nothing except that
it is; and its not being is a negation.

    Some people have acquired this opinion as other paradoxical
opinions have been acquired; when men cannot refute eristical
arguments, they give in to the argument and agree that the
conclusion is true. This, then, is why some express this view;
others do so because they demand a reason for everything. And the
starting-point in dealing with all such people is definition. Now
the definition rests on the necessity of their meaning something;
for the form of words of which the word is a sign will be its
definition.-While the doctrine of Heraclitus, that all things are
and are not, seems to make everything true, that of Anaxagoras, that
there is an intermediate between the terms of a contradiction, seems
to make everything false; for when things are mixed, the mixture is
neither good nor not-good, so that one cannot say anything that is
true.

                                   8

    In view of these distinctions it is obvious that the one-sided
theories which some people express about all things cannot be valid-on
the one hand the theory that nothing is true (for, say they, there
is nothing to prevent every statement from being like the statement
'the diagonal of a square is commensurate with the side'), on the
other hand the theory that everything is true. These views are
practically the same as that of Heraclitus; for he who says that all
things are true and all are false also makes each of these
statements separately, so that since they are impossible, the double
statement must be impossible too.-Again, there are obviously
contradictories which cannot be at the same time true-nor on the other
hand can all statements be false; yet this would seem more possible in
the light of what has been said.-But against all such views we must
postulate, as we said above,' not that something is or is not, but
that something has a meaning, so that we must argue from a definition,
viz. by assuming what falsity or truth means. If that which it is true
to affirm is nothing other than that which it is false to deny, it
is impossible that all statements should be false; for one side of the
contradiction must be true. Again, if it is necessary with regard to
everything either to assert or to deny it, it is impossible that
both should be false; for it is one side of the contradiction that
is false.-Therefore all such views are also exposed to the often
expressed objection, that they destroy themselves. For he who says
that everything is true makes even the statement contrary to his own
true, and therefore his own not true (for the contrary statement
denies that it is true), while he who says everything is false makes
himself also false.-And if the former person excepts the contrary
statement, saying it alone is not true, while the latter excepts his
own as being not false, none the less they are driven to postulate the
truth or falsity of an infinite number of statements; for that which
says the true statement is true is true, and this process will go on
to infinity.

    Evidently, again, those who say all things are at rest are not
right, nor are those who say all things are in movement. For if all
things are at rest, the same statements will always be true and the
same always false,-but this obviously changes; for he who makes a
statement, himself at one time was not and again will not be. And if
all things are in motion, nothing will be true; everything therefore
will be false. But it has been shown that this is impossible. Again,
it must be that which is that changes; for change is from something to
something. But again it is not the case that all things are at rest or
in motion sometimes, and nothing for ever; for there is something
which always moves the things that are in motion, and the first
mover is itself unmoved.

                                Book V

                                   1

    'BEGINNING' means (1) that part of a thing from which one would
start first, e.g a line or a road has a beginning in either of the
contrary directions. (2) That from which each thing would best be
originated, e.g. even in learning we must sometimes begin not from the
first point and the beginning of the subject, but from the point
from which we should learn most easily. (4) That from which, as an
immanent part, a thing first comes to be, e,g, as the keel of a ship
and the foundation of a house, while in animals some suppose the
heart, others the brain, others some other part, to be of this nature.
(4) That from which, not as an immanent part, a thing first comes to
be, and from which the movement or the change naturally first
begins, as a child comes from its father and its mother, and a fight
from abusive language. (5) That at whose will that which is moved is
moved and that which changes changes, e.g. the magistracies in cities,
and oligarchies and monarchies and tyrannies, are called arhchai,
and so are the arts, and of these especially the architectonic arts.
(6) That from which a thing can first be known,-this also is called
the beginning of the thing, e.g. the hypotheses are the beginnings
of demonstrations. (Causes are spoken of in an equal number of senses;
for all causes are beginnings.) It is common, then, to all
beginnings to be the first point from which a thing either is or comes
to be or is known; but of these some are immanent in the thing and
others are outside. Hence the nature of a thing is a beginning, and so
is the element of a thing, and thought and will, and essence, and
the final cause-for the good and the beautiful are the beginning
both of the knowledge and of the movement of many things.

                                   2

    'Cause' means (1) that from which, as immanent material, a thing
comes into being, e.g. the bronze is the cause of the statue and the
silver of the saucer, and so are the classes which include these.
(2) The form or pattern, i.e. the definition of the essence, and the
classes which include this (e.g. the ratio 2:1 and number in general
are causes of the octave), and the parts included in the definition.
(3) That from which the change or the resting from change first
begins; e.g. the adviser is a cause of the action, and the father a
cause of the child, and in general the maker a cause of the thing made
and the change-producing of the changing. (4) The end, i.e. that for
the sake of which a thing is; e.g. health is the cause of walking. For
'Why does one walk?' we say; 'that one may be healthy'; and in
speaking thus we think we have given the cause. The same is true of
all the means that intervene before the end, when something else has
put the process in motion, as e.g. thinning or purging or drugs or
instruments intervene before health is reached; for all these are
for the sake of the end, though they differ from one another in that
some are instruments and others are actions.

    These, then, are practically all the senses in which causes are
spoken of, and as they are spoken of in several senses it follows both
that there are several causes of the same thing, and in no
accidental sense (e.g. both the art of sculpture and the bronze are
causes of the statue not in respect of anything else but qua statue;
not, however, in the same way, but the one as matter and the other
as source of the movement), and that things can be causes of one
another (e.g. exercise of good condition, and the latter of
exercise; not, however, in the same way, but the one as end and the
other as source of movement).-Again, the same thing is the cause of
contraries; for that which when present causes a particular thing,
we sometimes charge, when absent, with the contrary, e.g. we impute
the shipwreck to the absence of the steersman, whose presence was
the cause of safety; and both-the presence and the privation-are
causes as sources of movement.

    All the causes now mentioned fall under four senses which are
the most obvious. For the letters are the cause of syllables, and
the material is the cause of manufactured things, and fire and earth
and all such things are the causes of bodies, and the parts are causes
of the whole, and the hypotheses are causes of the conclusion, in
the sense that they are that out of which these respectively are made;
but of these some are cause as the substratum (e.g. the parts), others
as the essence (the whole, the synthesis, and the form). The semen,
the physician, the adviser, and in general the agent, are all
sources of change or of rest. The remainder are causes as the end
and the good of the other things; for that for the sake of which other
things are tends to be the best and the end of the other things; let
us take it as making no difference whether we call it good or apparent
good.

    These, then, are the causes, and this is the number of their
kinds, but the varieties of causes are many in number, though when
summarized these also are comparatively few. Causes are spoken of in
many senses, and even of those which are of the same kind some are
causes in a prior and others in a posterior sense, e.g. both 'the
physician' and 'the professional man' are causes of health, and both
'the ratio 2:1' and 'number' are causes of the octave, and the classes
that include any particular cause are always causes of the
particular effect. Again, there are accidental causes and the
classes which include these; e.g. while in one sense 'the sculptor'
causes the statue, in another sense 'Polyclitus' causes it, because
the sculptor happens to be Polyclitus; and the classes that include
the accidental cause are also causes, e.g. 'man'-or in general
'animal'-is the cause of the statue, because Polyclitus is a man,
and man is an animal. Of accidental causes also some are more remote
or nearer than others, as, for instance, if 'the white' and 'the
musical' were called causes of the statue, and not only 'Polyclitus'
or 'man'. But besides all these varieties of causes, whether proper or
accidental, some are called causes as being able to act, others as
acting; e.g. the cause of the house's being built is a builder, or a
builder who is building.-The same variety of language will be found
with regard to the effects of causes; e.g. a thing may be called the
cause of this statue or of a statue or in general of an image, and
of this bronze or of bronze or of matter in general; and similarly
in the case of accidental effects. Again, both accidental and proper
causes may be spoken of in combination; e.g. we may say not
'Polyclitus' nor 'the sculptor' but 'Polyclitus the sculptor'. Yet all
these are but six in number, while each is spoken of in two ways;
for (A) they are causes either as the individual, or as the genus,
or as the accidental, or as the genus that includes the accidental,
and these either as combined, or as taken simply; and (B) all may be
taken as acting or as having a capacity. But they differ inasmuch as
the acting causes, i.e. the individuals, exist, or do not exist,
simultaneously with the things of which they are causes, e.g. this
particular man who is healing, with this particular man who is
recovering health, and this particular builder with this particular
thing that is being built; but the potential causes are not always
in this case; for the house does not perish at the same time as the
builder.

                                   3

    'Element' means (1) the primary component immanent in a thing, and
indivisible in kind into other kinds; e.g. the elements of speech
are the parts of which speech consists and into which it is ultimately
divided, while they are no longer divided into other forms of speech
different in kind from them. If they are divided, their parts are of
the same kind, as a part of water is water (while a part of the
syllable is not a syllable). Similarly those who speak of the elements
of bodies mean the things into which bodies are ultimately divided,
while they are no longer divided into other things differing in
kind; and whether the things of this sort are one or more, they call
these elements. The so-called elements of geometrical proofs, and in
general the elements of demonstrations, have a similar character;
for the primary demonstrations, each of which is implied in many
demonstrations, are called elements of demonstrations; and the primary
syllogisms, which have three terms and proceed by means of one middle,
are of this nature.

    (2) People also transfer the word 'element' from this meaning
and apply it to that which, being one and small, is useful for many
purposes; for which reason what is small and simple and indivisible is
called an element. Hence come the facts that the most universal things
are elements (because each of them being one and simple is present
in a plurality of things, either in all or in as many as possible),
and that unity and the point are thought by some to be first
principles. Now, since the so-called genera are universal and
indivisible (for there is no definition of them), some say the
genera are elements, and more so than the differentia, because the
genus is more universal; for where the differentia is present, the
genus accompanies it, but where the genus is present, the
differentia is not always so. It is common to all the meanings that
the element of each thing is the first component immanent in each.

                                   4

    'Nature' means (1) the genesis of growing things-the meaning which
would be suggested if one were to pronounce the 'u' in phusis long.
(2) That immanent part of a growing thing, from which its growth first
proceeds. (3) The source from which the primary movement in each
natural object is present in it in virtue of its own essence. Those
things are said to grow which derive increase from something else by
contact and either by organic unity, or by organic adhesion as in
the case of embryos. Organic unity differs from contact; for in the
latter case there need not be anything besides the contact, but in
organic unities there is something identical in both parts, which
makes them grow together instead of merely touching, and be one in
respect of continuity and quantity, though not of quality.-(4)
'Nature' means the primary material of which any natural object
consists or out of which it is made, which is relatively unshaped
and cannot be changed from its own potency, as e.g. bronze is said
to be the nature of a statue and of bronze utensils, and wood the
nature of wooden things; and so in all other cases; for when a product
is made out of these materials, the first matter is preserved
throughout. For it is in this way that people call the elements of
natural objects also their nature, some naming fire, others earth,
others air, others water, others something else of the sort, and
some naming more than one of these, and others all of them.-(5)
'Nature' means the essence of natural objects, as with those who say
the nature is the primary mode of composition, or as Empedocles says:-

                       Nothing that is has a nature,

           But only mixing and parting of the mixed,

           And nature is but a name given them by men.

  Hence as regards the things that are or come to be by nature, though
that from which they naturally come to be or are is already present,
we say they have not their nature yet, unless they have their form
or shape. That which comprises both of these exists by nature, e.g.
the animals and their parts; and not only is the first matter nature
(and this in two senses, either the first, counting from the thing, or
the first in general; e.g. in the case of works in bronze, bronze is
first with reference to them, but in general perhaps water is first,
if all things that can be melted are water), but also the form or
essence, which is the end of the process of becoming.-(6) By an
extension of meaning from this sense of 'nature' every essence in
general has come to be called a 'nature', because the nature of a
thing is one kind of essence.

    From what has been said, then, it is plain that nature in the
primary and strict sense is the essence of things which have in
themselves, as such, a source of movement; for the matter is called
the nature because it is qualified to receive this, and processes of
becoming and growing are called nature because they are movements
proceeding from this. And nature in this sense is the source of the
movement of natural objects, being present in them somehow, either
potentially or in complete reality.

                                   5

    We call 'necessary' (1) (a) that without which, as a condition,
a thing cannot live; e.g. breathing and food are necessary for an
animal; for it is incapable of existing without these; (b) the
conditions without which good cannot be or come to be, or without
which we cannot get rid or be freed of evil; e.g. drinking the
medicine is necessary in order that we may be cured of disease, and
a man's sailing to Aegina is necessary in order that he may get his
money.-(2) The compulsory and compulsion, i.e. that which impedes
and tends to hinder, contrary to impulse and purpose. For the
compulsory is called necessary (whence the necessary is painful, as
Evenus says: 'For every necessary thing is ever irksome'), and
compulsion is a form of necessity, as Sophocles says: 'But force
necessitates me to this act'. And necessity is held to be something
that cannot be persuaded-and rightly, for it is contrary to the
movement which accords with purpose and with reasoning.-(3) We say
that that which cannot be otherwise is necessarily as it is. And
from this sense of 'necessary' all the others are somehow derived; for
a thing is said to do or suffer what is necessary in the sense of
compulsory, only when it cannot act according to its impulse because
of the compelling forces-which implies that necessity is that
because of which a thing cannot be otherwise; and similarly as regards
the conditions of life and of good; for when in the one case good,
in the other life and being, are not possible without certain
conditions, these are necessary, and this kind of cause is a sort of
necessity. Again, demonstration is a necessary thing because the
conclusion cannot be otherwise, if there has been demonstration in the
unqualified sense; and the causes of this necessity are the first
premisses, i.e. the fact that the propositions from which the
syllogism proceeds cannot be otherwise.

    Now some things owe their necessity to something other than
themselves; others do not, but are themselves the source of
necessity in other things. Therefore the necessary in the primary
and strict sense is the simple; for this does not admit of more states
than one, so that it cannot even be in one state and also in
another; for if it did it would already be in more than one. If, then,
there are any things that are eternal and unmovable, nothing
compulsory or against their nature attaches to them.

                                   6

    'One' means (1) that which is one by accident, (2) that which is
one by its own nature. (1) Instances of the accidentally one are
'Coriscus and what is musical', and 'musical Coriscus' (for it is
the same thing to say 'Coriscus and what is musical', and 'musical
Coriscus'), and 'what is musical and what is just', and 'musical
Coriscus and just Coriscus'. For all of these are called one by virtue
of an accident, 'what is just and what is musical' because they are
accidents of one substance, 'what is musical and Coriscus' because the
one is an accident of the other; and similarly in a sense 'musical
Coriscus' is one with 'Coriscus' because one of the parts of the
phrase is an accident of the other, i.e. 'musical' is an accident of
Coriscus; and 'musical Coriscus' is one with 'just Coriscus' because
one part of each is an accident of one and the same subject. The
case is similar if the accident is predicated of a genus or of any
universal name, e.g. if one says that man is the same as 'musical
man'; for this is either because 'musical' is an accident of man,
which is one substance, or because both are accidents of some
individual, e.g. Coriscus. Both, however, do not belong to him in
the same way, but one presumably as genus and included in his
substance, the other as a state or affection of the substance.

    The things, then, that are called one in virtue of an accident,
are called so in this way. (2) Of things that are called one in virtue
of their own nature some (a) are so called because they are
continuous, e.g. a bundle is made one by a band, and pieces of wood
are made one by glue; and a line, even if it is bent, is called one if
it is continuous, as each part of the body is, e.g. the leg or the
arm. Of these themselves, the continuous by nature are more one than
the continuous by art. A thing is called continuous which has by its
own nature one movement and cannot have any other; and the movement is
one when it is indivisible, and it is indivisible in respect of
time. Those things are continuous by their own nature which are one
not merely by contact; for if you put pieces of wood touching one
another, you will not say these are one piece of wood or one body or
one continuum of any other sort. Things, then, that are continuous
in any way called one, even if they admit of being bent, and still
more those which cannot be bent; e.g. the shin or the thigh is more
one than the leg, because the movement of the leg need not be one. And
the straight line is more one than the bent; but that which is bent
and has an angle we call both one and not one, because its movement
may be either simultaneous or not simultaneous; but that of the
straight line is always simultaneous, and no part of it which has
magnitude rests while another moves, as in the bent line.

    (b)(i) Things are called one in another sense because their
substratum does not differ in kind; it does not differ in the case
of things whose kind is indivisible to sense. The substratum meant
is either the nearest to, or the farthest from, the final state.
For, one the one hand, wine is said to be one and water is said to
be one, qua indivisible in kind; and, on the other hand, all juices,
e.g. oil and wine, are said to be one, and so are all things that
can be melted, because the ultimate substratum of all is the same; for
all of these are water or air.

    (ii) Those things also are called one whose genus is one though
distinguished by opposite differentiae-these too are all called one
because the genus which underlies the differentiae is one (e.g. horse,
man, and dog form a unity, because all are animals), and indeed in a
way similar to that in which the matter is one. These are sometimes
called one in this way, but sometimes it is the higher genus that is
said to be the same (if they are infimae species of their genus)-the
genus above the proximate genera; e.g. the isosceles and the
equilateral are one and the same figure because both are triangles;
but they are not the same triangles.

    (c) Two things are called one, when the definition which states
the essence of one is indivisible from another definition which
shows us the other (though in itself every definition is divisible).
Thus even that which has increased or is diminishing is one, because
its definition is one, as, in the case of plane figures, is the
definition of their form. In general those things the thought of whose
essence is indivisible, and cannot separate them either in time or
in place or in definition, are most of all one, and of these
especially those which are substances. For in general those things
that do not admit of division are called one in so far as they do
not admit of it; e.g. if two things are indistinguishable qua man,
they are one kind of man; if qua animal, one kind of animal; if qua
magnitude, one kind of magnitude.-Now most things are called one
because they either do or have or suffer or are related to something
else that is one, but the things that are primarily called one are
those whose substance is one,-and one either in continuity or in
form or in definition; for we count as more than one either things
that are not continuous, or those whose form is not one, or those
whose definition is not one.

    While in a sense we call anything one if it is a quantity and
continuous, in a sense we do not unless it is a whole, i.e. unless
it has unity of form; e.g. if we saw the parts of a shoe put
together anyhow we should not call them one all the same (unless
because of their continuity); we do this only if they are put together
so as to be a shoe and to have already a certain single form. This
is why the circle is of all lines most truly one, because it is
whole and complete.

    (3) The essence of what is one is to be some kind of beginning
of number; for the first measure is the beginning, since that by which
we first know each class is the first measure of the class; the one,
then, is the beginning of the knowable regarding each class. But the
one is not the same in all classes. For here it is a quarter-tone, and
there it is the vowel or the consonant; and there is another unit of
weight and another of movement. But everywhere the one is
indivisible either in quantity or in kind. Now that which is
indivisible in quantity is called a unit if it is not divisible in any
dimension and is without position, a point if it is not divisible in
any dimension and has position, a line if it is divisible in one
dimension, a plane if in two, a body if divisible in quantity in
all--i.e. in three--dimensions. And, reversing the order, that which
is divisible in two dimensions is a plane, that which is divisible
in one a line, that which is in no way divisible in quantity is a
point or a unit,-that which has not position a unit, that which has
position a point.

    Again, some things are one in number, others in species, others in
genus, others by analogy; in number those whose matter is one, in
species those whose definition is one, in genus those to which the
same figure of predication applies, by analogy those which are related
as a third thing is to a fourth. The latter kinds of unity are
always found when the former are; e.g. things that are one in number
are also one in species, while things that are one in species are
not all one in number; but things that are one in species are all
one in genus, while things that are so in genus are not all one in
species but are all one by analogy; while things that are one by
analogy are not all one in genus.

    Evidently 'many' will have meanings opposite to those of 'one';
some things are many because they are not continuous, others because
their matter-either the proximate matter or the ultimate-is
divisible in kind, others because the definitions which state their
essence are more than one.

                                   7

    Things are said to 'be' (1) in an accidental sense, (2) by their
own nature.

    (1) In an accidental sense, e.g. we say 'the righteous doer is
musical', and 'the man is musical', and 'the musician is a man',
just as we say 'the musician builds', because the builder happens to
be musical or the musician to be a builder; for here 'one thing is
another' means 'one is an accident of another'. So in the cases we
have mentioned; for when we say 'the man is musical' and 'the musician
is a man', or 'he who is pale is musical' or 'the musician is pale',
the last two mean that both attributes are accidents of the same
thing; the first that the attribute is an accident of that which is,
while 'the musical is a man' means that 'musical' is an accident of
a man. (In this sense, too, the not-pale is said to be, because that
of which it is an accident is.) Thus when one thing is said in an
accidental sense to be another, this is either because both belong
to the same thing, and this is, or because that to which the attribute
belongs is, or because the subject which has as an attribute that of
which it is itself predicated, itself is.

    (2) The kinds of essential being are precisely those that are
indicated by the figures of predication; for the senses of 'being' are
just as many as these figures. Since, then, some predicates indicate
what the subject is, others its quality, others quantity, others
relation, others activity or passivity, others its 'where', others its
'when', 'being' has a meaning answering to each of these. For there is
no difference between 'the man is recovering' and 'the man
recovers', nor between 'the man is walking or cutting' and 'the man
walks' or 'cuts'; and similarly in all other cases.

    (3) Again, 'being' and 'is' mean that a statement is true, 'not
being' that it is not true but falses-and this alike in the case of
affirmation and of negation; e.g. 'Socrates is musical' means that
this is true, or 'Socrates is not-pale' means that this is true; but
'the diagonal of the square is not commensurate with the side' means
that it is false to say it is.

    (4) Again, 'being' and 'that which is' mean that some of the
things we have mentioned 'are' potentially, others in complete
reality. For we say both of that which sees potentially and of that
which sees actually, that it is 'seeing', and both of that which can
actualize its knowledge and of that which is actualizing it, that it
knows, and both of that to which rest is already present and of that
which can rest, that it rests. And similarly in the case of
substances; we say the Hermes is in the stone, and the half of the
line is in the line, and we say of that which is not yet ripe that
it is corn. When a thing is potential and when it is not yet potential
must be explained elsewhere.

                                   8

    We call 'substance' (1) the simple bodies, i.e. earth and fire and
water and everything of the sort, and in general bodies and the things
composed of them, both animals and divine beings, and the parts of
these. All these are called substance because they are not
predicated of a subject but everything else is predicated of them.-(2)
That which, being present in such things as are not predicated of a
subject, is the cause of their being, as the soul is of the being of
an animal.-(3) The parts which are present in such things, limiting
them and marking them as individuals, and by whose destruction the
whole is destroyed, as the body is by the destruction of the plane, as
some say, and the plane by the destruction of the line; and in general
number is thought by some to be of this nature; for if it is
destroyed, they say, nothing exists, and it limits all things.-(4) The
essence, the formula of which is a definition, is also called the
substance of each thing.

    It follows, then, that 'substance' has two senses, (A) ultimate
substratum, which is no longer predicated of anything else, and (B)
that which, being a 'this', is also separable and of this nature is
the shape or form of each thing.

                                   9

    'The same' means (1) that which is the same in an accidental
sense, e.g. 'the pale' and 'the musical' are the same because they are
accidents of the same thing, and 'a man' and 'musical' because the one
is an accident of the other; and 'the musical' is 'a man' because it
is an accident of the man. (The complex entity is the same as either
of the simple ones and each of these is the same as it; for both
'the man' and 'the musical' are said to be the same as 'the musical
man', and this the same as they.) This is why all of these
statements are made not universally; for it is not true to say that
every man is the same as 'the musical' (for universal attributes
belong to things in virtue of their own nature, but accidents do not
belong to them in virtue of their own nature); but of the
individuals the statements are made without qualification. For
'Socrates' and 'musical Socrates' are thought to be the same; but
'Socrates' is not predicable of more than one subject, and therefore
we do not say 'every Socrates' as we say 'every man'.

    Some things are said to be the same in this sense, others (2)
are the same by their own nature, in as many senses as that which is
one by its own nature is so; for both the things whose matter is one
either in kind or in number, and those whose essence is one, are
said to be the same. Clearly, therefore, sameness is a unity of the
being either of more than one thing or of one thing when it is treated
as more than one, ie. when we say a thing is the same as itself; for
we treat it as two.

    Things are called 'other' if either their kinds or their matters
or the definitions of their essence are more than one; and in
general 'other' has meanings opposite to those of 'the same'.

    'Different' is applied (1) to those things which though other
are the same in some respect, only not in number but either in species
or in genus or by analogy; (2) to those whose genus is other, and to
contraries, and to an things that have their otherness in their
essence.

    Those things are called 'like' which have the same attributes in
every respect, and those which have more attributes the same than
different, and those whose quality is one; and that which shares
with another thing the greater number or the more important of the
attributes (each of them one of two contraries) in respect of which
things are capable of altering, is like that other thing. The senses
of 'unlike' are opposite to those of 'like'.

                                  10

    The term 'opposite' is applied to contradictories, and to
contraries, and to relative terms, and to privation and possession,
and to the extremes from which and into which generation and
dissolution take place; and the attributes that cannot be present at
the same time in that which is receptive of both, are said to be
opposed,-either themselves of their constituents. Grey and white
colour do not belong at the same time to the same thing; hence their
constituents are opposed.

    The term 'contrary' is applied (1) to those attributes differing
in genus which cannot belong at the same time to the same subject, (2)
to the most different of the things in the same genus, (3) to the most
different of the attributes in the same recipient subject, (4) to
the most different of the things that fall under the same faculty, (5)
to the things whose difference is greatest either absolutely or in
genus or in species. The other things that are called contrary are
so called, some because they possess contraries of the above kind,
some because they are receptive of such, some because they are
productive of or susceptible to such, or are producing or suffering
them, or are losses or acquisitions, or possessions or privations,
of such. Since 'one' and 'being' have many senses, the other terms
which are derived from these, and therefore 'same', 'other', and
'contrary', must correspond, so that they must be different for each
category.

    The term 'other in species' is applied to things which being of
the same genus are not subordinate the one to the other, or which
being in the same genus have a difference, or which have a contrariety
in their substance; and contraries are other than one another in
species (either all contraries or those which are so called in the
primary sense), and so are those things whose definitions differ in
the infima species of the genus (e.g. man and horse are indivisible in
genus, but their definitions are different), and those which being
in the same substance have a difference. 'The same in species' has the
various meanings opposite to these.

                                  11

    The words 'prior' and 'posterior' are applied (1) to some things
(on the assumption that there is a first, i.e. a beginning, in each
class) because they are nearer some beginning determined either
absolutely and by nature, or by reference to something or in some
place or by certain people; e.g. things are prior in place because
they are nearer either to some place determined by nature (e.g. the
middle or the last place), or to some chance object; and that which is
farther is posterior.-Other things are prior in time; some by being
farther from the present, i.e. in the case of past events (for the
Trojan war is prior to the Persian, because it is farther from the
present), others by being nearer the present, i.e. in the case of
future events (for the Nemean games are prior to the Pythian, if we
treat the present as beginning and first point, because they are
nearer the present).-Other things are prior in movement; for that
which is nearer the first mover is prior (e.g. the boy is prior to the
man); and the prime mover also is a beginning absolutely.-Others are
prior in power; for that which exceeds in power, i.e. the more
powerful, is prior; and such is that according to whose will the
other-i.e. the posterior-must follow, so that if the prior does not
set it in motion the other does not move, and if it sets it in
motion it does move; and here will is a beginning.-Others are prior in
arrangement; these are the things that are placed at intervals in
reference to some one definite thing according to some rule, e.g. in
the chorus the second man is prior to the third, and in the lyre the
second lowest string is prior to the lowest; for in the one case the
leader and in the other the middle string is the beginning.

    These, then, are called prior in this sense, but (2) in another
sense that which is prior for knowledge is treated as also
absolutely prior; of these, the things that are prior in definition do
not coincide with those that are prior in relation to perception.
For in definition universals are prior, in relation to perception
individuals. And in definition also the accident is prior to the
whole, e.g. 'musical' to 'musical man', for the definition cannot
exist as a whole without the part; yet musicalness cannot exist unless
there is some one who is musical.

    (3) The attributes of prior things are called prior, e.g.
straightness is prior to smoothness; for one is an attribute of a line
as such, and the other of a surface.

    Some things then are called prior and posterior in this sense,
others (4) in respect of nature and substance, i.e. those which can be
without other things, while the others cannot be without them,-a
distinction which Plato used. (If we consider the various senses of
'being', firstly the subject is prior, so that substance is prior;
secondly, according as potency or complete reality is taken into
account, different things are prior, for some things are prior in
respect of potency, others in respect of complete reality, e.g. in
potency the half line is prior to the whole line, and the part to
the whole, and the matter to the concrete substance, but in complete
reality these are posterior; for it is only when the whole has been
dissolved that they will exist in complete reality.) In a sense,
therefore, all things that are called prior and posterior are so
called with reference to this fourth sense; for some things can
exist without others in respect of generation, e.g. the whole
without the parts, and others in respect of dissolution, e.g. the part
without the whole. And the same is true in all other cases.

                                  12

    'Potency' means (1) a source of movement or change, which is in
another thing than the thing moved or in the same thing qua other;
e.g. the art of building is a potency which is not in the thing built,
while the art of healing, which is a potency, may be in the man
healed, but not in him qua healed. 'Potency' then means the source, in
general, of change or movement in another thing or in the same thing
qua other, and also (2) the source of a thing's being moved by another
thing or by itself qua other. For in virtue of that principle, in
virtue of which a patient suffers anything, we call it 'capable' of
suffering; and this we do sometimes if it suffers anything at all,
sometimes not in respect of everything it suffers, but only if it
suffers a change for the better--(3) The capacity of performing this
well or according to intention; for sometimes we say of those who
merely can walk or speak but not well or not as they intend, that they
cannot speak or walk. So too (4) in the case of passivity--(5) The
states in virtue of which things are absolutely impassive or
unchangeable, or not easily changed for the worse, are called
potencies; for things are broken and crushed and bent and in general
destroyed not by having a potency but by not having one and by lacking
something, and things are impassive with respect to such processes
if they are scarcely and slightly affected by them, because of a
'potency' and because they 'can' do something and are in some positive
state.

    'Potency' having this variety of meanings, so too the 'potent'
or 'capable' in one sense will mean that which can begin a movement
(or a change in general, for even that which can bring things to
rest is a 'potent' thing) in another thing or in itself qua other; and
in one sense that over which something else has such a potency; and in
one sense that which has a potency of changing into something, whether
for the worse or for the better (for even that which perishes is
thought to be 'capable' of perishing, for it would not have perished
if it had not been capable of it; but, as a matter of fact, it has a
certain disposition and cause and principle which fits it to suffer
this; sometimes it is thought to be of this sort because it has
something, sometimes because it is deprived of something; but if
privation is in a sense 'having' or 'habit', everything will be
capable by having something, so that things are capable both by having
a positive habit and principle, and by having the privation of this,
if it is possible to have a privation; and if privation is not in a
sense 'habit', 'capable' is used in two distinct senses); and a
thing is capable in another sense because neither any other thing, nor
itself qua other, has a potency or principle which can destroy it.
Again, all of these are capable either merely because the thing
might chance to happen or not to happen, or because it might do so
well. This sort of potency is found even in lifeless things, e.g. in
instruments; for we say one lyre can speak, and another cannot speak
at all, if it has not a good tone.

    Incapacity is privation of capacity-i.e. of such a principle as
has been described either in general or in the case of something
that would naturally have the capacity, or even at the time when it
would naturally already have it; for the senses in which we should
call a boy and a man and a eunuch 'incapable of begetting' are
distinct.-Again, to either kind of capacity there is an opposite
incapacity-both to that which only can produce movement and to that
which can produce it well.

    Some things, then, are called adunata in virtue of this kind of
incapacity, while others are so in another sense; i.e. both dunaton
and adunaton are used as follows. The impossible is that of which
the contrary is of necessity true, e.g. that the diagonal of a
square is commensurate with the side is impossible, because such a
statement is a falsity of which the contrary is not only true but also
necessary; that it is commensurate, then, is not only false but also
of necessity false. The contrary of this, the possible, is found
when it is not necessary that the contrary is false, e.g. that a man
should be seated is possible; for that he is not seated is not of
necessity false. The possible, then, in one sense, as has been said,
means that which is not of necessity false; in one, that which is
true; in one, that which may be true.-A 'potency' or 'power' in
geometry is so called by a change of meaning.-These senses of
'capable' or 'possible' involve no reference to potency. But the
senses which involve a reference to potency all refer to the primary
kind of potency; and this is a source of change in another thing or in
the same thing qua other. For other things are called 'capable',
some because something else has such a potency over them, some because
it has not, some because it has it in a particular way. The same is
true of the things that are incapable. Therefore the proper definition
of the primary kind of potency will be 'a source of change in
another thing or in the same thing qua other'.

                                  13

    'Quantum' means that which is divisible into two or more
constituent parts of which each is by nature a 'one' and a 'this'. A
quantum is a plurality if it is numerable, a magnitude if it is a
measurable. 'Plurality' means that which is divisible potentially into
non-continuous parts, 'magnitude' that which is divisible into
continuous parts; of magnitude, that which is continuous in one
dimension is length; in two breadth, in three depth. Of these, limited
plurality is number, limited length is a line, breadth a surface,
depth a solid.

    Again, some things are called quanta in virtue of their own
nature, others incidentally; e.g. the line is a quantum by its own
nature, the musical is one incidentally. Of the things that are quanta
by their own nature some are so as substances, e.g. the line is a
quantum (for 'a certain kind of quantum' is present in the
definition which states what it is), and others are modifications
and states of this kind of substance, e.g. much and little, long and
short, broad and narrow, deep and shallow, heavy and light, and all
other such attributes. And also great and small, and greater and
smaller, both in themselves and when taken relatively to each other,
are by their own nature attributes of what is quantitative; but
these names are transferred to other things also. Of things that are
quanta incidentally, some are so called in the sense in which it was
said that the musical and the white were quanta, viz. because that
to which musicalness and whiteness belong is a quantum, and some are
quanta in the way in which movement and time are so; for these also
are called quanta of a sort and continuous because the things of which
these are attributes are divisible. I mean not that which is moved,
but the space through which it is moved; for because that is a quantum
movement also is a quantum, and because this is a quantum time is one.

                                  14

    'Quality' means (1) the differentia of the essence, e.g. man is an
animal of a certain quality because he is two-footed, and the horse is
so because it is four-footed; and a circle is a figure of particular
quality because it is without angles,-which shows that the essential
differentia is a quality.-This, then, is one meaning of quality-the
differentia of the essence, but (2) there is another sense in which it
applies to the unmovable objects of mathematics, the sense in which
the numbers have a certain quality, e.g. the composite numbers which
are not in one dimension only, but of which the plane and the solid
are copies (these are those which have two or three factors); and in
general that which exists in the essence of numbers besides quantity
is quality; for the essence of each is what it is once, e.g. that of
is not what it is twice or thrice, but what it is once; for 6 is
once 6.

    (3) All the modifications of substances that move (e.g. heat and
cold, whiteness and blackness, heaviness and lightness, and the others
of the sort) in virtue of which, when they change, bodies are said
to alter. (4) Quality in respect of virtue and vice, and in general,
of evil and good.

    Quality, then, seems to have practically two meanings, and one
of these is the more proper. The primary quality is the differentia of
the essence, and of this the quality in numbers is a part; for it is a
differentia of essences, but either not of things that move or not
of them qua moving. Secondly, there are the modifications of things
that move, qua moving, and the differentiae of movements. Virtue and
vice fall among these modifications; for they indicate differentiae of
the movement or activity, according to which the things in motion
act or are acted on well or badly; for that which can be moved or
act in one way is good, and that which can do so in another--the
contrary--way is vicious. Good and evil indicate quality especially in
living things, and among these especially in those which have purpose.

                                  15

    Things are 'relative' (1) as double to half, and treble to a
third, and in general that which contains something else many times to
that which is contained many times in something else, and that which
exceeds to that which is exceeded; (2) as that which can heat to
that which can be heated, and that which can cut to that which can
be cut, and in general the active to the passive; (3) as the
measurable to the measure, and the knowable to knowledge, and the
perceptible to perception.

    (1) Relative terms of the first kind are numerically related
either indefinitely or definitely, to numbers themselves or to 1. E.g.
the double is in a definite numerical relation to 1, and that which is
'many times as great' is in a numerical, but not a definite,
relation to 1, i.e. not in this or in that numerical relation to it;
the relation of that which is half as big again as something else to
that something is a definite numerical relation to a number; that
which is n+I/n times something else is in an indefinite relation to
that something, as that which is 'many times as great' is in an
indefinite relation to 1; the relation of that which exceeds to that
which is exceeded is numerically quite indefinite; for number is
always commensurate, and 'number' is not predicated of that which is
not commensurate, but that which exceeds is, in relation to that which
is exceeded, so much and something more; and this something is
indefinite; for it can, indifferently, be either equal or not equal to
that which is exceeded.-All these relations, then, are numerically
expressed and are determinations of number, and so in another way
are the equal and the like and the same. For all refer to unity. Those
things are the same whose substance is one; those are like whose
quality is one; those are equal whose quantity is one; and 1 is the
beginning and measure of number, so that all these relations imply
number, though not in the same way.

    (2) Things that are active or passive imply an active or a passive
potency and the actualizations of the potencies; e.g. that which is
capable of heating is related to that which is capable of being
heated, because it can heat it, and, again, that which heats is
related to that which is heated and that which cuts to that which is
cut, in the sense that they actually do these things. But numerical
relations are not actualized except in the sense which has been
elsewhere stated; actualizations in the sense of movement they have
not. Of relations which imply potency some further imply particular
periods of time, e.g. that which has made is relative to that which
has been made, and that which will make to that which will be made.
For it is in this way that a father is called the father of his son;
for the one has acted and the other has been acted on in a certain
way. Further, some relative terms imply privation of potency, i.e.
'incapable' and terms of this sort, e.g. 'invisible'.

    Relative terms which imply number or potency, therefore, are all
relative because their very essence includes in its nature a reference
to something else, not because something else involves a reference
to it; but (3) that which is measurable or knowable or thinkable is
called relative because something else involves a reference to it. For
'that which is thinkable' implies that the thought of it is
possible, but the thought is not relative to 'that of which it is
the thought'; for we should then have said the same thing twice.
Similarly sight is the sight of something, not 'of that of which it is
the sight' (though of course it is true to say this); in fact it is
relative to colour or to something else of the sort. But according
to the other way of speaking the same thing would be said
twice,-'the sight is of that of which it is.'

    Things that are by their own nature called relative are called
so sometimes in these senses, sometimes if the classes that include
them are of this sort; e.g. medicine is a relative term because its
genus, science, is thought to be a relative term. Further, there are
the properties in virtue of which the things that have them are called
relative, e.g. equality is relative because the equal is, and likeness
because the like is. Other things are relative by accident; e.g. a man
is relative because he happens to be double of something and double is
a relative term; or the white is relative, if the same thing happens
to be double and white.

                                  16

    What is called 'complete' is (1) that outside which it is not
possible to find any, even one, of its parts; e.g. the complete time
of each thing is that outside which it is not possible to find any
time which is a part proper to it.-(2) That which in respect of
excellence and goodness cannot be excelled in its kind; e.g. we have a
complete doctor or a complete flute-player, when they lack nothing
in respect of the form of their proper excellence. And thus,
transferring the word to bad things, we speak of a complete
scandal-monger and a complete thief; indeed we even call them good,
i.e. a good thief and a good scandal-monger. And excellence is a
completion; for each thing is complete and every substance is
complete, when in respect of the form of its proper excellence it
lacks no part of its natural magnitude.-(3) The things which have
attained their end, this being good, are called complete; for things
are complete in virtue of having attained their end. Therefore,
since the end is something ultimate, we transfer the word to bad
things and say a thing has been completely spoilt, and completely
destroyed, when it in no wise falls short of destruction and
badness, but is at its last point. This is why death, too, is by a
figure of speech called the end, because both are last things. But the
ultimate purpose is also an end.-Things, then, that are called
complete in virtue of their own nature are so called in all these
senses, some because in respect of goodness they lack nothing and
cannot be excelled and no part proper to them can be found outside
them, others in general because they cannot be exceeded in their
several classes and no part proper to them is outside them; the others
presuppose these first two kinds, and are called complete because they
either make or have something of the sort or are adapted to it or in
some way or other involve a reference to the things that are called
complete in the primary sense.

                                  17

    'Limit' means (1) the last point of each thing, i.e. the first
point beyond which it is not possible to find any part, and the
first point within which every part is; (2) the form, whatever it
may be, of a spatial magnitude or of a thing that has magnitude; (3)
the end of each thing (and of this nature is that towards which the
movement and the action are, not that from which they are-though
sometimes it is both, that from which and that to which the movement
is, i.e. the final cause); (4) the substance of each thing, and the
essence of each; for this is the limit of knowledge; and if of
knowledge, of the object also. Evidently, therefore, 'limit' has as
many senses as 'beginning', and yet more; for the beginning is a
limit, but not every limit is a beginning.

                                  18

    'That in virtue of which' has several meanings:-(1) the form or
substance of each thing, e.g. that in virtue of which a man is good is
the good itself, (2) the proximate subject in which it is the nature
of an attribute to be found, e.g. colour in a surface. 'That in virtue
of which', then, in the primary sense is the form, and in a
secondary sense the matter of each thing and the proximate
substratum of each.-In general 'that in virtue of which' will found in
the same number of senses as 'cause'; for we say indifferently (3)
in virtue of what has he come?' or 'for what end has he come?'; and
(4) in virtue of what has he inferred wrongly, or inferred?' or
'what is the cause of the inference, or of the wrong
inference?'-Further (5) Kath' d is used in reference to position, e.g.
'at which he stands' or 'along which he walks; for all such phrases
indicate place and position.

    Therefore 'in virtue of itself' must likewise have several
meanings. The following belong to a thing in virtue of itself:-(1) the
essence of each thing, e.g. Callias is in virtue of himself Callias
and what it was to be Callias;-(2) whatever is present in the
'what', e.g. Callias is in virtue of himself an animal. For 'animal'
is present in his definition; Callias is a particular animal.-(3)
Whatever attribute a thing receives in itself directly or in one of
its parts; e.g. a surface is white in virtue of itself, and a man is
alive in virtue of himself; for the soul, in which life directly
resides, is a part of the man.-(4) That which has no cause other
than itself; man has more than one cause--animal, two-footed--but
yet man is man in virtue of himself.-(5) Whatever attributes belong to
a thing alone, and in so far as they belong to it merely by virtue
of itself considered apart by itself.

                                  19

    'Disposition' means the arrangement of that which has parts, in
respect either of place or of potency or of kind; for there must be
a certain position, as even the word 'disposition' shows.

                                  20

    'Having' means (1) a kind of activity of the haver and of what
he has-something like an action or movement. For when one thing
makes and one is made, between them there is a making; so too
between him who has a garment and the garment which he has there is
a having. This sort of having, then, evidently we cannot have; for the
process will go on to infinity, if it is to be possible to have the
having of what we have.-(2) 'Having' or 'habit' means a disposition
according to which that which is disposed is either well or ill
disposed, and either in itself or with reference to something else;
e.g. health is a 'habit'; for it is such a disposition.-(3) We speak
of a 'habit' if there is a portion of such a disposition; and so
even the excellence of the parts is a 'habit' of the whole thing.

                                  21

    'Affection' means (1) a quality in respect of which a thing can be
altered, e.g. white and black, sweet and bitter, heaviness and
lightness, and all others of the kind.-(2) The actualization of
these-the already accomplished alterations.-(3) Especially,
injurious alterations and movements, and, above all painful
injuries.-(4) Misfortunes and painful experiences when on a large
scale are called affections.

                                  22

    We speak of 'privation' (1) if something has not one of the
attributes which a thing might naturally have, even if this thing
itself would not naturally have it; e.g. a plant is said to be
'deprived' of eyes.-(2) If, though either the thing itself or its
genus would naturally have an attribute, it has it not; e.g. a blind
man and a mole are in different senses 'deprived' of sight; the latter
in contrast with its genus, the former in contrast with his own normal
nature.-(3) If, though it would naturally have the attribute, and when
it would naturally have it, it has it not; for blindness is a
privation, but one is not 'blind' at any and every age, but only if
one has not sight at the age at which one would naturally have it.
Similarly a thing is called blind if it has not sight in the medium in
which, and in respect of the organ in respect of which, and with
reference to the object with reference to which, and in the
circumstances in which, it would naturally have it.-(4) The violent
taking away of anything is called privation.

    Indeed there are just as many kinds of privations as there are
of words with negative prefixes; for a thing is called unequal because
it has not equality though it would naturally have it, and invisible
either because it has no colour at all or because it has a poor
colour, and apodous either because it has no feet at all or because it
has imperfect feet. Again, a privative term may be used because the
thing has little of the attribute (and this means having it in a sense
imperfectly), e.g. 'kernel-less'; or because it has it not easily or
not well (e.g. we call a thing uncuttable not only if it cannot be cut
but also if it cannot be cut easily or well); or because it has not
the attribute at all; for it is not the one-eyed man but he who is
sightless in both eyes that is called blind. This is why not every man
is 'good' or 'bad', 'just' or 'unjust', but there is also an
intermediate state.

                                  23

    To 'have' or 'hold' means many things:-(1) to treat a thing
according to one's own nature or according to one's own impulse; so
that fever is said to have a man, and tyrants to have their cities,
and people to have the clothes they wear.-(2) That in which a thing is
present as in something receptive of it is said to have the thing;
e.g. the bronze has the form of the statue, and the body has the
disease.-(3) As that which contains holds the things contained; for
a thing is said to be held by that in which it is as in a container;
e.g. we say that the vessel holds the liquid and the city holds men
and the ship sailors; and so too that the whole holds the parts.-(4)
That which hinders a thing from moving or acting according to its
own impulse is said to hold it, as pillars hold the incumbent weights,
and as the poets make Atlas hold the heavens, implying that
otherwise they would collapse on the earth, as some of the natural
philosophers also say. In this way also that which holds things
together is said to hold the things it holds together, since they
would otherwise separate, each according to its own impulse.

    'Being in something' has similar and corresponding meanings to
'holding' or 'having'.

                                  24

    'To come from something' means (1) to come from something as
from matter, and this in two senses, either in respect of the
highest genus or in respect of the lowest species; e.g. in a sense all
things that can be melted come from water, but in a sense the statue
comes from bronze.-(2) As from the first moving principle; e.g.
'what did the fight come from?' From abusive language, because this
was the origin of the fight.-(3) From the compound of matter and
shape, as the parts come from the whole, and the verse from the Iliad,
and the stones from the house; (in every such case the whole is a
compound of matter and shape,) for the shape is the end, and only that
which attains an end is complete.-(4) As the form from its part,
e.g. man from 'two-footed'and syllable from 'letter'; for this is a
different sense from that in which the statue comes from bronze; for
the composite substance comes from the sensible matter, but the form
also comes from the matter of the form.-Some things, then, are said to
come from something else in these senses; but (5) others are so
described if one of these senses is applicable to a part of that other
thing; e.g. the child comes from its father and mother, and plants
come from the earth, because they come from a part of those
things.-(6) It means coming after a thing in time, e.g. night comes
from day and storm from fine weather, because the one comes after
the other. Of these things some are so described because they admit of
change into one another, as in the cases now mentioned; some merely
because they are successive in time, e.g. the voyage took place 'from'
the equinox, because it took place after the equinox, and the festival
of the Thargelia comes 'from' the Dionysia, because after the
Dionysia.

                                  25

    'Part' means (1) (a) that into which a quantum can in any way be
divided; for that which is taken from a quantum qua quantum is
always called a part of it, e.g. two is called in a sense a part of
three. It means (b), of the parts in the first sense, only those which
measure the whole; this is why two, though in one sense it is, in
another is not, called a part of three.-(2) The elements into which
a kind might be divided apart from the quantity are also called
parts of it; for which reason we say the species are parts of the
genus.-(3) The elements into which a whole is divided, or of which
it consists-the 'whole' meaning either the form or that which has
the form; e.g. of the bronze sphere or of the bronze cube both the
bronze-i.e. the matter in which the form is-and the characteristic
angle are parts.-(4) The elements in the definition which explains a
thing are also parts of the whole; this is why the genus is called a
part of the species, though in another sense the species is part of
the genus.

                                  26

    'A whole' means (1) that from which is absent none of the parts of
which it is said to be naturally a whole, and (2) that which so
contains the things it contains that they form a unity; and this in
two senses-either as being each severally one single thing, or as
making up the unity between them. For (a) that which is true of a
whole class and is said to hold good as a whole (which implies that it
is a kind whole) is true of a whole in the sense that it contains many
things by being predicated of each, and by all of them, e.g. man,
horse, god, being severally one single thing, because all are living
things. But (b) the continuous and limited is a whole, when it is a
unity consisting of several parts, especially if they are present only
potentially, but, failing this, even if they are present actually.
Of these things themselves, those which are so by nature are wholes in
a higher degree than those which are so by art, as we said in the case
of unity also, wholeness being in fact a sort of oneness.

    Again (3) of quanta that have a beginning and a middle and an end,
those to which the position does not make a difference are called
totals, and those to which it does, wholes. Those which admit of
both descriptions are both wholes and totals. These are the things
whose nature remains the same after transposition, but whose form does
not, e.g. wax or a coat; they are called both wholes and totals; for
they have both characteristics. Water and all liquids and number are
called totals, but 'the whole number' or 'the whole water' one does
not speak of, except by an extension of meaning. To things, to which
qua one the term 'total' is applied, the term 'all' is applied when
they are treated as separate; 'this total number,' 'all these units.'

                                  27

    It is not any chance quantitative thing that can be said to be
'mutilated'; it must be a whole as well as divisible. For not only
is two not 'mutilated' if one of the two ones is taken away (for the
part removed by mutilation is never equal to the remainder), but in
general no number is thus mutilated; for it is also necessary that the
essence remain; if a cup is mutilated, it must still be a cup; but the
number is no longer the same. Further, even if things consist of
unlike parts, not even these things can all be said to be mutilated,
for in a sense a number has unlike parts (e.g. two and three) as
well as like; but in general of the things to which their position
makes no difference, e.g. water or fire, none can be mutilated; to
be mutilated, things must be such as in virtue of their essence have a
certain position. Again, they must be continuous; for a musical
scale consists of unlike parts and has position, but cannot become
mutilated. Besides, not even the things that are wholes are
mutilated by the privation of any part. For the parts removed must
be neither those which determine the essence nor any chance parts,
irrespective of their position; e.g. a cup is not mutilated if it is
bored through, but only if the handle or a projecting part is removed,
and a man is mutilated not if the flesh or the spleen is removed,
but if an extremity is, and that not every extremity but one which
when completely removed cannot grow again. Therefore baldness is not a
mutilation.

                                  28

    The term 'race' or 'genus' is used (1) if generation of things
which have the same form is continuous, e.g. 'while the race of men
lasts' means 'while the generation of them goes on
continuously'.-(2) It is used with reference to that which first
brought things into existence; for it is thus that some are called
Hellenes by race and others Ionians, because the former proceed from
Hellen and the latter from Ion as their first begetter. And the word
is used in reference to the begetter more than to the matter, though
people also get a race-name from the female, e.g. 'the descendants
of Pyrrha'.-(3) There is genus in the sense in which 'plane' is the
genus of plane figures and solid' of solids; for each of the figures
is in the one case a plane of such and such a kind, and in the other a
solid of such and such a kind; and this is what underlies the
differentiae. Again (4) in definitions the first constituent
element, which is included in the 'what', is the genus, whose
differentiae the qualities are said to be 'Genus' then is used in
all these ways, (1) in reference to continuous generation of the
same kind, (2) in reference to the first mover which is of the same
kind as the things it moves, (3) as matter; for that to which the
differentia or quality belongs is the substratum, which we call
matter.

    Those things are said to be 'other in genus' whose proximate
substratum is different, and which are not analysed the one into the
other nor both into the same thing (e.g. form and matter are different
in genus); and things which belong to different categories of being
(for some of the things that are said to 'be' signify essence,
others a quality, others the other categories we have before
distinguished); these also are not analysed either into one another or
into some one thing.

                                  29

    'The false' means (1) that which is false as a thing, and that (a)
because it is not put together or cannot be put together, e.g. 'that
the diagonal of a square is commensurate with the side' or 'that you
are sitting'; for one of these is false always, and the other
sometimes; it is in these two senses that they are non-existent. (b)
There are things which exist, but whose nature it is to appear
either not to be such as they are or to be things that do not exist,
e.g. a sketch or a dream; for these are something, but are not the
things the appearance of which they produce in us. We call things
false in this way, then,-either because they themselves do not
exist, or because the appearance which results from them is that of
something that does not exist.

    (2) A false account is the account of non-existent objects, in
so far as it is false. Hence every account is false when applied to
something other than that of which it is true; e.g. the account of a
circle is false when applied to a triangle. In a sense there is one
account of each thing, i.e. the account of its essence, but in a sense
there are many, since the thing itself and the thing itself with an
attribute are in a sense the same, e.g. Socrates and musical
Socrates (a false account is not the account of anything, except in
a qualified sense). Hence Antisthenes was too simple-minded when he
claimed that nothing could be described except by the account proper
to it,-one predicate to one subject; from which the conclusion used to
be drawn that there could be no contradiction, and almost that there
could be no error. But it is possible to describe each thing not
only by the account of itself, but also by that of something else.
This may be done altogether falsely indeed, but there is also a way in
which it may be done truly; e.g. eight may be described as a double
number by the use of the definition of two.

    These things, then, are called false in these senses, but (3) a
false man is one who is ready at and fond of such accounts, not for
any other reason but for their own sake, and one who is good at
impressing such accounts on other people, just as we say things are
which produce a false appearance. This is why the proof in the Hippias
that the same man is false and true is misleading. For it assumes that
he is false who can deceive (i.e. the man who knows and is wise);
and further that he who is willingly bad is better. This is a false
result of induction-for a man who limps willingly is better than one
who does so unwillingly-by 'limping' Plato means 'mimicking a limp',
for if the man were lame willingly, he would presumably be worse in
this case as in the corresponding case of moral character.

                                  30

    'Accident' means (1) that which attaches to something and can be
truly asserted, but neither of necessity nor usually, e.g. if some one
in digging a hole for a plant has found treasure. This-the finding
of treasure-is for the man who dug the hole an accident; for neither
does the one come of necessity from the other or after the other, nor,
if a man plants, does he usually find treasure. And a musical man
might be pale; but since this does not happen of necessity nor
usually, we call it an accident. Therefore since there are
attributes and they attach to subjects, and some of them attach to
these only in a particular place and at a particular time, whatever
attaches to a subject, but not because it was this subject, or the
time this time, or the place this place, will be an accident.
Therefore, too, there is no definite cause for an accident, but a
chance cause, i.e. an indefinite one. Going to Aegina was an
accident for a man, if he went not in order to get there, but
because he was carried out of his way by a storm or captured by
pirates. The accident has happened or exists,-not in virtue of the
subject's nature, however, but of something else; for the storm was
the cause of his coming to a place for which he was not sailing, and
this was Aegina.

    'Accident' has also (2) another meaning, i.e. all that attaches to
each thing in virtue of itself but is not in its essence, as having
its angles equal to two right angles attaches to the triangle. And
accidents of this sort may be eternal, but no accident of the other
sort is. This is explained elsewhere.

                                Book VI

                                   1

    WE are seeking the principles and the causes of the things that
are, and obviously of them qua being. For, while there is a cause of
health and of good condition, and the objects of mathematics have
first principles and elements and causes, and in general every science
which is ratiocinative or at all involves reasoning deals with
causes and principles, more or less precise, all these sciences mark
off some particular being-some genus, and inquire into this, but not
into being simply nor qua being, nor do they offer any discussion of
the essence of the things of which they treat; but starting from the
essence-some making it plain to the senses, others assuming it as a
hypothesis-they then demonstrate, more or less cogently, the essential
attributes of the genus with which they deal. It is obvious,
therefore, that such an induction yields no demonstration of substance
or of the essence, but some other way of exhibiting it. And
similarly the sciences omit the question whether the genus with
which they deal exists or does not exist, because it belongs to the
same kind of thinking to show what it is and that it is.

    And since natural science, like other sciences, is in fact about
one class of being, i.e. to that sort of substance which has the
principle of its movement and rest present in itself, evidently it
is neither practical nor productive. For in the case of things made
the principle is in the maker-it is either reason or art or some
faculty, while in the case of things done it is in the doer-viz. will,
for that which is done and that which is willed are the same.
Therefore, if all thought is either practical or productive or
theoretical, physics must be a theoretical science, but it will
theorize about such being as admits of being moved, and about
substance-as-defined for the most part only as not separable from
matter. Now, we must not fail to notice the mode of being of the
essence and of its definition, for, without this, inquiry is but idle.
Of things defined, i.e. of 'whats', some are like 'snub', and some
like 'concave'. And these differ because 'snub' is bound up with
matter (for what is snub is a concave nose), while concavity is
independent of perceptible matter. If then all natural things are a
analogous to the snub in their nature; e.g. nose, eye, face, flesh,
bone, and, in general, animal; leaf, root, bark, and, in general,
plant (for none of these can be defined without reference to
movement-they always have matter), it is clear how we must seek and
define the 'what' in the case of natural objects, and also that it
belongs to the student of nature to study even soul in a certain
sense, i.e. so much of it as is not independent of matter.

    That physics, then, is a theoretical science, is plain from
these considerations. Mathematics also, however, is theoretical; but
whether its objects are immovable and separable from matter, is not at
present clear; still, it is clear that some mathematical theorems
consider them qua immovable and qua separable from matter. But if
there is something which is eternal and immovable and separable,
clearly the knowledge of it belongs to a theoretical science,-not,
however, to physics (for physics deals with certain movable things)
nor to mathematics, but to a science prior to both. For physics
deals with things which exist separately but are not immovable, and
some parts of mathematics deal with things which are immovable but
presumably do not exist separately, but as embodied in matter; while
the first science deals with things which both exist separately and
are immovable. Now all causes must be eternal, but especially these;
for they are the causes that operate on so much of the divine as
appears to us. There must, then, be three theoretical philosophies,
mathematics, physics, and what we may call theology, since it is
obvious that if the divine is present anywhere, it is present in
things of this sort. And the highest science must deal with the
highest genus. Thus, while the theoretical sciences are more to be
desired than the other sciences, this is more to be desired than the
other theoretical sciences. For one might raise the question whether
first philosophy is universal, or deals with one genus, i.e. some
one kind of being; for not even the mathematical sciences are all
alike in this respect,-geometry and astronomy deal with a certain
particular kind of thing, while universal mathematics applies alike to
all. We answer that if there is no substance other than those which
are formed by nature, natural science will be the first science; but
if there is an immovable substance, the science of this must be
prior and must be first philosophy, and universal in this way, because
it is first. And it will belong to this to consider being qua
being-both what it is and the attributes which belong to it qua being.

                                   2

    But since the unqualified term 'being' has several meanings, of
which one was seen' to be the accidental, and another the true
('non-being' being the false), while besides these there are the
figures of predication (e.g. the 'what', quality, quantity, place,
time, and any similar meanings which 'being' may have), and again
besides all these there is that which 'is' potentially or
actually:-since 'being' has many meanings, we must say regarding the
accidental, that there can be no scientific treatment of it. This is
confirmed by the fact that no science practical, productive, or
theoretical troubles itself about it. For on the one hand he who
produces a house does not produce all the attributes that come into
being along with the house; for these are innumerable; the house
that has been made may quite well be pleasant for some people, hurtful
for some, and useful to others, and different-to put it shortly from
all things that are; and the science of building does not aim at
producing any of these attributes. And in the same way the geometer
does not consider the attributes which attach thus to figures, nor
whether 'triangle' is different from 'triangle whose angles are
equal to two right angles'.-And this happens naturally enough; for the
accidental is practically a mere name. And so Plato was in a sense not
wrong in ranking sophistic as dealing with that which is not. For
the arguments of the sophists deal, we may say, above all with the
accidental; e.g. the question whether 'musical' and 'lettered' are
different or the same, and whether 'musical Coriscus' and 'Coriscus'
are the same, and whether 'everything which is, but is not eternal,
has come to be', with the paradoxical conclusion that if one who was
musical has come to be lettered, he must also have been lettered and
have come to be musical, and all the other arguments of this sort; the
accidental is obviously akin to non-being. And this is clear also from
arguments such as the following: things which are in another sense
come into being and pass out of being by a process, but things which
are accidentally do not. But still we must, as far as we can, say
further, regarding the accidental, what its nature is and from what
cause it proceeds; for it will perhaps at the same time become clear
why there is no science of it.

    Since, among things which are, some are always in the same state
and are of necessity (not necessity in the sense of compulsion but
that which we assert of things because they cannot be otherwise),
and some are not of necessity nor always, but for the most part,
this is the principle and this the cause of the existence of the
accidental; for that which is neither always nor for the most part, we
call accidental. For instance, if in the dog-days there is wintry
and cold weather, we say this is an accident, but not if there is
sultry heat, because the latter is always or for the most part so, but
not the former. And it is an accident that a man is pale (for this
is neither always nor for the most part so), but it is not by accident
that he is an animal. And that the builder produces health is an
accident, because it is the nature not of the builder but of the
doctor to do this,-but the builder happened to be a doctor. Again, a
confectioner, aiming at giving pleasure, may make something wholesome,
but not in virtue of the confectioner's art; and therefore we say
'it was an accident', and while there is a sense in which he makes it,
in the unqualified sense he does not. For to other things answer
faculties productive of them, but to accidental results there
corresponds no determinate art nor faculty; for of things which are or
come to be by accident, the cause also is accidental. Therefore, since
not all things either are or come to be of necessity and always,
but, the majority of things are for the most part, the accidental must
exist; for instance a pale man is not always nor for the most part
musical, but since this sometimes happens, it must be accidental (if
not, everything will be of necessity). The matter, therefore, which is
capable of being otherwise than as it usually is, must be the cause of
the accidental. And we must take as our starting-point the question
whether there is nothing that is neither always nor for the most part.
Surely this is impossible. There is, then, besides these something
which is fortuitous and accidental. But while the usual exists, can
nothing be said to be always, or are there eternal things? This must
be considered later,' but that there is no science of the accidental
is obvious; for all science is either of that which is always or of
that which is for the most part. (For how else is one to learn or to
teach another? The thing must be determined as occurring either always
or for the most part, e.g. that honey-water is useful for a patient in
a fever is true for the most part.) But that which is contrary to
the usual law science will be unable to state, i.e. when the thing
does not happen, e.g.'on the day of new moon'; for even that which
happens on the day of new moon happens then either always or for the
most part; but the accidental is contrary to such laws. We have
stated, then, what the accidental is, and from what cause it arises,
and that there is no science which deals with it.

                                   3

    That there are principles and causes which are generable and
destructible without ever being in course of being generated or
destroyed, is obvious. For otherwise all things will be of
necessity, since that which is being generated or destroyed must
have a cause which is not accidentally its cause. Will A exist or not?
It will if B happens; and if not, not. And B will exist if C
happens. And thus if time is constantly subtracted from a limited
extent of time, one will obviously come to the present. This man,
then, will die by violence, if he goes out; and he will do this if
he gets thirsty; and he will get thirsty if something else happens;
and thus we shall come to that which is now present, or to some past
event. For instance, he will go out if he gets thirsty; and he will
get thirsty if he is eating pungent food; and this is either the
case or not; so that he will of necessity die, or of necessity not
die. And similarly if one jumps over to past events, the same
account will hold good; for this-I mean the past condition-is
already present in something. Everything, therefore, that will be,
will be of necessity; e.g. it is necessary that he who lives shall one
day die; for already some condition has come into existence, e.g.
the presence of contraries in the same body. But whether he is to
die by disease or by violence is not yet determined, but depends on
the happening of something else. Clearly then the process goes back to
a certain starting-point, but this no longer points to something
further. This then will be the starting-point for the fortuitous,
and will have nothing else as cause of its coming to be. But to what
sort of starting-point and what sort of cause we thus refer the
fortuitous-whether to matter or to the purpose or to the motive power,
must be carefully considered.

                                   4

    Let us dismiss accidental being; for we have sufficiently
determined its nature. But since that which is in the sense of being
true, or is not in the sense of being false, depends on combination
and separation, and truth and falsity together depend on the
allocation of a pair of contradictory judgements (for the true
judgement affirms where the subject and predicate really are combined,
and denies where they are separated, while the false judgement has the
opposite of this allocation; it is another question, how it happens
that we think things together or apart; by 'together' and 'apart' I
mean thinking them so that there is no succession in the thoughts
but they become a unity); for falsity and truth are not in things-it
is not as if the good were true, and the bad were in itself
false-but in thought; while with regard to simple concepts and 'whats'
falsity and truth do not exist even in thought--this being so, we must
consider later what has to be discussed with regard to that which is
or is not in this sense. But since the combination and the
separation are in thought and not in the things, and that which is
in this sense is a different sort of 'being' from the things that
are in the full sense (for the thought attaches or removes either
the subject's 'what' or its having a certain quality or quantity or
something else), that which is accidentally and that which is in the
sense of being true must be dismissed. For the cause of the former
is indeterminate, and that of the latter is some affection of the
thought, and both are related to the remaining genus of being, and
do not indicate the existence of any separate class of being.
Therefore let these be dismissed, and let us consider the causes and
the principles of being itself, qua being. (It was clear in our
discussion of the various meanings of terms, that 'being' has
several meanings.)

                                Book VII

                                   1

    THERE are several senses in which a thing may be said to 'be',
as we pointed out previously in our book on the various senses of
words;' for in one sense the 'being' meant is 'what a thing is' or a
'this', and in another sense it means a quality or quantity or one
of the other things that are predicated as these are. While 'being'
has all these senses, obviously that which 'is' primarily is the
'what', which indicates the substance of the thing. For when we say of
what quality a thing is, we say that it is good or bad, not that it is
three cubits long or that it is a man; but when we say what it is,
we do not say 'white' or 'hot' or 'three cubits long', but 'a man'
or 'a 'god'. And all other things are said to be because they are,
some of them, quantities of that which is in this primary sense,
others qualities of it, others affections of it, and others some other
determination of it. And so one might even raise the question
whether the words 'to walk', 'to be healthy', 'to sit' imply that each
of these things is existent, and similarly in any other case of this
sort; for none of them is either self-subsistent or capable of being
separated from substance, but rather, if anything, it is that which
walks or sits or is healthy that is an existent thing. Now these are
seen to be more real because there is something definite which
underlies them (i.e. the substance or individual), which is implied in
such a predicate; for we never use the word 'good' or 'sitting'
without implying this. Clearly then it is in virtue of this category
that each of the others also is. Therefore that which is primarily,
i.e. not in a qualified sense but without qualification, must be
substance.

    Now there are several senses in which a thing is said to be first;
yet substance is first in every sense-(1) in definition, (2) in
order of knowledge, (3) in time. For (3) of the other categories
none can exist independently, but only substance. And (1) in
definition also this is first; for in the definition of each term
the definition of its substance must be present. And (2) we think we
know each thing most fully, when we know what it is, e.g. what man
is or what fire is, rather than when we know its quality, its
quantity, or its place; since we know each of these predicates also,
only when we know what the quantity or the quality is.

    And indeed the question which was raised of old and is raised
now and always, and is always the subject of doubt, viz. what being
is, is just the question, what is substance? For it is this that
some assert to be one, others more than one, and that some assert to
be limited in number, others unlimited. And so we also must consider
chiefly and primarily and almost exclusively what that is which is
in this sense.

                                   2

    Substance is thought to belong most obviously to bodies; and so we
say that not only animals and plants and their parts are substances,
but also natural bodies such as fire and water and earth and
everything of the sort, and all things that are either parts of
these or composed of these (either of parts or of the whole bodies),
e.g. the physical universe and its parts, stars and moon and sun.
But whether these alone are substances, or there are also others, or
only some of these, or others as well, or none of these but only
some other things, are substances, must be considered. Some think
the limits of body, i.e. surface, line, point, and unit, are
substances, and more so than body or the solid.

    Further, some do not think there is anything substantial besides
sensible things, but others think there are eternal substances which
are more in number and more real; e.g. Plato posited two kinds of
substance-the Forms and objects of mathematics-as well as a third
kind, viz. the substance of sensible bodies. And Speusippus made still
more kinds of substance, beginning with the One, and assuming
principles for each kind of substance, one for numbers, another for
spatial magnitudes, and then another for the soul; and by going on
in this way he multiplies the kinds of substance. And some say Forms
and numbers have the same nature, and the other things come after
them-lines and planes-until we come to the substance of the material
universe and to sensible bodies.

    Regarding these matters, then, we must inquire which of the common
statements are right and which are not right, and what substances
there are, and whether there are or are not any besides sensible
substances, and how sensible substances exist, and whether there is
a substance capable of separate existence (and if so why and how) or
no such substance, apart from sensible substances; and we must first
sketch the nature of substance.

                                   3

    The word 'substance' is applied, if not in more senses, still at
least to four main objects; for both the essence and the universal and
the genus, are thought to be the substance of each thing, and fourthly
the substratum. Now the substratum is that of which everything else is
predicated, while it is itself not predicated of anything else. And so
we must first determine the nature of this; for that which underlies a
thing primarily is thought to be in the truest sense its substance.
And in one sense matter is said to be of the nature of substratum,
in another, shape, and in a third, the compound of these. (By the
matter I mean, for instance, the bronze, by the shape the pattern of
its form, and by the compound of these the statue, the concrete
whole.) Therefore if the form is prior to the matter and more real, it
will be prior also to the compound of both, for the same reason.

    We have now outlined the nature of substance, showing that it is
that which is not predicated of a stratum, but of which all else is
predicated. But we must not merely state the matter thus; for this
is not enough. The statement itself is obscure, and further, on this
view, matter becomes substance. For if this is not substance, it
baffles us to say what else is. When all else is stripped off
evidently nothing but matter remains. For while the rest are
affections, products, and potencies of bodies, length, breadth, and
depth are quantities and not substances (for a quantity is not a
substance), but the substance is rather that to which these belong
primarily. But when length and breadth and depth are taken away we see
nothing left unless there is something that is bounded by these; so
that to those who consider the question thus matter alone must seem to
be substance. By matter I mean that which in itself is neither a
particular thing nor of a certain quantity nor assigned to any other
of the categories by which being is determined. For there is something
of which each of these is predicated, whose being is different from
that of each of the predicates (for the predicates other than
substance are predicated of substance, while substance is predicated
of matter). Therefore the ultimate substratum is of itself neither a
particular thing nor of a particular quantity nor otherwise positively
characterized; nor yet is it the negations of these, for negations
also will belong to it only by accident.

    If we adopt this point of view, then, it follows that matter is
substance. But this is impossible; for both separability and
'thisness' are thought to belong chiefly to substance. And so form and
the compound of form and matter would be thought to be substance,
rather than matter. The substance compounded of both, i.e. of matter
and shape, may be dismissed; for it is posterior and its nature is
obvious. And matter also is in a sense manifest. But we must inquire
into the third kind of substance; for this is the most perplexing.

    Some of the sensible substances are generally admitted to be
substances, so that we must look first among these. For it is an
advantage to advance to that which is more knowable. For learning
proceeds for all in this way-through that which is less knowable by
nature to that which is more knowable; and just as in conduct our task
is to start from what is good for each and make what is without
qualification good good for each, so it is our task to start from what
is more knowable to oneself and make what is knowable by nature
knowable to oneself. Now what is knowable and primary for particular
sets of people is often knowable to a very small extent, and has
little or nothing of reality. But yet one must start from that which
is barely knowable but knowable to oneself, and try to know what is
knowable without qualification, passing, as has been said, by way of
those very things which one does know.

                                   4

    Since at the start we distinguished the various marks by which
we determine substance, and one of these was thought to be the
essence, we must investigate this. And first let us make some
linguistic remarks about it. The essence of each thing is what it is
said to be propter se. For being you is not being musical, since you
are not by your very nature musical. What, then, you are by your
very nature is your essence.

    Nor yet is the whole of this the essence of a thing; not that
which is propter se as white is to a surface, because being a
surface is not identical with being white. But again the combination
of both-'being a white surface'-is not the essence of surface, because
'surface' itself is added. The formula, therefore, in which the term
itself is not present but its meaning is expressed, this is the
formula of the essence of each thing. Therefore if to be a white
surface is to be a smooth surface, to be white and to be smooth are
one and the same.

    But since there are also compounds answering to the other
categories (for there is a substratum for each category, e.g. for
quality, quantity, time, place, and motion), we must inquire whether
there is a formula of the essence of each of them, i.e. whether to
these compounds also there belongs an essence, e.g. 'white man'. Let
the compound be denoted by 'cloak'. What is the essence of cloak? But,
it may be said, this also is not a propter se expression. We reply
that there are just two ways in which a predicate may fail to be
true of a subject propter se, and one of these results from the
addition, and the other from the omission, of a determinant. One
kind of predicate is not propter se because the term that is being
defined is combined with another determinant, e.g. if in defining
the essence of white one were to state the formula of white man; the
other because in the subject another determinant is combined with that
which is expressed in the formula, e.g. if 'cloak' meant 'white
man', and one were to define cloak as white; white man is white
indeed, but its essence is not to be white.

    But is being-a-cloak an essence at all? Probably not. For the
essence is precisely what something is; but when an attribute is
asserted of a subject other than itself, the complex is not
precisely what some 'this' is, e.g. white man is not precisely what
some 'this' is, since thisness belongs only to substances. Therefore
there is an essence only of those things whose formula is a
definition. But we have a definition not where we have a word and a
formula identical in meaning (for in that case all formulae or sets of
words would be definitions; for there will be some name for any set of
words whatever, so that even the Iliad will be a definition), but
where there is a formula of something primary; and primary things
are those which do not imply the predication of one element in them of
another element. Nothing, then, which is not a species of a genus will
have an essence-only species will have it, for these are thought to
imply not merely that the subject participates in the attribute and
has it as an affection, or has it by accident; but for ever thing else
as well, if it has a name, there be a formula of its meaning-viz. that
this attribute belongs to this subject; or instead of a simple formula
we shall be able to give a more accurate one; but there will be no
definition nor essence.

    Or has 'definition', like 'what a thing is', several meanings?
'What a thing is' in one sense means substance and the 'this', in
another one or other of the predicates, quantity, quality, and the
like. For as 'is' belongs to all things, not however in the same
sense, but to one sort of thing primarily and to others in a secondary
way, so too 'what a thing is' belongs in the simple sense to
substance, but in a limited sense to the other categories. For even of
a quality we might ask what it is, so that quality also is a 'what a
thing is',-not in the simple sense, however, but just as, in the
case of that which is not, some say, emphasizing the linguistic
form, that that is which is not is-not is simply, but is non-existent;
so too with quality.

    We must no doubt inquire how we should express ourselves on each
point, but certainly not more than how the facts actually stand. And
so now also, since it is evident what language we use, essence will
belong, just as 'what a thing is' does, primarily and in the simple
sense to substance, and in a secondary way to the other categories
also,-not essence in the simple sense, but the essence of a quality or
of a quantity. For it must be either by an equivocation that we say
these are, or by adding to and taking from the meaning of 'are' (in
the way in which that which is not known may be said to be known),-the
truth being that we use the word neither ambiguously nor in the same
sense, but just as we apply the word 'medical' by virtue of a
reference to one and the same thing, not meaning one and the same
thing, nor yet speaking ambiguously; for a patient and an operation
and an instrument are called medical neither by an ambiguity nor
with a single meaning, but with reference to a common end. But it does
not matter at all in which of the two ways one likes to describe the
facts; this is evident, that definition and essence in the primary and
simple sense belong to substances. Still they belong to other things
as well, only not in the primary sense. For if we suppose this it does
not follow that there is a definition of every word which means the
same as any formula; it must mean the same as a particular kind of
formula; and this condition is satisfied if it is a formula of
something which is one, not by continuity like the Iliad or the things
that are one by being bound together, but in one of the main senses of
'one', which answer to the senses of 'is'; now 'that which is' in
one sense denotes a 'this', in another a quantity, in another a
quality. And so there can be a formula or definition even of white
man, but not in the sense in which there is a definition either of
white or of a substance.

                                   5

    It is a difficult question, if one denies that a formula with an
added determinant is a definition, whether any of the terms that are
not simple but coupled will be definable. For we must explain them
by adding a determinant. E.g. there is the nose, and concavity, and
snubness, which is compounded out of the two by the presence of the
one in the other, and it is not by accident that the nose has the
attribute either of concavity or of snubness, but in virtue of its
nature; nor do they attach to it as whiteness does to Callias, or to
man (because Callias, who happens to be a man, is white), but as
'male' attaches to animal and 'equal' to quantity, and as all
so-called 'attributes propter se' attach to their subjects. And such
attributes are those in which is involved either the formula or the
name of the subject of the particular attribute, and which cannot be
explained without this; e.g. white can be explained apart from man,
but not female apart from animal. Therefore there is either no essence
and definition of any of these things, or if there is, it is in
another sense, as we have said.

    But there is also a second difficulty about them. For if snub nose
and concave nose are the same thing, snub and concave will be the
thing; but if snub and concave are not the same (because it is
impossible to speak of snubness apart from the thing of which it is an
attribute propter se, for snubness is concavity-in-a-nose), either
it is impossible to say 'snub nose' or the same thing will have been
said twice, concave-nose nose; for snub nose will be concave-nose
nose. And so it is absurd that such things should have an essence;
if they have, there will be an infinite regress; for in snub-nose nose
yet another 'nose' will be involved.

    Clearly, then, only substance is definable. For if the other
categories also are definable, it must be by addition of a
determinant, e.g. the qualitative is defined thus, and so is the
odd, for it cannot be defined apart from number; nor can female be
defined apart from animal. (When I say 'by addition' I mean the
expressions in which it turns out that we are saying the same thing
twice, as in these instances.) And if this is true, coupled terms
also, like 'odd number', will not be definable (but this escapes our
notice because our formulae are not accurate.). But if these also
are definable, either it is in some other way or, as we definition and
essence must be said to have more than one sense. Therefore in one
sense nothing will have a definition and nothing will have an essence,
except substances, but in another sense other things will have them.
Clearly, then, definition is the formula of the essence, and essence
belongs to substances either alone or chiefly and primarily and in the
unqualified sense.

                                   6

    We must inquire whether each thing and its essence are the same or
different. This is of some use for the inquiry concerning substance;
for each thing is thought to be not different from its substance,
and the essence is said to be the substance of each thing.

    Now in the case of accidental unities the two would be generally
thought to be different, e.g. white man would be thought to be
different from the essence of white man. For if they are the same, the
essence of man and that of white man are also the same; for a man
and a white man are the same thing, as people say, so that the essence
of white man and that of man would be also the same. But perhaps it
does not follow that the essence of accidental unities should be the
same as that of the simple terms. For the extreme terms are not in the
same way identical with the middle term. But perhaps this might be
thought to follow, that the extreme terms, the accidents, should
turn out to be the same, e.g. the essence of white and that of
musical; but this is not actually thought to be the case.

    But in the case of so-called self-subsistent things, is a thing
necessarily the same as its essence? E.g. if there are some substances
which have no other substances nor entities prior to them-substances
such as some assert the Ideas to be?-If the essence of good is to be
different from good-itself, and the essence of animal from
animal-itself, and the essence of being from being-itself, there will,
firstly, be other substances and entities and Ideas besides those
which are asserted, and, secondly, these others will be prior
substances, if essence is substance. And if the posterior substances
and the prior are severed from each other, (a) there will be no
knowledge of the former, and (b) the latter will have no being. (By
'severed' I mean, if the good-itself has not the essence of good,
and the latter has not the property of being good.) For (a) there is
knowledge of each thing only when we know its essence. And (b) the
case is the same for other things as for the good; so that if the
essence of good is not good, neither is the essence of reality real,
nor the essence of unity one. And all essences alike exist or none
of them does; so that if the essence of reality is not real, neither
is any of the others. Again, that to which the essence of good does
not belong is not good.-The good, then, must be one with the essence
of good, and the beautiful with the essence of beauty, and so with all
things which do not depend on something else but are self-subsistent
and primary. For it is enough if they are this, even if they are not
Forms; or rather, perhaps, even if they are Forms. (At the same time
it is clear that if there are Ideas such as some people say there are,
it will not be substratum that is substance; for these must be
substances, but not predicable of a substratum; for if they were
they would exist only by being participated in.)

    Each thing itself, then, and its essence are one and the same in
no merely accidental way, as is evident both from the preceding
arguments and because to know each thing, at least, is just to know
its essence, so that even by the exhibition of instances it becomes
clear that both must be one.

    (But of an accidental term, e.g.'the musical' or 'the white',
since it has two meanings, it is not true to say that it itself is
identical with its essence; for both that to which the accidental
quality belongs, and the accidental quality, are white, so that in a
sense the accident and its essence are the same, and in a sense they
are not; for the essence of white is not the same as the man or the
white man, but it is the same as the attribute white.)

    The absurdity of the separation would appear also if one were to
assign a name to each of the essences; for there would be yet
another essence besides the original one, e.g. to the essence of horse
there will belong a second essence. Yet why should not some things
be their essences from the start, since essence is substance? But
indeed not only are a thing and its essence one, but the formula of
them is also the same, as is clear even from what has been said; for
it is not by accident that the essence of one, and the one, are one.
Further, if they are to be different, the process will go on to
infinity; for we shall have (1) the essence of one, and (2) the one,
so that to terms of the former kind the same argument will be
applicable.

    Clearly, then, each primary and self-subsistent thing is one and
the same as its essence. The sophistical objections to this
position, and the question whether Socrates and to be Socrates are the
same thing, are obviously answered by the same solution; for there
is no difference either in the standpoint from which the question
would be asked, or in that from which one could answer it
successfully. We have explained, then, in what sense each thing is the
same as its essence and in what sense it is not.

                                   7

    Of things that come to be, some come to be by nature, some by art,
some spontaneously. Now everything that comes to be comes to be by the
agency of something and from something and comes to be something.
And the something which I say it comes to be may be found in any
category; it may come to be either a 'this' or of some size or of some
quality or somewhere.

    Now natural comings to be are the comings to be of those things
which come to be by nature; and that out of which they come to be is
what we call matter; and that by which they come to be is something
which exists naturally; and the something which they come to be is a
man or a plant or one of the things of this kind, which we say are
substances if anything is-all things produced either by nature or by
art have matter; for each of them is capable both of being and of
not being, and this capacity is the matter in each-and, in general,
both that from which they are produced is nature, and the type
according to which they are produced is nature (for that which is
produced, e.g. a plant or an animal, has a nature), and so is that
by which they are produced--the so-called 'formal' nature, which is
specifically the same (though this is in another individual); for
man begets man.

    Thus, then, are natural products produced; all other productions
are called 'makings'. And all makings proceed either from art or
from a faculty or from thought. Some of them happen also spontaneously
or by luck just as natural products sometimes do; for there also the
same things sometimes are produced without seed as well as from
seed. Concerning these cases, then, we must inquire later, but from
art proceed the things of which the form is in the soul of the artist.
(By form I mean the essence of each thing and its primary
substance.) For even contraries have in a sense the same form; for the
substance of a privation is the opposite substance, e.g. health is the
substance of disease (for disease is the absence of health); and
health is the formula in the soul or the knowledge of it. The
healthy subject is produced as the result of the following train of
thought:-since this is health, if the subject is to be healthy this
must first be present, e.g. a uniform state of body, and if this is to
be present, there must be heat; and the physician goes on thinking
thus until he reduces the matter to a final something which he himself
can produce. Then the process from this point onward, i.e. the process
towards health, is called a 'making'. Therefore it follows that in a
sense health comes from health and house from house, that with
matter from that without matter; for the medical art and the
building art are the form of health and of the house, and when I speak
of substance without matter I mean the essence.

    Of the productions or processes one part is called thinking and
the other making,-that which proceeds from the starting-point and
the form is thinking, and that which proceeds from the final step of
the thinking is making. And each of the other, intermediate, things is
produced in the same way. I mean, for instance, if the subject is to
be healthy his bodily state must be made uniform. What then does being
made uniform imply? This or that. And this depends on his being made
warm. What does this imply? Something else. And this something is
present potentially; and what is present potentially is already in the
physician's power.

    The active principle then and the starting point for the process
of becoming healthy is, if it happens by art, the form in the soul,
and if spontaneously, it is that, whatever it is, which starts the
making, for the man who makes by art, as in healing the starting-point
is perhaps the production of warmth (and this the physician produces
by rubbing). Warmth in the body, then, is either a part of health or
is followed (either directly or through several intermediate steps) by
something similar which is a part of health; and this, viz. that which
produces the part of health, is the limiting-point--and so too with
a house (the stones are the limiting-point here) and in all other
cases. Therefore, as the saying goes, it is impossible that anything
should be produced if there were nothing existing before. Obviously
then some part of the result will pre-exist of necessity; for the
matter is a part; for this is present in the process and it is this
that becomes something. But is the matter an element even in the
formula? We certainly describe in both ways what brazen circles are;
we describe both the matter by saying it is brass, and the form by
saying that it is such and such a figure; and figure is the
proximate genus in which it is placed. The brazen circle, then, has
its matter in its formula.

    As for that out of which as matter they are produced, some
things are said, when they have been produced, to be not that but
'thaten'; e.g. the statue is not gold but golden. And a healthy man is
not said to be that from which he has come. The reason is that
though a thing comes both from its privation and from its
substratum, which we call its matter (e.g. what becomes healthy is
both a man and an invalid), it is said to come rather from its
privation (e.g. it is from an invalid rather than from a man that a
healthy subject is produced). And so the healthy subject is not said
to he an invalid, but to be a man, and the man is said to be
healthy. But as for the things whose privation is obscure and
nameless, e.g. in brass the privation of a particular shape or in
bricks and timber the privation of arrangement as a house, the thing
is thought to be produced from these materials, as in the former
case the healthy man is produced from an invalid. And so, as there
also a thing is not said to be that from which it comes, here the
statue is not said to be wood but is said by a verbal change to be
wooden, not brass but brazen, not gold but golden, and the house is
said to be not bricks but bricken (though we should not say without
qualification, if we looked at the matter carefully, even that a
statue is produced from wood or a house from bricks, because coming to
be implies change in that from which a thing comes to be, and not
permanence). It is for this reason, then, that we use this way of
speaking.

                                   8

    Since anything which is produced is produced by something (and
this I call the starting-point of the production), and from
something (and let this be taken to be not the privation but the
matter; for the meaning we attach to this has already been explained),
and since something is produced (and this is either a sphere or a
circle or whatever else it may chance to be), just as we do not make
the substratum (the brass), so we do not make the sphere, except
incidentally, because the brazen sphere is a sphere and we make the
forme. For to make a 'this' is to make a 'this' out of the
substratum in the full sense of the word. (I mean that to make the
brass round is not to make the round or the sphere, but something
else, i.e. to produce this form in something different from itself.
For if we make the form, we must make it out of something else; for
this was assumed. E.g. we make a brazen sphere; and that in the
sense that out of this, which is brass, we make this other, which is a
sphere.) If, then, we also make the substratum itself, clearly we
shall make it in the same way, and the processes of making will
regress to infinity. Obviously then the form also, or whatever we
ought to call the shape present in the sensible thing, is not
produced, nor is there any production of it, nor is the essence
produced; for this is that which is made to be in something else
either by art or by nature or by some faculty. But that there is a
brazen sphere, this we make. For we make it out of brass and the
sphere; we bring the form into this particular matter, and the
result is a brazen sphere. But if the essence of sphere in general
is to be produced, something must be produced out of something. For
the product will always have to be divisible, and one part must be
this and another that; I mean the one must be matter and the other
form. If, then, a sphere is 'the figure whose circumference is at
all points equidistant from the centre', part of this will be the
medium in which the thing made will be, and part will be in that
medium, and the whole will be the thing produced, which corresponds to
the brazen sphere. It is obvious, then, from what has been said,
that that which is spoken of as form or substance is not produced, but
the concrete thing which gets its name from this is produced, and that
in everything which is generated matter is present, and one part of
the thing is matter and the other form.

    Is there, then, a sphere apart from the individual spheres or a
house apart from the bricks? Rather we may say that no 'this' would
ever have been coming to be, if this had been so, but that the
'form' means the 'such', and is not a 'this'-a definite thing; but the
artist makes, or the father begets, a 'such' out of a 'this'; and when
it has been begotten, it is a 'this such'. And the whole 'this',
Callias or Socrates, is analogous to 'this brazen sphere', but man and
animal to 'brazen sphere' in general. Obviously, then, the cause which
consists of the Forms (taken in the sense in which some maintain the
existence of the Forms, i.e. if they are something apart from the
individuals) is useless, at least with regard to comings-to-be and
to substances; and the Forms need not, for this reason at least, be
self-subsistent substances. In some cases indeed it is even obvious
that the begetter is of the same kind as the begotten (not, however,
the same nor one in number, but in form), i.e. in the case of
natural products (for man begets man), unless something happens
contrary to nature, e.g. the production of a mule by a horse. (And
even these cases are similar; for that which would be found to be
common to horse and ass, the genus next above them, has not received a
name, but it would doubtless be both in fact something like a mule.)
Obviously, therefore, it is quite unnecessary to set up a Form as a
pattern (for we should have looked for Forms in these cases if in any;
for these are substances if anything is so); the begetter is
adequate to the making of the product and to the causing of the form
in the matter. And when we have the whole, such and such a form in
this flesh and in these bones, this is Callias or Socrates; and they
are different in virtue of their matter (for that is different), but
the same in form; for their form is indivisible.

                                   9

    The question might be raised, why some things are produced
spontaneously as well as by art, e.g. health, while others are not,
e.g. a house. The reason is that in some cases the matter which
governs the production in the making and producing of any work of art,
and in which a part of the product is present,-some matter is such
as to be set in motion by itself and some is not of this nature, and
of the former kind some can move itself in the particular way
required, while other matter is incapable of this; for many things can
be set in motion by themselves but not in some particular way, e.g.
that of dancing. The things, then, whose matter is of this sort,
e.g. stones, cannot be moved in the particular way required, except by
something else, but in another way they can move themselves-and so
it is with fire. Therefore some things will not exist apart from
some one who has the art of making them, while others will; for motion
will be started by these things which have not the art but can
themselves be moved by other things which have not the art or with a
motion starting from a part of the product.

    And it is clear also from what has been said that in a sense every
product of art is produced from a thing which shares its name (as
natural products are produced), or from a part of itself which
shares its name (e.g. the house is produced from a house, qua produced
by reason; for the art of building is the form of the house), or
from something which contains a art of it,-if we exclude things
produced by accident; for the cause of the thing's producing the
product directly per se is a part of the product. The heat in the
movement caused heat in the body, and this is either health, or a part
of health, or is followed by a part of health or by health itself. And
so it is said to cause health, because it causes that to which
health attaches as a consequence.

    Therefore, as in syllogisms, substance is the starting-point of
everything. It is from 'what a thing is' that syllogisms start; and
from it also we now find processes of production to start.

    Things which are formed by nature are in the same case as these
products of art. For the seed is productive in the same way as the
things that work by art; for it has the form potentially, and that
from which the seed comes has in a sense the same name as the
offspring only in a sense, for we must not expect parent and offspring
always to have exactly the same name, as in the production of 'human
being' from 'human' for a 'woman' also can be produced by a
'man'-unless the offspring be an imperfect form; which is the reason
why the parent of a mule is not a mule. The natural things which (like
the artificial objects previously considered) can be produced
spontaneously are those whose matter can be moved even by itself in
the way in which the seed usually moves it; those things which have
not such matter cannot be produced except from the parent animals
themselves.

    But not only regarding substance does our argument prove that
its form does not come to be, but the argument applies to all the
primary classes alike, i.e. quantity, quality, and the other
categories. For as the brazen sphere comes to be, but not the sphere
nor the brass, and so too in the case of brass itself, if it comes
to be, it is its concrete unity that comes to be (for the matter and
the form must always exist before), so is it both in the case of
substance and in that of quality and quantity and the other categories
likewise; for the quality does not come to be, but the wood of that
quality, and the quantity does not come to be, but the wood or the
animal of that size. But we may learn from these instances a
peculiarity of substance, that there must exist beforehand in complete
reality another substance which produces it, e.g. an animal if an
animal is produced; but it is not necessary that a quality or quantity
should pre-exist otherwise than potentially.

                                  10

    Since a definition is a formula, and every formula has parts,
and as the formula is to the thing, so is the part of the formula to
the part of the thing, the question is already being asked whether the
formula of the parts must be present in the formula of the whole or
not. For in some cases the formulae of the parts are seen to be
present, and in some not. The formula of the circle does not include
that of the segments, but that of the syllable includes that of the
letters; yet the circle is divided into segments as the syllable is
into letters.-And further if the parts are prior to the whole, and the
acute angle is a part of the right angle and the finger a part of
the animal, the acute angle will be prior to the right angle and
finger to the man. But the latter are thought to be prior; for in
formula the parts are explained by reference to them, and in respect
also of the power of existing apart from each other the wholes are
prior to the parts.

    Perhaps we should rather say that 'part' is used in several
senses. One of these is 'that which measures another thing in
respect of quantity'. But let this sense be set aside; let us
inquire about the parts of which substance consists. If then matter is
one thing, form another, the compound of these a third, and both the
matter and the form and the compound are substance even the matter
is in a sense called part of a thing, while in a sense it is not,
but only the elements of which the formula of the form consists.
E.g. of concavity flesh (for this is the matter in which it is
produced) is not a part, but of snubness it is a part; and the
bronze is a part of the concrete statue, but not of the statue when
this is spoken of in the sense of the form. (For the form, or the
thing as having form, should be said to be the thing, but the material
element by itself must never be said to be so.) And so the formula
of the circle does not include that of the segments, but the formula
of the syllable includes that of the letters; for the letters are
parts of the formula of the form, and not matter, but the segments are
parts in the sense of matter on which the form supervenes; yet they
are nearer the form than the bronze is when roundness is produced in
bronze. But in a sense not even every kind of letter will be present
in the formula of the syllable, e.g. particular waxen letters or the
letters as movements in the air; for in these also we have already
something that is part of the syllable only in the sense that it is
its perceptible matter. For even if the line when divided passes
away into its halves, or the man into bones and muscles and flesh,
it does not follow that they are composed of these as parts of their
essence, but rather as matter; and these are parts of the concrete
thing, but not also of the form, i.e. of that to which the formula
refers; wherefore also they are not present in the formulae. In one
kind of formula, then, the formula of such parts will be present,
but in another it must not be present, where the formula does not
refer to the concrete object. For it is for this reason that some
things have as their constituent principles parts into which they pass
away, while some have not. Those things which are the form and the
matter taken together, e.g. the snub, or the bronze circle, pass
away into these materials, and the matter is a part of them; but those
things which do not involve matter but are without matter, and whose
formulae are formulae of the form only, do not pass away,-either not
at all or at any rate not in this way. Therefore these materials are
principles and parts of the concrete things, while of the form they
are neither parts nor principles. And therefore the clay statue is
resolved into clay and the ball into bronze and Callias into flesh and
bones, and again the circle into its segments; for there is a sense of
'circle' in which involves matter. For 'circle' is used ambiguously,
meaning both the circle, unqualified, and the individual circle,
because there is no name peculiar to the individuals.

    The truth has indeed now been stated, but still let us state it
yet more clearly, taking up the question again. The parts of the
formula, into which the formula is divided, are prior to it, either
all or some of them. The formula of the right angle, however, does not
include the formula of the acute, but the formula of the acute
includes that of the right angle; for he who defines the acute uses
the right angle; for the acute is 'less than a right angle'. The
circle and the semicircle also are in a like relation; for the
semicircle is defined by the circle; and so is the finger by the whole
body, for a finger is 'such and such a part of a man'. Therefore the
parts which are of the nature of matter, and into which as its
matter a thing is divided, are posterior; but those which are of the
nature of parts of the formula, and of the substance according to
its formula, are prior, either all or some of them. And since the soul
of animals (for this is the substance of a living being) is their
substance according to the formula, i.e. the form and the essence of a
body of a certain kind (at least we shall define each part, if we
define it well, not without reference to its function, and this cannot
belong to it without perception), so that the parts of soul are prior,
either all or some of them, to the concrete 'animal', and so too
with each individual animal; and the body and parts are posterior to
this, the essential substance, and it is not the substance but the
concrete thing that is divided into these parts as its matter:-this
being so, to the concrete thing these are in a sense prior, but in a
sense they are not. For they cannot even exist if severed from the
whole; for it is not a finger in any and every state that is the
finger of a living thing, but a dead finger is a finger only in
name. Some parts are neither prior nor posterior to the whole, i.e.
those which are dominant and in which the formula, i.e. the
essential substance, is immediately present, e.g. perhaps the heart or
the brain; for it does not matter in the least which of the two has
this quality. But man and horse and terms which are thus applied to
individuals, but universally, are not substance but something composed
of this particular formula and this particular matter treated as
universal; and as regards the individual, Socrates already includes in
him ultimate individual matter; and similarly in all other cases. 'A
part' may be a part either of the form (i.e. of the essence), or of
the compound of the form and the matter, or of the matter itself.
But only the parts of the form are parts of the formula, and the
formula is of the universal; for 'being a circle' is the same as the
circle, and 'being a soul' the same as the soul. But when we come to
the concrete thing, e.g. this circle, i.e. one of the individual
circles, whether perceptible or intelligible (I mean by intelligible
circles the mathematical, and by perceptible circles those of bronze
and of wood),-of these there is no definition, but they are known by
the aid of intuitive thinking or of perception; and when they pass out
of this complete realization it is not clear whether they exist or
not; but they are always stated and recognized by means of the
universal formula. But matter is unknowable in itself. And some matter
is perceptible and some intelligible, perceptible matter being for
instance bronze and wood and all matter that is changeable, and
intelligible matter being that which is present in perceptible
things not qua perceptible, i.e. the objects of mathematics.

    We have stated, then, how matters stand with regard to whole and
part, and their priority and posteriority. But when any one asks
whether the right angle and the circle and the animal are prior, or
the things into which they are divided and of which they consist, i.e.
the parts, we must meet the inquiry by saying that the question cannot
be answered simply. For if even bare soul is the animal or the
living thing, or the soul of each individual is the individual itself,
and 'being a circle' is the circle, and 'being a right angle' and
the essence of the right angle is the right angle, then the whole in
one sense must be called posterior to the art in one sense, i.e. to
the parts included in the formula and to the parts of the individual
right angle (for both the material right angle which is made of
bronze, and that which is formed by individual lines, are posterior to
their parts); while the immaterial right angle is posterior to the
parts included in the formula, but prior to those included in the
particular instance, and the question must not be answered simply. If,
however, the soul is something different and is not identical with the
animal, even so some parts must, as we have maintained, be called
prior and others must not.

                                  11

    Another question is naturally raised, viz. what sort of parts
belong to the form and what sort not to the form, but to the
concrete thing. Yet if this is not plain it is not possible to
define any thing; for definition is of the universal and of the
form. If then it is not evident what sort of parts are of the nature
of matter and what sort are not, neither will the formula of the thing
be evident. In the case of things which are found to occur in
specifically different materials, as a circle may exist in bronze or
stone or wood, it seems plain that these, the bronze or the stone, are
no part of the essence of the circle, since it is found apart from
them. Of things which are not seen to exist apart, there is no
reason why the same may not be true, just as if all circles that had
ever been seen were of bronze; for none the less the bronze would be
no part of the form; but it is hard to eliminate it in thought. E.g.
the form of man is always found in flesh and bones and parts of this
kind; are these then also parts of the form and the formula? No,
they are matter; but because man is not found also in other matters we
are unable to perform the abstraction.

    Since this is thought to be possible, but it is not clear when
it is the case, some people already raise the question even in the
case of the circle and the triangle, thinking that it is not right
to define these by reference to lines and to the continuous, but
that all these are to the circle or the triangle as flesh and bones
are to man, and bronze or stone to the statue; and they reduce all
things to numbers, and they say the formula of 'line' is that of
'two'. And of those who assert the Ideas some make 'two' the
line-itself, and others make it the Form of the line; for in some
cases they say the Form and that of which it is the Form are the same,
e.g. 'two' and the Form of two; but in the case of 'line' they say
this is no longer so.

    It follows then that there is one Form for many things whose
form is evidently different (a conclusion which confronted the
Pythagoreans also); and it is possible to make one thing the
Form-itself of all, and to hold that the others are not Forms; but
thus all things will be one.

    We have pointed out, then, that the question of definitions
contains some difficulty, and why this is so. And so to reduce all
things thus to Forms and to eliminate the matter is useless labour;
for some things surely are a particular form in a particular matter,
or particular things in a particular state. And the comparison which
Socrates the younger used to make in the case of 'animal' is not
sound; for it leads away from the truth, and makes one suppose that
man can possibly exist without his parts, as the circle can without
the bronze. But the case is not similar; for an animal is something
perceptible, and it is not possible to define it without reference
to movement-nor, therefore, without reference to the parts' being in a
certain state. For it is not a hand in any and every state that is a
part of man, but only when it can fulfil its work, and therefore
only when it is alive; if it is not alive it is not a part.

    Regarding the objects of mathematics, why are the formulae of
the parts not parts of the formulae of the wholes; e.g. why are not
the semicircles included in the formula of the circle? It cannot be
said, 'because these parts are perceptible things'; for they are
not. But perhaps this makes no difference; for even some things
which are not perceptible must have matter; indeed there is some
matter in everything which is not an essence and a bare form but a
'this'. The semicircles, then, will not be parts of the universal
circle, but will be parts of the individual circles, as has been
said before; for while one kind of matter is perceptible, there is
another which is intelligible.

    It is clear also that the soul is the primary substance and the
body is matter, and man or animal is the compound of both taken
universally; and 'Socrates' or 'Coriscus', if even the soul of
Socrates may be called Socrates, has two meanings (for some mean by
such a term the soul, and others mean the concrete thing), but if
'Socrates' or 'Coriscus' means simply this particular soul and this
particular body, the individual is analogous to the universal in its
composition.

    Whether there is, apart from the matter of such substances,
another kind of matter, and one should look for some substance other
than these, e.g. numbers or something of the sort, must be
considered later. For it is for the sake of this that we are trying to
determine the nature of perceptible substances as well, since in a
sense the inquiry about perceptible substances is the work of physics,
i.e. of second philosophy; for the physicist must come to know not
only about the matter, but also about the substance expressed in the
formula, and even more than about the other. And in the case of
definitions, how the elements in the formula are parts of the
definition, and why the definition is one formula (for clearly the
thing is one, but in virtue of what is the thing one, although it
has parts?),-this must be considered later.

    What the essence is and in what sense it is independent, has
been stated universally in a way which is true of every case, and also
why the formula of the essence of some things contains the parts of
the thing defined, while that of others does not. And we have stated
that in the formula of the substance the material parts will not be
present (for they are not even parts of the substance in that sense,
but of the concrete substance; but of this there is in a sense a
formula, and in a sense there is not; for there is no formula of it
with its matter, for this is indefinite, but there is a formula of
it with reference to its primary substance-e.g. in the case of man the
formula of the soul-, for the substance is the indwelling form, from
which and the matter the so-called concrete substance is derived; e.g.
concavity is a form of this sort, for from this and the nose arise
'snub nose' and 'snubness'); but in the concrete substance, e.g. a
snub nose or Callias, the matter also will be present. And we have
stated that the essence and the thing itself are in some cases the
same; ie. in the case of primary substances, e.g. curvature and the
essence of curvature if this is primary. (By a 'primary' substance I
mean one which does not imply the presence of something in something
else, i.e. in something that underlies it which acts as matter.) But
things which are of the nature of matter, or of wholes that include
matter, are not the same as their essences, nor are accidental unities
like that of 'Socrates' and 'musical'; for these are the same only
by accident.

                                  12

    Now let us treat first of definition, in so far as we have not
treated of it in the Analytics; for the problem stated in them is
useful for our inquiries concerning substance. I mean this
problem:-wherein can consist the unity of that, the formula of which
we call a definition, as for instance, in the case of man, 'two-footed
animal'; for let this be the formula of man. Why, then, is this one,
and not many, viz. 'animal' and 'two-footed'? For in the case of 'man'
and 'pale' there is a plurality when one term does not belong to the
other, but a unity when it does belong and the subject, man, has a
certain attribute; for then a unity is produced and we have 'the
pale man'. In the present case, on the other hand, one does not
share in the other; the genus is not thought to share in its
differentiae (for then the same thing would share in contraries; for
the differentiae by which the genus is divided are contrary). And even
if the genus does share in them, the same argument applies, since
the differentiae present in man are many, e.g. endowed with feet,
two-footed, featherless. Why are these one and not many? Not because
they are present in one thing; for on this principle a unity can be
made out of all the attributes of a thing. But surely all the
attributes in the definition must be one; for the definition is a
single formula and a formula of substance, so that it must be a
formula of some one thing; for substance means a 'one' and a 'this',
as we maintain.

    We must first inquire about definitions reached by the method of
divisions. There is nothing in the definition except the first-named
and the differentiae. The other genera are the first genus and along
with this the differentiae that are taken with it, e.g. the first
may be 'animal', the next 'animal which is two-footed', and again
'animal which is two-footed and featherless', and similarly if the
definition includes more terms. And in general it makes no
difference whether it includes many or few terms,-nor, therefore,
whether it includes few or simply two; and of the two the one is
differentia and the other genus; e.g. in 'two-footed animal'
'animal' is genus, and the other is differentia.

    If then the genus absolutely does not exist apart from the
species-of-a-genus, or if it exists but exists as matter (for the
voice is genus and matter, but its differentiae make the species, i.e.
the letters, out of it), clearly the definition is the formula which
comprises the differentiae.

    But it is also necessary that the division be by the differentia
of the diferentia; e.g. 'endowed with feet' is a differentia of
'animal'; again the differentia of 'animal endowed with feet' must
be of it qua endowed with feet. Therefore we must not say, if we are
to speak rightly, that of that which is endowed with feet one part has
feathers and one is featherless (if we do this we do it through
incapacity); we must divide it only into cloven-footed and not cloven;
for these are differentiae in the foot; cloven-footedness is a form of
footedness. And the process wants always to go on so till it reaches
the species that contain no differences. And then there will be as
many kinds of foot as there are differentiae, and the kinds of animals
endowed with feet will be equal in number to the differentiae. If then
this is so, clearly the last differentia will be the substance of
the thing and its definition, since it is not right to state the
same things more than once in our definitions; for it is
superfluous. And this does happen; for when we say 'animal endowed
with feet and two-footed' we have said nothing other than 'animal
having feet, having two feet'; and if we divide this by the proper
division, we shall be saying the same thing more than once-as many
times as there are differentiae.

    If then a differentia of a differentia be taken at each step,
one differentia-the last-will be the form and the substance; but if we
divide according to accidental qualities, e.g. if we were to divide
that which is endowed with feet into the white and the black, there
will be as many differentiae as there are cuts. Therefore it is
plain that the definition is the formula which contains the
differentiae, or, according to the right method, the last of these.
This would be evident, if we were to change the order of such
definitions, e.g. of that of man, saying 'animal which is two-footed
and endowed with feet'; for 'endowed with feet' is superfluous when
'two-footed' has been said. But there is no order in the substance;
for how are we to think the one element posterior and the other prior?
Regarding the definitions, then, which are reached by the method of
divisions, let this suffice as our first attempt at stating their
nature.

                                  13

    Let us return to the subject of our inquiry, which is substance.
As the substratum and the essence and the compound of these are called
substance, so also is the universal. About two of these we have
spoken; both about the essence and about the substratum, of which we
have said that it underlies in two senses, either being a 'this'-which
is the way in which an animal underlies its attributes-or as the
matter underlies the complete reality. The universal also is thought
by some to be in the fullest sense a cause, and a principle; therefore
let us attack the discussion of this point also. For it seems
impossible that any universal term should be the name of a
substance. For firstly the substance of each thing is that which is
peculiar to it, which does not belong to anything else; but the
universal is common, since that is called universal which is such as
to belong to more than one thing. Of which individual then will this
be the substance? Either of all or of none; but it cannot be the
substance of all. And if it is to be the substance of one, this one
will be the others also; for things whose substance is one and whose
essence is one are themselves also one.

    Further, substance means that which is not predicable of a
subject, but the universal is predicable of some subject always.

    But perhaps the universal, while it cannot be substance in the way
in which the essence is so, can be present in this; e.g. 'animal'
can be present in 'man' and 'horse'. Then clearly it is a formula of
the essence. And it makes no difference even if it is not a formula of
everything that is in the substance; for none the less the universal
will be the substance of something, as 'man' is the substance of the
individual man in whom it is present, so that the same result will
follow once more; for the universal, e.g. 'animal', will be the
substance of that in which it is present as something peculiar to
it. And further it is impossible and absurd that the 'this', i.e.
the substance, if it consists of parts, should not consist of
substances nor of what is a 'this', but of quality; for that which
is not substance, i.e. the quality, will then be prior to substance
and to the 'this'. Which is impossible; for neither in formula nor
in time nor in coming to be can the modifications be prior to the
substance; for then they will also be separable from it. Further,
Socrates will contain a substance present in a substance, so that this
will be the substance of two things. And in general it follows, if man
and such things are substance, that none of the elements in their
formulae is the substance of anything, nor does it exist apart from
the species or in anything else; I mean, for instance, that no
'animal' exists apart from the particular kinds of animal, nor does
any other of the elements present in formulae exist apart.

    If, then, we view the matter from these standpoints, it is plain
that no universal attribute is a substance, and this is plain also
from the fact that no common predicate indicates a 'this', but
rather a 'such'. If not, many difficulties follow and especially the
'third man'.

    The conclusion is evident also from the following consideration. A
substance cannot consist of substances present in it in complete
reality; for things that are thus in complete reality two are never in
complete reality one, though if they are potentially two, they can
be one (e.g. the double line consists of two halves-potentially; for
the complete realization of the halves divides them from one another);
therefore if the substance is one, it will not consist of substances
present in it and present in this way, which Democritus describes
rightly; he says one thing cannot be made out of two nor two out of
one; for he identifies substances with his indivisible magnitudes.
It is clear therefore that the same will hold good of number, if
number is a synthesis of units, as is said by some; for two is
either not one, or there is no unit present in it in complete reality.
But our result involves a difficulty. If no substance can consist of
universals because a universal indicates a 'such', not a 'this', and
if no substance can be composed of substances existing in complete
reality, every substance would be incomposite, so that there would not
even be a formula of any substance. But it is thought by all and was
stated long ago that it is either only, or primarily, substance that
can defined; yet now it seems that not even substance can. There
cannot, then, be a definition of anything; or in a sense there can be,
and in a sense there cannot. And what we are saying will be plainer
from what follows.

                                  14

    It is clear also from these very facts what consequence
confronts those who say the Ideas are substances capable of separate
existence, and at the same time make the Form consist of the genus and
the differentiae. For if the Forms exist and 'animal' is present in
'man' and 'horse', it is either one and the same in number, or
different. (In formula it is clearly one; for he who states the
formula will go through the formula in either case.) If then there
is a 'man-in-himself' who is a 'this' and exists apart, the parts also
of which he consists, e.g. 'animal' and 'two-footed', must indicate
'thises', and be capable of separate existence, and substances;
therefore 'animal', as well as 'man', must be of this sort.

    Now (1) if the 'animal' in 'the horse' and in 'man' is one and the
same, as you are with yourself, (a) how will the one in things that
exist apart be one, and how will this 'animal' escape being divided
even from itself?

    Further, (b) if it is to share in 'two-footed' and
'many-footed', an impossible conclusion follows; for contrary
attributes will belong at the same time to it although it is one and a
'this'. If it is not to share in them, what is the relation implied
when one says the animal is two-footed or possessed of feet? But
perhaps the two things are 'put together' and are 'in contact', or are
'mixed'. Yet all these expressions are absurd.

    But (2) suppose the Form to be different in each species. Then
there will be practically an infinite number of things whose substance
is animal'; for it is not by accident that 'man' has 'animal' for
one of its elements. Further, many things will be 'animal-itself'. For
(i) the 'animal' in each species will be the substance of the species;
for it is after nothing else that the species is called; if it were,
that other would be an element in 'man', i.e. would be the genus of
man. And further, (ii) all the elements of which 'man' is composed
will be Ideas. None of them, then, will be the Idea of one thing and
the substance of another; this is impossible. The 'animal', then,
present in each species of animals will be animal-itself. Further,
from what is this 'animal' in each species derived, and how will it be
derived from animal-itself? Or how can this 'animal', whose essence is
simply animality, exist apart from animal-itself?

     Further, (3)in the case of sensible things both these
consequences and others still more absurd follow. If, then, these
consequences are impossible, clearly there are not Forms of sensible
things in the sense in which some maintain their existence.

                                  15

    Since substance is of two kinds, the concrete thing and the
formula (I mean that one kind of substance is the formula taken with
the matter, while another kind is the formula in its generality),
substances in the former sense are capable of destruction (for they
are capable also of generation), but there is no destruction of the
formula in the sense that it is ever in course of being destroyed (for
there is no generation of it either; the being of house is not
generated, but only the being of this house), but without generation
and destruction formulae are and are not; for it has been shown that
no one begets nor makes these. For this reason, also, there is neither
definition of nor demonstration about sensible individual
substances, because they have matter whose nature is such that they
are capable both of being and of not being; for which reason all the
individual instances of them are destructible. If then demonstration
is of necessary truths and definition is a scientific process, and if,
just as knowledge cannot be sometimes knowledge and sometimes
ignorance, but the state which varies thus is opinion, so too
demonstration and definition cannot vary thus, but it is opinion
that deals with that which can be otherwise than as it is, clearly
there can neither be definition of nor demonstration about sensible
individuals. For perishing things are obscure to those who have the
relevant knowledge, when they have passed from our perception; and
though the formulae remain in the soul unchanged, there will no longer
be either definition or demonstration. And so when one of the
definition-mongers defines any individual, he must recognize that
his definition may always be overthrown; for it is not possible to
define such things.

    Nor is it possible to define any Idea. For the Idea is, as its
supporters say, an individual, and can exist apart; and the formula
must consist of words; and he who defines must not invent a word
(for it would be unknown), but the established words are common to all
the members of a class; these then must apply to something besides the
thing defined; e.g. if one were defining you, he would say 'an
animal which is lean' or 'pale', or something else which will apply
also to some one other than you. If any one were to say that perhaps
all the attributes taken apart may belong to many subjects, but
together they belong only to this one, we must reply first that they
belong also to both the elements; e.g. 'two-footed animal' belongs
to animal and to the two-footed. (And in the case of eternal
entities this is even necessary, since the elements are prior to and
parts of the compound; nay more, they can also exist apart, if 'man'
can exist apart. For either neither or both can. If, then, neither
can, the genus will not exist apart from the various species; but if
it does, the differentia will also.) Secondly, we must reply that
'animal' and 'two-footed' are prior in being to 'two-footed animal';
and things which are prior to others are not destroyed when the others
are.

    Again, if the Ideas consist of Ideas (as they must, since elements
are simpler than the compound), it will be further necessary that
the elements also of which the Idea consists, e.g. 'animal' and
'two-footed', should be predicated of many subjects. If not, how
will they come to be known? For there will then be an Idea which
cannot be predicated of more subjects than one. But this is not
thought possible-every Idea is thought to be capable of being shared.

    As has been said, then, the impossibility of defining
individuals escapes notice in the case of eternal things, especially
those which are unique, like the sun or the moon. For people err not
only by adding attributes whose removal the sun would survive, e.g.
'going round the earth' or 'night-hidden' (for from their view it
follows that if it stands still or is visible, it will no longer be
the sun; but it is strange if this is so; for 'the sun' means a
certain substance); but also by the mention of attributes which can
belong to another subject; e.g. if another thing with the stated
attributes comes into existence, clearly it will be a sun; the formula
therefore is general. But the sun was supposed to be an individual,
like Cleon or Socrates. After all, why does not one of the
supporters of the Ideas produce a definition of an Idea? It would
become clear, if they tried, that what has now been said is true.

                                  16

    Evidently even of the things that are thought to be substances,
most are only potencies,-both the parts of animals (for none of them
exists separately; and when they are separated, then too they exist,
all of them, merely as matter) and earth and fire and air; for none of
them is a unity, but as it were a mere heap, till they are worked up
and some unity is made out of them. One might most readily suppose the
parts of living things and the parts of the soul nearly related to
them to turn out to be both, i.e. existent in complete reality as well
as in potency, because they have sources of movement in something in
their joints; for which reason some animals live when divided. Yet all
the parts must exist only potentially, when they are one and
continuous by nature,-not by force or by growing into one, for such
a phenomenon is an abnormality.

    Since the term 'unity' is used like the term 'being', and the
substance of that which is one is one, and things whose substance is
numerically one are numerically one, evidently neither unity nor being
can be the substance of things, just as being an element or a
principle cannot be the substance, but we ask what, then, the
principle is, that we may reduce the thing to something more knowable.
Now of these concepts 'being' and 'unity' are more substantial than
'principle' or 'element' or 'cause', but not even the former are
substance, since in general nothing that is common is substance; for
substance does not belong to anything but to itself and to that
which has it, of which it is the substance. Further, that which is one
cannot be in many places at the same time, but that which is common is
present in many places at the same time; so that clearly no
universal exists apart from its individuals.

    But those who say the Forms exist, in one respect are right, in
giving the Forms separate existence, if they are substances; but in
another respect they are not right, because they say the one over many
is a Form. The reason for their doing this is that they cannot declare
what are the substances of this sort, the imperishable substances
which exist apart from the individual and sensible substances. They
make them, then, the same in kind as the perishable things (for this
kind of substance we know)--'man-himself' and 'horse-itself', adding
to the sensible things the word 'itself'. Yet even if we had not
seen the stars, none the less, I suppose, would they have been eternal
substances apart from those which we knew; so that now also if we do
not know what non-sensible substances there are, yet it is doubtless
necessary that there should he some.-Clearly, then, no universal
term is the name of a substance, and no substance is composed of
substances.

                                  17

    Let us state what, i.e. what kind of thing, substance should be
said to be, taking once more another starting-point; for perhaps
from this we shall get a clear view also of that substance which
exists apart from sensible substances. Since, then, substance is a
principle and a cause, let us pursue it from this starting-point.
The 'why' is always sought in this form--'why does one thing attach to
some other?' For to inquire why the musical man is a musical man, is
either to inquire--as we have said why the man is musical, or it is
something else. Now 'why a thing is itself' is a meaningless inquiry
(for (to give meaning to the question 'why') the fact or the existence
of the thing must already be evident-e.g. that the moon is
eclipsed-but the fact that a thing is itself is the single reason
and the single cause to be given in answer to all such questions as
why the man is man, or the musician musical', unless one were to
answer 'because each thing is inseparable from itself, and its being
one just meant this'; this, however, is common to all things and is
a short and easy way with the question). But we can inquire why man is
an animal of such and such a nature. This, then, is plain, that we are
not inquiring why he who is a man is a man. We are inquiring, then,
why something is predicable of something (that it is predicable must
be clear; for if not, the inquiry is an inquiry into nothing). E.g.
why does it thunder? This is the same as 'why is sound produced in the
clouds?' Thus the inquiry is about the predication of one thing of
another. And why are these things, i.e. bricks and stones, a house?
Plainly we are seeking the cause. And this is the essence (to speak
abstractly), which in some cases is the end, e.g. perhaps in the
case of a house or a bed, and in some cases is the first mover; for
this also is a cause. But while the efficient cause is sought in the
case of genesis and destruction, the final cause is sought in the case
of being also.

    The object of the inquiry is most easily overlooked where one term
is not expressly predicated of another (e.g. when we inquire 'what man
is'), because we do not distinguish and do not say definitely that
certain elements make up a certain whole. But we must articulate our
meaning before we begin to inquire; if not, the inquiry is on the
border-line between being a search for something and a search for
nothing. Since we must have the existence of the thing as something
given, clearly the question is why the matter is some definite
thing; e.g. why are these materials a house? Because that which was
the essence of a house is present. And why is this individual thing,
or this body having this form, a man? Therefore what we seek is the
cause, i.e. the form, by reason of which the matter is some definite
thing; and this is the substance of the thing. Evidently, then, in the
case of simple terms no inquiry nor teaching is possible; our attitude
towards such things is other than that of inquiry.

    Since that which is compounded out of something so that the
whole is one, not like a heap but like a syllable-now the syllable
is not its elements, ba is not the same as b and a, nor is flesh
fire and earth (for when these are separated the wholes, i.e. the
flesh and the syllable, no longer exist, but the elements of the
syllable exist, and so do fire and earth); the syllable, then, is
something-not only its elements (the vowel and the consonant) but also
something else, and the flesh is not only fire and earth or the hot
and the cold, but also something else:-if, then, that something must
itself be either an element or composed of elements, (1) if it is an
element the same argument will again apply; for flesh will consist
of this and fire and earth and something still further, so that the
process will go on to infinity. But (2) if it is a compound, clearly
it will be a compound not of one but of more than one (or else that
one will be the thing itself), so that again in this case we can use
the same argument as in the case of flesh or of the syllable. But it
would seem that this 'other' is something, and not an element, and
that it is the cause which makes this thing flesh and that a syllable.
And similarly in all other cases. And this is the substance of each
thing (for this is the primary cause of its being); and since, while
some things are not substances, as many as are substances are formed
in accordance with a nature of their own and by a process of nature,
their substance would seem to be this kind of 'nature', which is not
an element but a principle. An element, on the other hand, is that
into which a thing is divided and which is present in it as matter;
e.g. a and b are the elements of the syllable.

                                Book VIII

                                   1

    WE must reckon up the results arising from what has been said, and
compute the sum of them, and put the finishing touch to our inquiry.
We have said that the causes, principles, and elements of substances
are the object of our search. And some substances are recognized by
every one, but some have been advocated by particular schools. Those
generally recognized are the natural substances, i.e. fire, earth,
water, air, &c., the simple bodies; second plants and their parts, and
animals and the parts of animals; and finally the physical universe
and its parts; while some particular schools say that Forms and the
objects of mathematics are substances. But there are arguments which
lead to the conclusion that there are other substances, the essence
and the substratum. Again, in another way the genus seems more
substantial than the various spccies, and the universal than the
particulars. And with the universal and the genus the Ideas are
connected; it is in virtue of the same argument that they are
thought to be substances. And since the essence is substance, and
the definition is a formula of the essence, for this reason we have
discussed definition and essential predication. Since the definition
is a formula, and a formula has parts, we had to consider also with
respect to the notion of 'part', what are parts of the substance and
what are not, and whether the parts of the substance are also parts of
the definition. Further, too, neither the universal nor the genus is a
substance; we must inquire later into the Ideas and the objects of
mathematics; for some say these are substances as well as the sensible
substances.

    But now let us resume the discussion of the generally recognized
substances. These are the sensible substances, and sensible substances
all have matter. The substratum is substance, and this is in one sense
the matter (and by matter I mean that which, not being a 'this'
actually, is potentially a 'this'), and in another sense the formula
or shape (that which being a 'this' can be separately formulated), and
thirdly the complex of these two, which alone is generated and
destroyed, and is, without qualification, capable of separate
existence; for of substances completely expressible in a formula
some are separable and some are separable and some are not.

    But clearly matter also is substance; for in all the opposite
changes that occur there is something which underlies the changes,
e.g. in respect of place that which is now here and again elsewhere,
and in respect of increase that which is now of one size and again
less or greater, and in respect of alteration that which is now
healthy and again diseased; and similarly in respect of substance
there is something that is now being generated and again being
destroyed, and now underlies the process as a 'this' and again
underlies it in respect of a privation of positive character. And in
this change the others are involved. But in either one or two of the
others this is not involved; for it is not necessary if a thing has
matter for change of place that it should also have matter for
generation and destruction.

    The difference between becoming in the full sense and becoming
in a qualified sense has been stated in our physical works.

                                   2

    Since the substance which exists as underlying and as matter is
generally recognized, and this that which exists potentially, it
remains for us to say what is the substance, in the sense of
actuality, of sensible things. Democritus seems to think there are
three kinds of difference between things; the underlying body, the
matter, is one and the same, but they differ either in rhythm, i.e.
shape, or in turning, i.e. position, or in inter-contact, i.e.
order. But evidently there are many differences; for instance, some
things are characterized by the mode of composition of their matter,
e.g. the things formed by blending, such as honey-water; and others by
being bound together, e.g. bundle; and others by being glued together,
e.g. a book; and others by being nailed together, e.g. a casket; and
others in more than one of these ways; and others by position, e.g.
threshold and lintel (for these differ by being placed in a certain
way); and others by time, e.g. dinner and breakfast; and others by
place, e.g. the winds; and others by the affections proper to sensible
things, e.g. hardness and softness, density and rarity, dryness and
wetness; and some things by some of these qualities, others by them
all, and in general some by excess and some by defect. Clearly,
then, the word 'is' has just as many meanings; a thing is a
threshold because it lies in such and such a position, and its being
means its lying in that position, while being ice means having been
solidified in such and such a way. And the being of some things will
be defined by all these qualities, because some parts of them are
mixed, others are blended, others are bound together, others are
solidified, and others use the other differentiae; e.g. the hand or
the foot requires such complex definition. We must grasp, then, the
kinds of differentiae (for these will be the principles of the being
of things), e.g. the things characterized by the more and the less, or
by the dense and the rare, and by other such qualities; for all
these are forms of excess and defect. And anything that is
characterized by shape or by smoothness and roughness is characterized
by the straight and the curved. And for other things their being
will mean their being mixed, and their not being will mean the
opposite.

    It is clear, then, from these facts that, since its substance is
the cause of each thing's being, we must seek in these differentiae
what is the cause of the being of each of these things. Now none of
these differentiae is substance, even when coupled with matter, yet it
is what is analogous to substance in each case; and as in substances
that which is predicated of the matter is the actuality itself, in all
other definitions also it is what most resembles full actuality.
E.g. if we had to define a threshold, we should say 'wood or stone
in such and such a position', and a house we should define as
'bricks and timbers in such and such a position',(or a purpose may
exist as well in some cases), and if we had to define ice we should
say 'water frozen or solidified in such and such a way', and harmony
is 'such and such a blending of high and low'; and similarly in all
other cases.

    Obviously, then, the actuality or the formula is different when
the matter is different; for in some cases it is the composition, in
others the mixing, and in others some other of the attributes we
have named. And so, of the people who go in for defining, those who
define a house as stones, bricks, and timbers are speaking of the
potential house, for these are the matter; but those who propose 'a
receptacle to shelter chattels and living beings', or something of the
sort, speak of the actuality. Those who combine both of these speak of
the third kind of substance, which is composed of matter and form (for
the formula that gives the differentiae seems to be an account of
the form or actuality, while that which gives the components is rather
an account of the matter); and the same is true of the kind of
definitions which Archytas used to accept; they are accounts of the
combined form and matter. E.g. what is still weather? Absence of
motion in a large expanse of air; air is the matter, and absence of
motion is the actuality and substance. What is a calm? Smoothness of
sea; the material substratum is the sea, and the actuality or shape is
smoothness. It is obvious then, from what has been said, what sensible
substance is and how it exists-one kind of it as matter, another as
form or actuality, while the third kind is that which is composed of
these two.

                                   3

    We must not fail to notice that sometimes it is not clear
whether a name means the composite substance, or the actuality or
form, e.g. whether 'house' is a sign for the composite thing, 'a
covering consisting of bricks and stones laid thus and thus', or for
the actuality or form, 'a covering', and whether a line is 'twoness in
length' or 'twoness', and whether an animal is soul in a body' or 'a
soul'; for soul is the substance or actuality of some body. 'Animal'
might even be applied to both, not as something definable by one
formula, but as related to a single thing. But this question, while
important for another purpose, is of no importance for the inquiry
into sensible substance; for the essence certainly attaches to the
form and the actuality. For 'soul' and 'to be soul' are the same,
but 'to be man' and 'man' are not the same, unless even the bare
soul is to be called man; and thus on one interpretation the thing
is the same as its essence, and on another it is not.

    If we examine we find that the syllable does not consist of the
letters + juxtaposition, nor is the house bricks + juxtaposition.
And this is right; for the juxtaposition or mixing does not consist of
those things of which it is the juxtaposition or mixing. And the
same is true in all other cases; e.g. if the threshold is
characterized by its position, the position is not constituted by
the threshold, but rather the latter is constituted by the former. Nor
is man animal + biped, but there must be something besides these, if
these are matter,-something which is neither an element in the whole
nor a compound, but is the substance; but this people eliminate, and
state only the matter. If, then, this is the cause of the thing's
being, and if the cause of its being is its substance, they will not
be stating the substance itself.

    (This, then, must either be eternal or it must be destructible
without being ever in course of being destroyed, and must have come to
be without ever being in course of coming to be. But it has been
proved and explained elsewhere that no one makes or begets the form,
but it is the individual that is made, i.e. the complex of form and
matter that is generated. Whether the substances of destructible
things can exist apart, is not yet at all clear; except that obviously
this is impossible in some cases-in the case of things which cannot
exist apart from the individual instances, e.g. house or utensil.
Perhaps, indeed, neither these things themselves, nor any of the other
things which are not formed by nature, are substances at all; for
one might say that the nature in natural objects is the only substance
to be found in destructible things.)

    Therefore the difficulty which used to be raised by the school
of Antisthenes and other such uneducated people has a certain
timeliness. They said that the 'what' cannot be defined (for the
definition so called is a 'long rigmarole') but of what sort a
thing, e.g. silver, is, they thought it possible actually to
explain, not saying what it is, but that it is like tin. Therefore one
kind of substance can be defined and formulated, i.e. the composite
kind, whether it be perceptible or intelligible; but the primary parts
of which this consists cannot be defined, since a definitory formula
predicates something of something, and one part of the definition must
play the part of matter and the other that of form.

    It is also obvious that, if substances are in a sense numbers,
they are so in this sense and not, as some say, as numbers of units.
For a definition is a sort of number; for (1) it is divisible, and
into indivisible parts (for definitory formulae are not infinite), and
number also is of this nature. And (2) as, when one of the parts of
which a number consists has been taken from or added to the number, it
is no longer the same number, but a different one, even if it is the
very smallest part that has been taken away or added, so the
definition and the essence will no longer remain when anything has
been taken away or added. And (3) the number must be something in
virtue of which it is one, and this these thinkers cannot state,
what makes it one, if it is one (for either it is not one but a sort
of heap, or if it is, we ought to say what it is that makes one out of
many); and the definition is one, but similarly they cannot say what
makes it one. And this is a natural result; for the same reason is
applicable, and substance is one in the sense which we have explained,
and not, as some say, by being a sort of unit or point; each is a
complete reality and a definite nature. And (4) as number does not
admit of the more and the less, neither does substance, in the sense
of form, but if any substance does, it is only the substance which
involves matter. Let this, then, suffice for an account of the
generation and destruction of so-called substances in what sense it is
possible and in what sense impossible--and of the reduction of
things to number.

                                   4

    Regarding material substance we must not forget that even if all
things come from the same first cause or have the same things for
their first causes, and if the same matter serves as starting-point
for their generation, yet there is a matter proper to each, e.g. for
phlegm the sweet or the fat, and for bile the bitter, or something
else; though perhaps these come from the same original matter. And
there come to be several matters for the same thing, when the one
matter is matter for the other; e.g. phlegm comes from the fat and
from the sweet, if the fat comes from the sweet; and it comes from
bile by analysis of the bile into its ultimate matter. For one thing
comes from another in two senses, either because it will be found at a
later stage, or because it is produced if the other is analysed into
its original constituents. When the matter is one, different things
may be produced owing to difference in the moving cause; e.g. from
wood may be made both a chest and a bed. But some different things
must have their matter different; e.g. a saw could not be made of
wood, nor is this in the power of the moving cause; for it could not
make a saw of wool or of wood. But if, as a matter of fact, the same
thing can be made of different material, clearly the art, i.e. the
moving principle, is the same; for if both the matter and the moving
cause were different, the product would be so too.

    When one inquires into the cause of something, one should, since
'causes' are spoken of in several senses, state all the possible
causes. what is the material cause of man? Shall we say 'the menstrual
fluid'? What is moving cause? Shall we say 'the seed'? The formal
cause? His essence. The final cause? His end. But perhaps the latter
two are the same.-It is the proximate causes we must state. What is
the material cause? We must name not fire or earth, but the matter
peculiar to the thing.

    Regarding the substances that are natural and generable, if the
causes are really these and of this number and we have to learn the
causes, we must inquire thus, if we are to inquire rightly. But in the
case of natural but eternal substances another account must be
given. For perhaps some have no matter, or not matter of this sort but
only such as can be moved in respect of place. Nor does matter
belong to those things which exist by nature but are not substances;
their substratum is the substance. E.g what is the cause of eclipse?
What is its matter? There is none; the moon is that which suffers
eclipse. What is the moving cause which extinguished the light? The
earth. The final cause perhaps does not exist. The formal principle is
the definitory formula, but this is obscure if it does not include the
cause. E.g. what is eclipse? Deprivation of light. But if we add 'by
the earth's coming in between', this is the formula which includes the
cause. In the case of sleep it is not clear what it is that
proximately has this affection. Shall we say that it is the animal?
Yes, but the animal in virtue of what, i.e. what is the proximate
subject? The heart or some other part. Next, by what is it produced?
Next, what is the affection-that of the proximate subject, not of
the whole animal? Shall we say that it is immobility of such and
such a kind? Yes, but to what process in the proximate subject is this
due?

                                   5

    Since some things are and are not, without coming to be and
ceasing to be, e.g. points, if they can be said to be, and in
general forms (for it is not 'white' comes to be, but the wood comes
to be white, if everything that comes to be comes from something and
comes to be something), not all contraries can come from one
another, but it is in different senses that a pale man comes from a
dark man, and pale comes from dark. Nor has everything matter, but
only those things which come to be and change into one another.
Those things which, without ever being in course of changing, are or
are not, have no matter.

    There is difficulty in the question how the matter of each thing
is related to its contrary states. E.g. if the body is potentially
healthy, and disease is contrary to health, is it potentially both
healthy and diseased? And is water potentially wine and vinegar? We
answer that it is the matter of one in virtue of its positive state
and its form, and of the other in virtue of the privation of its
positive state and the corruption of it contrary to its nature. It
is also hard to say why wine is not said to be the matter of vinegar
nor potentially vinegar (though vinegar is produced from it), and
why a living man is not said to be potentially dead. In fact they
are not, but the corruptions in question are accidental, and it is the
matter of the animal that is itself in virtue of its corruption the
potency and matter of a corpse, and it is water that is the matter
of vinegar. For the corpse comes from the animal, and vinegar from
wine, as night from day. And all the things which change thus into one
another must go back to their matter; e.g. if from a corpse is
produced an animal, the corpse first goes back to its matter, and only
then becomes an animal; and vinegar first goes back to water, and only
then becomes wine.

                                   6

    To return to the difficulty which has been stated with respect
both to definitions and to numbers, what is the cause of their
unity? In the case of all things which have several parts and in which
the totality is not, as it were, a mere heap, but the whole is
something beside the parts, there is a cause; for even in bodies
contact is the cause of unity in some cases, and in others viscosity
or some other such quality. And a definition is a set of words which
is one not by being connected together, like the Iliad, but by dealing
with one object.-What then, is it that makes man one; why is he one
and not many, e.g. animal + biped, especially if there are, as some
say, an animal-itself and a biped-itself? Why are not those Forms
themselves the man, so that men would exist by participation not in
man, nor in-one Form, but in two, animal and biped, and in general man
would be not one but more than one thing, animal and biped?

    Clearly, then, if people proceed thus in their usual manner of
definition and speech, they cannot explain and solve the difficulty.
But if, as we say, one element is matter and another is form, and
one is potentially and the other actually, the question will no longer
be thought a difficulty. For this difficulty is the same as would
arise if 'round bronze' were the definition of 'cloak'; for this
word would be a sign of the definitory formula, so that the question
is, what is the cause of the unity of 'round' and 'bronze'? The
difficulty disappears, because the one is matter, the other form.
What, then, causes this-that which was potentially to be
actually-except, in the case of things which are generated, the agent?
For there is no other cause of the potential sphere's becoming
actually a sphere, but this was the essence of either. Of matter
some is intelligible, some perceptible, and in a formula there is
always an element of matter as well as one of actuality; e.g. the
circle is 'a plane figure'. But of the things which have no matter,
either intelligible or perceptible, each is by its nature
essentially a kind of unity, as it is essentially a kind of
being-individual substance, quality, or quantity (and so neither
'existent' nor 'one' is present in their definitions), and the essence
of each of them is by its very nature a kind of unity as it is a
kind of being-and so none of these has any reason outside itself,
for being one, nor for being a kind of being; for each is by its
nature a kind of being and a kind of unity, not as being in the
genus 'being' or 'one' nor in the sense that being and unity can exist
apart from particulars.

    Owing to the difficulty about unity some speak of 'participation',
and raise the question, what is the cause of participation and what is
it to participate; and others speak of 'communion', as Lycophron
says knowledge is a communion of knowing with the soul; and others say
life is a 'composition' or 'connexion' of soul with body. Yet the same
account applies to all cases; for being healthy, too, will on this
showing be either a 'communion' or a 'connexion' or a 'composition' of
soul and health, and the fact that the bronze is a triangle will be
a 'composition' of bronze and triangle, and the fact that a thing is
white will be a 'composition' of surface and whiteness. The reason
is that people look for a unifying formula, and a difference,
between potency and complete reality. But, as has been said, the
proximate matter and the form are one and the same thing, the one
potentially, and the other actually. Therefore it is like asking
what in general is the cause of unity and of a thing's being one;
for each thing is a unity, and the potential and the actual are
somehow one. Therefore there is no other cause here unless there is
something which caused the movement from potency into actuality. And
all things which have no matter are without qualification
essentially unities.

                                Book IX

                                   1

    WE have treated of that which is primarily and to which all the
other categories of being are referred-i.e. of substance. For it is in
virtue of the concept of substance that the others also are said to
be-quantity and quality and the like; for all will be found to involve
the concept of substance, as we said in the first part of our work.
And since 'being' is in one way divided into individual thing,
quality, and quantity, and is in another way distinguished in
respect of potency and complete reality, and of function, let us now
add a discussion of potency and complete reality. And first let us
explain potency in the strictest sense, which is, however, not the
most useful for our present purpose. For potency and actuality
extend beyond the cases that involve a reference to motion. But when
we have spoken of this first kind, we shall in our discussions of
actuality' explain the other kinds of potency as well.

    We have pointed out elsewhere that 'potency' and the word 'can'
have several senses. Of these we may neglect all the potencies that
are so called by an equivocation. For some are called so by analogy,
as in geometry we say one thing is or is not a 'power' of another by
virtue of the presence or absence of some relation between them. But
all potencies that conform to the same type are originative sources of
some kind, and are called potencies in reference to one primary kind
of potency, which is an originative source of change in another
thing or in the thing itself qua other. For one kind is a potency of
being acted on, i.e. the originative source, in the very thing acted
on, of its being passively changed by another thing or by itself qua
other; and another kind is a state of insusceptibility to change for
the worse and to destruction by another thing or by the thing itself
qua other by virtue of an originative source of change. In all these
definitions is implied the formula if potency in the primary
sense.-And again these so-called potencies are potencies either of
merely acting or being acted on, or of acting or being acted on
well, so that even in the formulae of the latter the formulae of the
prior kinds of potency are somehow implied.

    Obviously, then, in a sense the potency of acting and of being
acted on is one (for a thing may be 'capable' either because it can
itself be acted on or because something else can be acted on by it),
but in a sense the potencies are different. For the one is in the
thing acted on; it is because it contains a certain originative
source, and because even the matter is an originative source, that the
thing acted on is acted on, and one thing by one, another by
another; for that which is oily can be burnt, and that which yields in
a particular way can be crushed; and similarly in all other cases. But
the other potency is in the agent, e.g. heat and the art of building
are present, one in that which can produce heat and the other in the
man who can build. And so, in so far as a thing is an organic unity,
it cannot be acted on by itself; for it is one and not two different
things. And 'impotence'and 'impotent' stand for the privation which is
contrary to potency of this sort, so that every potency belongs to the
same subject and refers to the same process as a corresponding
impotence. Privation has several senses; for it means (1) that which
has not a certain quality and (2) that which might naturally have it
but has not it, either (a) in general or (b) when it might naturally
have it, and either (a) in some particular way, e.g. when it has not
it completely, or (b) when it has not it at all. And in certain
cases if things which naturally have a quality lose it by violence, we
say they have suffered privation.

                                   2

    Since some such originative sources are present in soulless
things, and others in things possessed of soul, and in soul, and in
the rational part of the soul, clearly some potencies will, be
non-rational and some will be non-rational and some will be
accompanied by a rational formula. This is why all arts, i.e. all
productive forms of knowledge, are potencies; they are originative
sources of change in another thing or in the artist himself considered
as other.

    And each of those which are accompanied by a rational formula is
alike capable of contrary effects, but one non-rational power produces
one effect; e.g. the hot is capable only of heating, but the medical
art can produce both disease and health. The reason is that science is
a rational formula, and the same rational formula explains a thing and
its privation, only not in the same way; and in a sense it applies
to both, but in a sense it applies rather to the positive fact.
Therefore such sciences must deal with contraries, but with one in
virtue of their own nature and with the other not in virtue of their
nature; for the rational formula applies to one object in virtue of
that object's nature, and to the other, in a sense, accidentally.
For it is by denial and removal that it exhibits the contrary; for the
contrary is the primary privation, and this is the removal of the
positive term. Now since contraries do not occur in the same thing,
but science is a potency which depends on the possession of a rational
formula, and the soul possesses an originative source of movement;
therefore, while the wholesome produces only health and the
calorific only heat and the frigorific only cold, the scientific man
produces both the contrary effects. For the rational formula is one
which applies to both, though not in the same way, and it is in a soul
which possesses an originative source of movement; so that the soul
will start both processes from the same originative source, having
linked them up with the same thing. And so the things whose potency is
according to a rational formula act contrariwise to the things whose
potency is non-rational; for the products of the former are included
under one originative source, the rational formula.

    It is obvious also that the potency of merely doing a thing or
having it done to one is implied in that of doing it or having it done
well, but the latter is not always implied in the former: for he who
does a thing well must also do it, but he who does it merely need
not also do it well.

                                   3

    There are some who say, as the Megaric school does, that a thing
'can' act only when it is acting, and when it is not acting it
'cannot' act, e.g. that he who is not building cannot build, but
only he who is building, when he is building; and so in all other
cases. It is not hard to see the absurdities that attend this view.

    For it is clear that on this view a man will not be a builder
unless he is building (for to be a builder is to be able to build),
and so with the other arts. If, then, it is impossible to have such
arts if one has not at some time learnt and acquired them, and it is
then impossible not to have them if one has not sometime lost them
(either by forgetfulness or by some accident or by time; for it cannot
be by the destruction of the object, for that lasts for ever), a man
will not have the art when he has ceased to use it, and yet he may
immediately build again; how then will he have got the art? And
similarly with regard to lifeless things; nothing will be either
cold or hot or sweet or perceptible at all if people are not
perceiving it; so that the upholders of this view will have to
maintain the doctrine of Protagoras. But, indeed, nothing will even
have perception if it is not perceiving, i.e. exercising its
perception. If, then, that is blind which has not sight though it
would naturally have it, when it would naturally have it and when it
still exists, the same people will be blind many times in the
day-and deaf too.

    Again, if that which is deprived of potency is incapable, that
which is not happening will be incapable of happening; but he who says
of that which is incapable of happening either that it is or that it
will be will say what is untrue; for this is what incapacity meant.
Therefore these views do away with both movement and becoming. For
that which stands will always stand, and that which sits will always
sit, since if it is sitting it will not get up; for that which, as
we are told, cannot get up will be incapable of getting up. But we
cannot say this, so that evidently potency and actuality are different
(but these views make potency and actuality the same, and so it is
no small thing they are seeking to annihilate), so that it is possible
that a thing may be capable of being and not he, and capable of not
being and yet he, and similarly with the other kinds of predicate;
it may be capable of walking and yet not walk, or capable of not
walking and yet walk. And a thing is capable of doing something if
there will be nothing impossible in its having the actuality of that
of which it is said to have the capacity. I mean, for instance, if a
thing is capable of sitting and it is open to it to sit, there will be
nothing impossible in its actually sitting; and similarly if it is
capable of being moved or moving, or of standing or making to stand,
or of being or coming to be, or of not being or not coming to be.

    The word 'actuality', which we connect with 'complete reality',
has, in the main, been extended from movements to other things; for
actuality in the strict sense is thought to be identical with
movement. And so people do not assign movement to non-existent things,
though they do assign some other predicates. E.g. they say that
non-existent things are objects of thought and desire, but not that
they are moved; and this because, while ex hypothesi they do not
actually exist, they would have to exist actually if they were
moved. For of non-existent things some exist potentially; but they
do not exist, because they do not exist in complete reality.

                                   4

    If what we have described is identical with the capable or
convertible with it, evidently it cannot be true to say 'this is
capable of being but will not be', which would imply that the things
incapable of being would on this showing vanish. Suppose, for
instance, that a man-one who did not take account of that which is
incapable of being-were to say that the diagonal of the square is
capable of being measured but will not be measured, because a thing
may well be capable of being or coming to be, and yet not be or be
about to be. But from the premisses this necessarily follows, that
if we actually supposed that which is not, but is capable of being, to
be or to have come to be, there will be nothing impossible in this;
but the result will be impossible, for the measuring of the diagonal
is impossible. For the false and the impossible are not the same; that
you are standing now is false, but that you should be standing is
not impossible.

    At the same time it is clear that if, when A is real, B must be
real, then, when A is possible, B also must be possible. For if B need
not be possible, there is nothing to prevent its not being possible.
Now let A be supposed possible. Then, when A was possible, we agreed
that nothing impossible followed if A were supposed to be real; and
then B must of course be real. But we supposed B to be impossible. Let
it be impossible then. If, then, B is impossible, A also must be so.
But the first was supposed impossible; therefore the second also is
impossible. If, then, A is possible, B also will be possible, if
they were so related that if A,is real, B must be real. If, then, A
and B being thus related, B is not possible on this condition, and B
will not be related as was supposed. And if when A is possible, B must
be possible, then if A is real, B also must be real. For to say that B
must be possible, if A is possible, means this, that if A is real both
at the time when and in the way in which it was supposed capable of
being real, B also must then and in that way be real.

                                   5

    As all potencies are either innate, like the senses, or come by
practice, like the power of playing the flute, or by learning, like
artistic power, those which come by practice or by rational formula we
must acquire by previous exercise but this is not necessary with those
which are not of this nature and which imply passivity.

    Since that which is 'capable' is capable of something and at
some time in some way (with all the other qualifications which must be
present in the definition), and since some things can produce change
according to a rational formula and their potencies involve such a
formula, while other things are nonrational and their potencies are
non-rational, and the former potencies must be in a living thing,
while the latter can be both in the living and in the lifeless; as
regards potencies of the latter kind, when the agent and the patient
meet in the way appropriate to the potency in question, the one must
act and the other be acted on, but with the former kind of potency
this is not necessary. For the nonrational potencies are all
productive of one effect each, but the rational produce contrary
effects, so that if they produced their effects necessarily they would
produce contrary effects at the same time; but this is impossible.
There must, then, be something else that decides; I mean by this,
desire or will. For whichever of two things the animal desires
decisively, it will do, when it is present, and meets the passive
object, in the way appropriate to the potency in question. Therefore
everything which has a rational potency, when it desires that for
which it has a potency and in the circumstances in which it has the
potency, must do this. And it has the potency in question when the
passive object is present and is in a certain state; if not it will
not be able to act. (To add the qualification 'if nothing external
prevents it' is not further necessary; for it has the potency on the
terms on which this is a potency of acting, and it is this not in
all circumstances but on certain conditions, among which will be the
exclusion of external hindrances; for these are barred by some of
the positive qualifications.) And so even if one has a rational
wish, or an appetite, to do two things or contrary things at the
same time, one will not do them; for it is not on these terms that one
has the potency for them, nor is it a potency of doing both at the
same time, since one will do the things which it is a potency of
doing, on the terms on which one has the potency.

                                   6

    Since we have treated of the kind of potency which is related to
movement, let us discuss actuality-what, and what kind of thing,
actuality is. For in the course of our analysis it will also become
clear, with regard to the potential, that we not only ascribe
potency to that whose nature it is to move something else, or to be
moved by something else, either without qualification or in some
particular way, but also use the word in another sense, which is the
reason of the inquiry in the course of which we have discussed these
previous senses also. Actuality, then, is the existence of a thing not
in the way which we express by 'potentially'; we say that potentially,
for instance, a statue of Hermes is in the block of wood and the
half-line is in the whole, because it might be separated out, and we
call even the man who is not studying a man of science, if he is
capable of studying; the thing that stands in contrast to each of
these exists actually. Our meaning can be seen in the particular cases
by induction, and we must not seek a definition of everything but be
content to grasp the analogy, that it is as that which is building
is to that which is capable of building, and the waking to the
sleeping, and that which is seeing to that which has its eyes shut but
has sight, and that which has been shaped out of the matter to the
matter, and that which has been wrought up to the unwrought. Let
actuality be defined by one member of this antithesis, and the
potential by the other. But all things are not said in the same
sense to exist actually, but only by analogy-as A is in B or to B, C
is in D or to D; for some are as movement to potency, and the others
as substance to some sort of matter.

    But also the infinite and the void and all similar things are said
to exist potentially and actually in a different sense from that which
applies to many other things, e.g. to that which sees or walks or is
seen. For of the latter class these predicates can at some time be
also truly asserted without qualification; for the seen is so called
sometimes because it is being seen, sometimes because it is capable of
being seen. But the infinite does not exist potentially in the sense
that it will ever actually have separate existence; it exists
potentially only for knowledge. For the fact that the process of
dividing never comes to an end ensures that this activity exists
potentially, but not that the infinite exists separately.

    Since of the actions which have a limit none is an end but all are
relative to the end, e.g. the removing of fat, or fat-removal, and the
bodily parts themselves when one is making them thin are in movement
in this way (i.e. without being already that at which the movement
aims), this is not an action or at least not a complete one (for it is
not an end); but that movement in which the end is present is an
action. E.g. at the same time we are seeing and have seen, are
understanding and have understood, are thinking and have thought
(while it is not true that at the same time we are learning and have
learnt, or are being cured and have been cured). At the same time we
are living well and have lived well, and are happy and have been
happy. If not, the process would have had sometime to cease, as the
process of making thin ceases: but, as things are, it does not
cease; we are living and have lived. Of these processes, then, we must
call the one set movements, and the other actualities. For every
movement is incomplete-making thin, learning, walking, building; these
are movements, and incomplete at that. For it is not true that at
the same time a thing is walking and has walked, or is building and
has built, or is coming to be and has come to be, or is being moved
and has been moved, but what is being moved is different from what has
been moved, and what is moving from what has moved. But it is the same
thing that at the same time has seen and is seeing, seeing, or is
thinking and has thought. The latter sort of process, then, I call
an actuality, and the former a movement.

                                   7

    What, and what kind of thing, the actual is, may be taken as
explained by these and similar considerations. But we must distinguish
when a thing exists potentially and when it does not; for it is not at
any and every time. E.g. is earth potentially a man? No-but rather
when it has already become seed, and perhaps not even then. It is just
as it is with being healed; not everything can be healed by the
medical art or by luck, but there is a certain kind of thing which
is capable of it, and only this is potentially healthy. And (1) the
delimiting mark of that which as a result of thought comes to exist in
complete reality from having existed potentially is that if the
agent has willed it it comes to pass if nothing external hinders,
while the condition on the other side-viz. in that which is
healed-is that nothing in it hinders the result. It is on similar
terms that we have what is potentially a house; if nothing in the
thing acted on-i.e. in the matter-prevents it from becoming a house,
and if there is nothing which must be added or taken away or
changed, this is potentially a house; and the same is true of all
other things the source of whose becoming is external. And (2) in
the cases in which the source of the becoming is in the very thing
which comes to be, a thing is potentially all those things which it
will be of itself if nothing external hinders it. E.g. the seed is not
yet potentially a man; for it must be deposited in something other
than itself and undergo a change. But when through its own motive
principle it has already got such and such attributes, in this state
it is already potentially a man; while in the former state it needs
another motive principle, just as earth is not yet potentially a
statue (for it must first change in order to become brass.)

    It seems that when we call a thing not something else but
'thaten'-e.g. a casket is not 'wood' but 'wooden', and wood is not
'earth' but 'earthen', and again earth will illustrate our point if it
is similarly not something else but 'thaten'-that other thing is
always potentially (in the full sense of that word) the thing which
comes after it in this series. E.g. a casket is not 'earthen' nor
'earth', but 'wooden'; for this is potentially a casket and this is
the matter of a casket, wood in general of a casket in general, and
this particular wood of this particular casket. And if there is a
first thing, which is no longer, in reference to something else,
called 'thaten', this is prime matter; e.g. if earth is 'airy' and air
is not 'fire' but 'fiery', fire is prime matter, which is not a
'this'. For the subject or substratum is differentiated by being a
'this' or not being one; i.e. the substratum of modifications is, e.g.
a man, i.e. a body and a soul, while the modification is 'musical'
or 'pale'. (The subject is called, when music comes to be present in
it, not 'music' but 'musical', and the man is not 'paleness' but
'pale', and not 'ambulation' or 'movement' but 'walking' or
'moving',-which is akin to the 'thaten'.) Wherever this is so, then,
the ultimate subject is a substance; but when this is not so but the
predicate is a form and a 'this', the ultimate subject is matter and
material substance. And it is only right that 'thaten' should be
used with reference both to the matter and to the accidents; for
both are indeterminates.

    We have stated, then, when a thing is to be said to exist
potentially and when it is not.

                                   8

    From our discussion of the various senses of 'prior', it is
clear that actuality is prior to potency. And I mean by potency not
only that definite kind which is said to be a principle of change in
another thing or in the thing itself regarded as other, but in general
every principle of movement or of rest. For nature also is in the same
genus as potency; for it is a principle of movement-not, however, in
something else but in the thing itself qua itself. To all such
potency, then, actuality is prior both in formula and in
substantiality; and in time it is prior in one sense, and in another
not.

    (1) Clearly it is prior in formula; for that which is in the
primary sense potential is potential because it is possible for it
to become active; e.g. I mean by 'capable of building' that which
can build, and by 'capable of seeing' that which can see, and by
'visible' that which can be seen. And the same account applies to
all other cases, so that the formula and the knowledge of the one must
precede the knowledge of the other.

    (2) In time it is prior in this sense: the actual which is
identical in species though not in number with a potentially
existing thing is to it. I mean that to this particular man who now
exists actually and to the corn and to the seeing subject the matter
and the seed and that which is capable of seeing, which are
potentially a man and corn and seeing, but not yet actually so, are
prior in time; but prior in time to these are other actually
existing things, from which they were produced. For from the
potentially existing the actually existing is always produced by an
actually existing thing, e.g. man from man, musician by musician;
there is always a first mover, and the mover already exists
actually. We have said in our account of substance that everything
that is produced is something produced from something and by
something, and that the same in species as it.

    This is why it is thought impossible to be a builder if one has
built nothing or a harper if one has never played the harp; for he who
learns to play the harp learns to play it by playing it, and all other
learners do similarly. And thence arose the sophistical quibble,
that one who does not possess a science will be doing that which is
the object of the science; for he who is learning it does not
possess it. But since, of that which is coming to be, some part must
have come to be, and, of that which, in general, is changing, some
part must have changed (this is shown in the treatise on movement), he
who is learning must, it would seem, possess some part of the science.
But here too, then, it is clear that actuality is in this sense
also, viz. in order of generation and of time, prior to potency.

    But (3) it is also prior in substantiality; firstly, (a) because
the things that are posterior in becoming are prior in form and in
substantiality (e.g. man is prior to boy and human being to seed;
for the one already has its form, and the other has not), and
because everything that comes to be moves towards a principle, i.e. an
end (for that for the sake of which a thing is, is its principle,
and the becoming is for the sake of the end), and the actuality is the
end, and it is for the sake of this that the potency is acquired.
For animals do not see in order that they may have sight, but they
have sight that they may see. And similarly men have the art of
building that they may build, and theoretical science that they may
theorize; but they do not theorize that they may have theoretical
science, except those who are learning by practice; and these do not
theorize except in a limited sense, or because they have no need to
theorize. Further, matter exists in a potential state, just because it
may come to its form; and when it exists actually, then it is in its
form. And the same holds good in all cases, even those in which the
end is a movement. And so, as teachers think they have achieved
their end when they have exhibited the pupil at work, nature does
likewise. For if this is not the case, we shall have Pauson's Hermes
over again, since it will be hard to say about the knowledge, as about
the figure in the picture, whether it is within or without. For the
action is the end, and the actuality is the action. And so even the
word 'actuality' is derived from 'action', and points to the
complete reality.

    And while in some cases the exercise is the ultimate thing (e.g.
in sight the ultimate thing is seeing, and no other product besides
this results from sight), but from some things a product follows (e.g.
from the art of building there results a house as well as the act of
building), yet none the less the act is in the former case the end and
in the latter more of an end than the potency is. For the act of
building is realized in the thing that is being built, and comes to
be, and is, at the same time as the house.

    Where, then, the result is something apart from the exercise,
the actuality is in the thing that is being made, e.g. the act of
building is in the thing that is being built and that of weaving in
the thing that is being woven, and similarly in all other cases, and
in general the movement is in the thing that is being moved; but where
there is no product apart from the actuality, the actuality is present
in the agents, e.g. the act of seeing is in the seeing subject and
that of theorizing in the theorizing subject and the life is in the
soul (and therefore well-being also; for it is a certain kind of
life).

    Obviously, therefore, the substance or form is actuality.
According to this argument, then, it is obvious that actuality is
prior in substantial being to potency; and as we have said, one
actuality always precedes another in time right back to the
actuality of the eternal prime mover.

    But (b) actuality is prior in a stricter sense also; for eternal
things are prior in substance to perishable things, and no eternal
thing exists potentially. The reason is this. Every potency is at
one and the same time a potency of the opposite; for, while that which
is not capable of being present in a subject cannot be present,
everything that is capable of being may possibly not be actual.
That, then, which is capable of being may either be or not be; the
same thing, then, is capable both of being and of not being. And
that which is capable of not being may possibly not be; and that which
may possibly not be is perishable, either in the full sense, or in the
precise sense in which it is said that it possibly may not be, i.e. in
respect either of place or of quantity or quality; 'in the full sense'
means 'in respect of substance'. Nothing, then, which is in the full
sense imperishable is in the full sense potentially existent (though
there is nothing to prevent its being so in some respect, e.g.
potentially of a certain quality or in a certain place); all
imperishable things, then, exist actually. Nor can anything which is
of necessity exist potentially; yet these things are primary; for if
these did not exist, nothing would exist. Nor does eternal movement,
if there be such, exist potentially; and, if there is an eternal
mobile, it is not in motion in virtue of a potentiality, except in
respect of 'whence' and 'whither' (there is nothing to prevent its
having matter which makes it capable of movement in various
directions). And so the sun and the stars and the whole heaven are
ever active, and there is no fear that they may sometime stand
still, as the natural philosophers fear they may. Nor do they tire
in this activity; for movement is not for them, as it is for
perishable things, connected with the potentiality for opposites, so
that the continuity of the movement should be laborious; for it is
that kind of substance which is matter and potency, not actuality,
that causes this.

    Imperishable things are imitated by those that are involved in
change, e.g. earth and fire. For these also are ever active; for
they have their movement of themselves and in themselves. But the
other potencies, according to our previous discussion, are all
potencies for opposites; for that which can move another in this way
can also move it not in this way, i.e. if it acts according to a
rational formula; and the same non-rational potencies will produce
opposite results by their presence or absence.

    If, then, there are any entities or substances such as the
dialecticians say the Ideas are, there must be something much more
scientific than science-itself and something more mobile than
movement-itself; for these will be more of the nature of
actualities, while science-itself and movement-itself are potencies
for these.

    Obviously, then, actuality is prior both to potency and to every
principle of change.

                                   9

    That the actuality is also better and more valuable than the
good potency is evident from the following argument. Everything of
which we say that it can do something, is alike capable of contraries,
e.g. that of which we say that it can be well is the same as that
which can be ill, and has both potencies at once; for the same potency
is a potency of health and illness, of rest and motion, of building
and throwing down, of being built and being thrown down. The
capacity for contraries, then, is present at the same time; but
contraries cannot be present at the same time, and the actualities
also cannot be present at the same time, e.g. health and illness.
Therefore, while the good must be one of them, the capacity is both
alike, or neither; the actuality, then, is better. Also in the case of
bad things the end or actuality must be worse than the potency; for
that which 'can' is both contraries alike. Clearly, then, the bad does
not exist apart from bad things; for the bad is in its nature
posterior to the potency. And therefore we may also say that in the
things which are from the beginning, i.e. in eternal things, there
is nothing bad, nothing defective, nothing perverted (for perversion
is something bad).

    It is an activity also that geometrical constructions are
discovered; for we find them by dividing. If the figures had been
already divided, the constructions would have been obvious; but as
it is they are present only potentially. Why are the angles of the
triangle equal to two right angles? Because the angles about one point
are equal to two right angles. If, then, the line parallel to the side
had been already drawn upwards, the reason would have been evident
to any one as soon as he saw the figure. Why is the angle in a
semicircle in all cases a right angle? If three lines are equal the
two which form the base, and the perpendicular from the centre-the
conclusion is evident at a glance to one who knows the former
proposition. Obviously, therefore, the potentially existing
constructions are discovered by being brought to actuality; the reason
is that the geometer's thinking is an actuality; so that the potency
proceeds from an actuality; and therefore it is by making
constructions that people come to know them (though the single
actuality is later in generation than the corresponding potency).
(See diagram.)

                                  10

    The terms 'being' and 'non-being' are employed firstly with
reference to the categories, and secondly with reference to the
potency or actuality of these or their non-potency or nonactuality,
and thirdly in the sense of true and false. This depends, on the
side of the objects, on their being combined or separated, so that
he who thinks the separated to be separated and the combined to be
combined has the truth, while he whose thought is in a state
contrary to that of the objects is in error. This being so, when is
what is called truth or falsity present, and when is it not? We must
consider what we mean by these terms. It is not because we think truly
that you are pale, that you are pale, but because you are pale we
who say this have the truth. If, then, some things are always combined
and cannot be separated, and others are always separated and cannot be
combined, while others are capable either of combination or of
separation, 'being' is being combined and one, and 'not being' is
being not combined but more than one. Regarding contingent facts,
then, the same opinion or the same statement comes to be false and
true, and it is possible for it to be at one time correct and at
another erroneous; but regarding things that cannot be otherwise
opinions are not at one time true and at another false, but the same
opinions are always true or always false.

    But with regard to incomposites, what is being or not being, and
truth or falsity? A thing of this sort is not composite, so as to 'be'
when it is compounded, and not to 'be' if it is separated, like
'that the wood is white' or 'that the diagonal is incommensurable';
nor will truth and falsity be still present in the same way as in
the previous cases. In fact, as truth is not the same in these
cases, so also being is not the same; but (a) truth or falsity is as
follows--contact and assertion are truth (assertion not being the same
as affirmation), and ignorance is non-contact. For it is not
possible to be in error regarding the question what a thing is, save
in an accidental sense; and the same holds good regarding
non-composite substances (for it is not possible to be in error
about them). And they all exist actually, not potentially; for
otherwise they would have come to be and ceased to be; but, as it
is, being itself does not come to be (nor cease to be); for if it
had done so it would have had to come out of something. About the
things, then, which are essences and actualities, it is not possible
to be in error, but only to know them or not to know them. But we do
inquire what they are, viz. whether they are of such and such a nature
or not.

    (b) As regards the 'being' that answers to truth and the
'non-being' that answers to falsity, in one case there is truth if the
subject and the attribute are really combined, and falsity if they are
not combined; in the other case, if the object is existent it exists
in a particular way, and if it does not exist in this way does not
exist at all. And truth means knowing these objects, and falsity
does not exist, nor error, but only ignorance-and not an ignorance
which is like blindness; for blindness is akin to a total absence of
the faculty of thinking.

    It is evident also that about unchangeable things there can be
no error in respect of time, if we assume them to be unchangeable.
E.g. if we suppose that the triangle does not change, we shall not
suppose that at one time its angles are equal to two right angles
while at another time they are not (for that would imply change). It
is possible, however, to suppose that one member of such a class has a
certain attribute and another has not; e.g. while we may suppose
that no even number is prime, we may suppose that some are and some
are not. But regarding a numerically single number not even this
form of error is possible; for we cannot in this case suppose that one
instance has an attribute and another has not, but whether our
judgement be true or false, it is implied that the fact is eternal.

                                Book X

                                   1

    WE have said previously, in our distinction of the various
meanings of words, that 'one' has several meanings; the things that
are directly and of their own nature and not accidentally called one
may be summarized under four heads, though the word is used in more
senses. (1) There is the continuous, either in general, or
especially that which is continuous by nature and not by contact nor
by being together; and of these, that has more unity and is prior,
whose movement is more indivisible and simpler. (2) That which is a
whole and has a certain shape and form is one in a still higher
degree; and especially if a thing is of this sort by nature, and not
by force like the things which are unified by glue or nails or by
being tied together, i.e. if it has in itself the cause of its
continuity. A thing is of this sort because its movement is one and
indivisible in place and time; so that evidently if a thing has by
nature a principle of movement that is of the first kind (i.e. local
movement) and the first in that kind (i.e. circular movement), this is
in the primary sense one extended thing. Some things, then, are one in
this way, qua continuous or whole, and the other things that are one
are those whose definition is one. Of this sort are the things the
thought of which is one, i.e. those the thought of which is
indivisible; and it is indivisible if the thing is indivisible in kind
or in number. (3) In number, then, the individual is indivisible,
and (4) in kind, that which in intelligibility and in knowledge is
indivisible, so that that which causes substances to be one must be
one in the primary sense. 'One', then, has all these meanings-the
naturally continuous and the whole, and the individual and the
universal. And all these are one because in some cases the movement,
in others the thought or the definition is indivisible.

    But it must be observed that the questions, what sort of things
are said to be one, and what it is to be one and what is the
definition of it, should not be assumed to be the same. 'One' has
all these meanings, and each of the things to which one of these kinds
of unity belongs will be one; but 'to be one' will sometimes mean
being one of these things, and sometimes being something else which is
even nearer to the meaning of the word 'one' while these other
things approximate to its application. This is also true of
'element' or 'cause', if one had both to specify the things of which
it is predicable and to render the definition of the word. For in a
sense fire is an element (and doubtless also 'the indefinite' or
something else of the sort is by its own nature the element), but in a
sense it is not; for it is not the same thing to be fire and to be
an element, but while as a particular thing with a nature of its own
fire is an element, the name 'element' means that it has this
attribute, that there is something which is made of it as a primary
constituent. And so with 'cause' and 'one' and all such terms. For
this reason, too, 'to be one' means 'to be indivisible, being
essentially one means a "this" and capable of being isolated either in
place, or in form or thought'; or perhaps 'to be whole and
indivisible'; but it means especially 'to be the first measure of a
kind', and most strictly of quantity; for it is from this that it
has been extended to the other categories. For measure is that by
which quantity is known; and quantity qua quantity is known either
by a 'one' or by a number, and all number is known by a 'one'.
Therefore all quantity qua quantity is known by the one, and that by
which quantities are primarily known is the one itself; and so the one
is the starting-point of number qua number. And hence in the other
classes too 'measure' means that by which each is first known, and the
measure of each is a unit-in length, in breadth, in depth, in
weight, in speed. (The words 'weight' and 'speed' are common to both
contraries; for each of them has two meanings-'weight' means both that
which has any amount of gravity and that which has an excess of
gravity, and 'speed' both that which has any amount of movement and
that which has an excess of movement; for even the slow has a
certain speed and the comparatively light a certain weight.)

    In all these, then, the measure and starting-point is something
one and indivisible, since even in lines we treat as indivisible the
line a foot long. For everywhere we seek as the measure something
one and indivisible; and this is that which is simple either in
quality or in quantity. Now where it is thought impossible to take
away or to add, there the measure is exact (hence that of number is
most exact; for we posit the unit as indivisible in every respect);
but in all other cases we imitate this sort of measure. For in the
case of a furlong or a talent or of anything comparatively large any
addition or subtraction might more easily escape our notice than in
the case of something smaller; so that the first thing from which,
as far as our perception goes, nothing can be subtracted, all men make
the measure, whether of liquids or of solids, whether of weight or
of size; and they think they know the quantity when they know it by
means of this measure. And indeed they know movement too by the simple
movement and the quickest; for this occupies least time. And so in
astronomy a 'one' of this sort is the starting-point and measure
(for they assume the movement of the heavens to be uniform and the
quickest, and judge the others by reference to it), and in music the
quarter-tone (because it is the least interval), and in speech the
letter. And all these are ones in this sense--not that 'one' is
something predicable in the same sense of all of these, but in the
sense we have mentioned.

    But the measure is not always one in number--sometimes there are
several; e.g. the quarter-tones (not to the ear, but as determined
by the ratios) are two, and the articulate sounds by which we
measure are more than one, and the diagonal of the square and its side
are measured by two quantities, and all spatial magnitudes reveal
similar varieties of unit. Thus, then, the one is the measure of all
things, because we come to know the elements in the substance by
dividing the things either in respect of quantity or in respect of
kind. And the one is indivisible just because the first of each
class of things is indivisible. But it is not in the same way that
every 'one' is indivisible e.g. a foot and a unit; the latter is
indivisible in every respect, while the former must be placed among
things which are undivided to perception, as has been said
already-only to perception, for doubtless every continuous thing is
divisible.

    The measure is always homogeneous with the thing measured; the
measure of spatial magnitudes is a spatial magnitude, and in
particular that of length is a length, that of breadth a breadth, that
of articulate sound an articulate sound, that of weight a weight, that
of units a unit. (For we must state the matter so, and not say that
the measure of numbers is a number; we ought indeed to say this if
we were to use the corresponding form of words, but the claim does not
really correspond-it is as if one claimed that the measure of units is
units and not a unit; number is a plurality of units.)

    Knowledge, also, and perception, we call the measure of things for
the same reason, because we come to know something by them-while as
a matter of fact they are measured rather than measure other things.
But it is with us as if some one else measured us and we came to
know how big we are by seeing that he applied the cubit-measure to
such and such a fraction of us. But Protagoras says 'man is the
measure of all things', as if he had said 'the man who knows' or
'the man who perceives'; and these because they have respectively
knowledge and perception, which we say are the measures of objects.
Such thinkers are saying nothing, then, while they appear to be saying
something remarkable.

    Evidently, then, unity in the strictest sense, if we define it
according to the meaning of the word, is a measure, and most
properly of quantity, and secondly of quality. And some things will be
one if they are indivisible in quantity, and others if they are
indivisible in quality; and so that which is one is indivisible,
either absolutely or qua one.

                                   2

    With regard to the substance and nature of the one we must ask
in which of two ways it exists. This is the very question that we
reviewed in our discussion of problems, viz. what the one is and how
we must conceive of it, whether we must take the one itself as being a
substance (as both the Pythagoreans say in earlier and Plato in
later times), or there is, rather, an underlying nature and the one
should be described more intelligibly and more in the manner of the
physical philosophers, of whom one says the one is love, another
says it is air, and another the indefinite.

    If, then, no universal can be a substance, as has been said our
discussion of substance and being, and if being itself cannot be a
substance in the sense of a one apart from the many (for it is
common to the many), but is only a predicate, clearly unity also
cannot be a substance; for being and unity are the most universal of
all predicates. Therefore, on the one hand, genera are not certain
entities and substances separable from other things; and on the
other hand the one cannot be a genus, for the same reasons for which
being and substance cannot be genera.

    Further, the position must be similar in all the kinds of unity.
Now 'unity' has just as many meanings as 'being'; so that since in the
sphere of qualities the one is something definite-some particular kind
of thing-and similarly in the sphere of quantities, clearly we must in
every category ask what the one is, as we must ask what the existent
is, since it is not enough to say that its nature is just to be one or
existent. But in colours the one is a colour, e.g. white, and then the
other colours are observed to be produced out of this and black, and
black is the privation of white, as darkness of light. Therefore if
all existent things were colours, existent things would have been a
number, indeed, but of what? Clearly of colours; and the 'one' would
have been a particular 'one', i.e. white. And similarly if all
existing things were tunes, they would have been a number, but a
number of quarter-tones, and their essence would not have been number;
and the one would have been something whose substance was not to be
one but to be the quarter-tone. And similarly if all existent things
had been articulate sounds, they would have been a number of
letters, and the one would have been a vowel. And if all existent
things were rectilinear figures, they would have been a number of
figures, and the one would have been the triangle. And the same
argument applies to all other classes. Since, therefore, while there
are numbers and a one both in affections and in qualities and in
quantities and in movement, in all cases the number is a number of
particular things and the one is one something, and its substance is
not just to be one, the same must be true of substances also; for it
is true of all cases alike.

    That the one, then, in every class is a definite thing, and in
no case is its nature just this, unity, is evident; but as in
colours the one-itself which we must seek is one colour, so too in
substance the one-itself is one substance. That in a sense unity means
the same as being is clear from the facts that its meanings correspond
to the categories one to one, and it is not comprised within any
category (e.g. it is comprised neither in 'what a thing is' nor in
quality, but is related to them just as being is); that in 'one man'
nothing more is predicated than in 'man' (just as being is nothing
apart from substance or quality or quantity); and that to be one is
just to be a particular thing.

                                   3

    The one and the many are opposed in several ways, of which one
is the opposition of the one and plurality as indivisible and
divisible; for that which is either divided or divisible is called a
plurality, and that which is indivisible or not divided is called one.
Now since opposition is of four kinds, and one of these two terms is
privative in meaning, they must be contraries, and neither
contradictory nor correlative in meaning. And the one derives its name
and its explanation from its contrary, the indivisible from the
divisible, because plurality and the divisible is more perceptible
than the indivisible, so that in definition plurality is prior to
the indivisible, because of the conditions of perception.

    To the one belong, as we indicated graphically in our
distinction of the contraries, the same and the like and the equal,
and to plurality belong the other and the unlike and the unequal. 'The
same' has several meanings; (1) we sometimes mean 'the same
numerically'; again, (2) we call a thing the same if it is one both in
definition and in number, e.g. you are one with yourself both in
form and in matter; and again, (3) if the definition of its primary
essence is one; e.g. equal straight lines are the same, and so are
equal and equal-angled quadrilaterals; there are many such, but in
these equality constitutes unity.

    Things are like if, not being absolutely the same, nor without
difference in respect of their concrete substance, they are the same
in form; e.g. the larger square is like the smaller, and unequal
straight lines are like; they are like, but not absolutely the same.
Other things are like, if, having the same form, and being things in
which difference of degree is possible, they have no difference of
degree. Other things, if they have a quality that is in form one and
same-e.g. whiteness-in a greater or less degree, are called like
because their form is one. Other things are called like if the
qualities they have in common are more numerous than those in which
they differ-either the qualities in general or the prominent
qualities; e.g. tin is like silver, qua white, and gold is like
fire, qua yellow and red.

    Evidently, then, 'other' and 'unlike' also have several
meanings. And the other in one sense is the opposite of the same (so
that everything is either the same as or other than everything
else). In another sense things are other unless both their matter
and their definition are one (so that you are other than your
neighbour). The other in the third sense is exemplified in the objects
of mathematics. 'Other or the same' can therefore be predicated of
everything with regard to everything else-but only if the things are
one and existent, for 'other' is not the contradictory of 'the
same'; which is why it is not predicated of non-existent things (while
'not the same' is so predicated). It is predicated of all existing
things; for everything that is existent and one is by its very
nature either one or not one with anything else.

    The other, then, and the same are thus opposed. But difference
is not the same as otherness. For the other and that which it is other
than need not be other in some definite respect (for everything that
is existent is either other or the same), but that which is
different is different from some particular thing in some particular
respect, so that there must be something identical whereby they
differ. And this identical thing is genus or species; for everything
that differs differs either in genus or in species, in genus if the
things have not their matter in common and are not generated out of
each other (i.e. if they belong to different figures of
predication), and in species if they have the same genus ('genus'
meaning that identical thing which is essentially predicated of both
the different things).

    Contraries are different, and contrariety is a kind of difference.
That we are right in this supposition is shown by induction. For all
of these too are seen to be different; they are not merely other,
but some are other in genus, and others are in the same line of
predication, and therefore in the same genus, and the same in genus.
We have distinguished elsewhere what sort of things are the same or
other in genus.

                                   4

    Since things which differ may differ from one another more or
less, there is also a greatest difference, and this I call
contrariety. That contrariety is the greatest difference is made clear
by induction. For things which differ in genus have no way to one
another, but are too far distant and are not comparable; and for
things that differ in species the extremes from which generation takes
place are the contraries, and the distance between extremes-and
therefore that between the contraries-is the greatest.

    But surely that which is greatest in each class is complete. For
that is greatest which cannot be exceeded, and that is complete beyond
which nothing can be found. For the complete difference marks the
end of a series (just as the other things which are called complete
are so called because they have attained an end), and beyond the end
there is nothing; for in everything it is the extreme and includes all
else, and therefore there is nothing beyond the end, and the
complete needs nothing further. From this, then, it is clear that
contrariety is complete difference; and as contraries are so called in
several senses, their modes of completeness will answer to the various
modes of contrariety which attach to the contraries.

    This being so, it is clear that one thing have more than one
contrary (for neither can there be anything more extreme than the
extreme, nor can there be more than two extremes for the one
interval), and, to put the matter generally, this is clear if
contrariety is a difference, and if difference, and therefore also the
complete difference, must be between two things.

    And the other commonly accepted definitions of contraries are also
necessarily true. For not only is (1) the complete difference the
greatest difference (for we can get no difference beyond it of
things differing either in genus or in species; for it has been
shown that there is no 'difference' between anything and the things
outside its genus, and among the things which differ in species the
complete difference is the greatest); but also (2) the things in the
same genus which differ most are contrary (for the complete difference
is the greatest difference between species of the same genus); and (3)
the things in the same receptive material which differ most are
contrary (for the matter is the same for contraries); and (4) of the
things which fall under the same faculty the most different are
contrary (for one science deals with one class of things, and in these
the complete difference is the greatest).

    The primary contrariety is that between positive state and
privation-not every privation, however (for 'privation' has several
meanings), but that which is complete. And the other contraries must
be called so with reference to these, some because they possess these,
others because they produce or tend to produce them, others because
they are acquisitions or losses of these or of other contraries. Now
if the kinds of opposition are contradiction and privation and
contrariety and relation, and of these the first is contradiction, and
contradiction admits of no intermediate, while contraries admit of
one, clearly contradiction and contrariety are not the same. But
privation is a kind of contradiction; for what suffers privation,
either in general or in some determinate way, either that which is
quite incapable of having some attribute or that which, being of
such a nature as to have it, has it not; here we have already a
variety of meanings, which have been distinguished elsewhere.
Privation, therefore, is a contradiction or incapacity which is
determinate or taken along with the receptive material. This is the
reason why, while contradiction does not admit of an intermediate,
privation sometimes does; for everything is equal or not equal, but
not everything is equal or unequal, or if it is, it is only within the
sphere of that which is receptive of equality. If, then, the
comings-to-be which happen to the matter start from the contraries,
and proceed either from the form and the possession of the form or
from a privation of the form or shape, clearly all contrariety must be
privation, but presumably not all privation is contrariety (the reason
being that that has suffered privation may have suffered it in several
ways); for it is only the extremes from which changes proceed that are
contraries.

    And this is obvious also by induction. For every contrariety
involves, as one of its terms, a privation, but not all cases are
alike; inequality is the privation of equality and unlikeness of
likeness, and on the other hand vice is the privation of virtue. But
the cases differ in a way already described; in one case we mean
simply that the thing has suffered privation, in another case that
it has done so either at a certain time or in a certain part (e.g.
at a certain age or in the dominant part), or throughout. This is
why in some cases there is a mean (there are men who are neither
good nor bad), and in others there is not (a number must be either odd
or even). Further, some contraries have their subject defined,
others have not. Therefore it is evident that one of the contraries is
always privative; but it is enough if this is true of the first-i.e.
the generic-contraries, e.g. the one and the many; for the others
can be reduced to these.

                                   5

    Since one thing has one contrary, we might raise the question
how the one is opposed to the many, and the equal to the great and the
small. For if we used the word 'whether' only in an antithesis such as
'whether it is white or black', or 'whether it is white or not
white' (we do not ask 'whether it is a man or white'), unless we are
proceeding on a prior assumption and asking something such as 'whether
it was Cleon or Socrates that came' as this is not a necessary
disjunction in any class of things; yet even this is an extension from
the case of opposites; for opposites alone cannot be present together;
and we assume this incompatibility here too in asking which of the two
came; for if they might both have come, the question would have been
absurd; but if they might, even so this falls just as much into an
antithesis, that of the 'one or many', i.e. 'whether both came or
one of the two':-if, then, the question 'whether' is always
concerned with opposites, and we can ask 'whether it is greater or
less or equal', what is the opposition of the equal to the other
two? It is not contrary either to one alone or to both; for why should
it be contrary to the greater rather than to the less? Further, the
equal is contrary to the unequal. Therefore if it is contrary to the
greater and the less, it will be contrary to more things than one. But
if the unequal means the same as both the greater and the less
together, the equal will be opposite to both (and the difficulty
supports those who say the unequal is a 'two'), but it follows that
one thing is contrary to two others, which is impossible. Again, the
equal is evidently intermediate between the great and the small, but
no contrariety is either observed to be intermediate, or, from its
definition, can be so; for it would not be complete if it were
intermediate between any two things, but rather it always has
something intermediate between its own terms.

    It remains, then, that it is opposed either as negation or as
privation. It cannot be the negation or privation of one of the two;
for why of the great rather than of the small? It is, then, the
privative negation of both. This is why 'whether' is said with
reference to both, not to one of the two (e.g. 'whether it is
greater or equal' or 'whether it is equal or less'); there are
always three cases. But it is not a necessary privation; for not
everything which is not greater or less is equal, but only the
things which are of such a nature as to have these attributes.

    The equal, then, is that which is neither great nor small but is
naturally fitted to be either great or small; and it is opposed to
both as a privative negation (and therefore is also intermediate). And
that which is neither good nor bad is opposed to both, but has no
name; for each of these has several meanings and the recipient subject
is not one; but that which is neither white nor black has more claim
to unity. Yet even this has not one name, though the colours of
which this negation is privatively predicated are in a way limited;
for they must be either grey or yellow or something else of the
kind. Therefore it is an incorrect criticism that is passed by those
who think that all such phrases are used in the same way, so that that
which is neither a shoe nor a hand would be intermediate between a
shoe and a hand, since that which is neither good nor bad is
intermediate between the good and the bad-as if there must be an
intermediate in all cases. But this does not necessarily follow. For
the one phrase is a joint denial of opposites between which there is
an intermediate and a certain natural interval; but between the
other two there is no 'difference'; for the things, the denials of
which are combined, belong to different classes, so that the
substratum is not one.

                                   6

    We might raise similar questions about the one and the many. For
if the many are absolutely opposed to the one, certain impossible
results follow. One will then be few, whether few be treated here as
singular or plural; for the many are opposed also to the few. Further,
two will be many, since the double is multiple and 'double' derives
its meaning from 'two'; therefore one will be few; for what is that in
comparison with which two are many, except one, which must therefore
be few? For there is nothing fewer. Further, if the much and the
little are in plurality what the long and the short are in length, and
whatever is much is also many, and the many are much (unless,
indeed, there is a difference in the case of an easily-bounded
continuum), the little (or few) will be a plurality. Therefore one
is a plurality if it is few; and this it must be, if two are many. But
perhaps, while the 'many' are in a sense said to be also 'much', it is
with a difference; e.g. water is much but not many. But 'many' is
applied to the things that are divisible; in the one sense it means
a plurality which is excessive either absolutely or relatively
(while 'few' is similarly a plurality which is deficient), and in
another sense it means number, in which sense alone it is opposed to
the one. For we say 'one or many', just as if one were to say 'one and
ones' or 'white thing and white things', or to compare the things that
have been measured with the measure. It is in this sense also that
multiples are so called. For each number is said to be many because it
consists of ones and because each number is measurable by one; and
it is 'many' as that which is opposed to one, not to the few. In
this sense, then, even two is many-not, however, in the sense of a
plurality which is excessive either relatively or absolutely; it is
the first plurality. But without qualification two is few; for it is
first plurality which is deficient (for this reason Anaxagoras was not
right in leaving the subject with the statement that 'all things
were together, boundless both in plurality and in smallness'-where for
'and in smallness' he should have said 'and in fewness'; for they
could not have been boundless in fewness), since it is not one, as
some say, but two, that make a few.

    The one is opposed then to the many in numbers as measure to thing
measurable; and these are opposed as are the relatives which are not
from their very nature relatives. We have distinguished elsewhere
the two senses in which relatives are so called:-(1) as contraries;
(2) as knowledge to thing known, a term being called relative
because another is relative to it. There is nothing to prevent one
from being fewer than something, e.g. than two; for if one is fewer,
it is not therefore few. Plurality is as it were the class to which
number belongs; for number is plurality measurable by one, and one and
number are in a sense opposed, not as contrary, but as we have said
some relative terms are opposed; for inasmuch as one is measure and
the other measurable, they are opposed. This is why not everything
that is one is a number; i.e. if the thing is indivisible it is not
a number. But though knowledge is similarly spoken of as relative to
the knowable, the relation does not work out similarly; for while
knowledge might be thought to be the measure, and the knowable the
thing measured, the fact that all knowledge is knowable, but not all
that is knowable is knowledge, because in a sense knowledge is
measured by the knowable.-Plurality is contrary neither to the few
(the many being contrary to this as excessive plurality to plurality
exceeded), nor to the one in every sense; but in the one sense these
are contrary, as has been said, because the former is divisible and
the latter indivisible, while in another sense they are relative as
knowledge is to knowable, if plurality is number and the one is a
measure.

                                   7

    Since contraries admit of an intermediate and in some cases have
it, intermediates must be composed of the contraries. For (1) all
intermediates are in the same genus as the things between which they
stand. For we call those things intermediates, into which that which
changes must change first; e.g. if we were to pass from the highest
string to the lowest by the smallest intervals, we should come
sooner to the intermediate notes, and in colours if we were to pass
from white to black, we should come sooner to crimson and grey than to
black; and similarly in all other cases. But to change from one
genus to another genus is not possible except in an incidental way, as
from colour to figure. Intermediates, then, must be in the same
genus both as one another and as the things they stand between.

    But (2) all intermediates stand between opposites of some kind;
for only between these can change take place in virtue of their own
nature (so that an intermediate is impossible between things which are
not opposite; for then there would be change which was not from one
opposite towards the other). Of opposites, contradictories admit of no
middle term; for this is what contradiction is-an opposition, one or
other side of which must attach to anything whatever, i.e. which has
no intermediate. Of other opposites, some are relative, others
privative, others contrary. Of relative terms, those which are not
contrary have no intermediate; the reason is that they are not in
the same genus. For what intermediate could there be between knowledge
and knowable? But between great and small there is one.

    (3) If intermediates are in the same genus, as has been shown, and
stand between contraries, they must be composed of these contraries.
For either there will be a genus including the contraries or there
will be none. And if (a) there is to be a genus in such a way that
it is something prior to the contraries, the differentiae which
constituted the contrary species-of-a-genus will be contraries prior
to the species; for species are composed of the genus and the
differentiae. (E.g. if white and black are contraries, and one is a
piercing colour and the other a compressing colour, these
differentiae-'piercing' and 'compressing'-are prior; so that these are
prior contraries of one another.) But, again, the species which differ
contrariwise are the more truly contrary species. And the
other.species, i.e. the intermediates, must be composed of their genus
and their differentiae. (E.g. all colours which are between white
and black must be said to be composed of the genus, i.e. colour, and
certain differentiae. But these differentiae will not be the primary
contraries; otherwise every colour would be either white or black.
They are different, then, from the primary contraries; and therefore
they will be between the primary contraries; the primary
differentiae are 'piercing' and 'compressing'.)

    Therefore it is (b) with regard to these contraries which do not
fall within a genus that we must first ask of what their intermediates
are composed. (For things which are in the same genus must be composed
of terms in which the genus is not an element, or else be themselves
incomposite.) Now contraries do not involve one another in their
composition, and are therefore first principles; but the intermediates
are either all incomposite, or none of them. But there is something
compounded out of the contraries, so that there can be a change from a
contrary to it sooner than to the other contrary; for it will have
less of the quality in question than the one contrary and more than
the other. This also, then, will come between the contraries. All
the other intermediates also, therefore, are composite; for that which
has more of a quality than one thing and less than another is
compounded somehow out of the things than which it is said to have
more and less respectively of the quality. And since there are no
other things prior to the contraries and homogeneous with the
intermediates, all intermediates must be compounded out of the
contraries. Therefore also all the inferior classes, both the
contraries and their intermediates, will be compounded out of the
primary contraries. Clearly, then, intermediates are (1) all in the
same genus and (2) intermediate between contraries, and (3) all
compounded out of the contraries.

                                   8

    That which is other in species is other than something in
something, and this must belong to both; e.g. if it is an animal other
in species, both are animals. The things, then, which are other in
species must be in the same genus. For by genus I mean that one
identical thing which is predicated of both and is differentiated in
no merely accidental way, whether conceived as matter or otherwise.
For not only must the common nature attach to the different things,
e.g. not only must both be animals, but this very animality must
also be different for each (e.g. in the one case equinity, in the
other humanity), and so this common nature is specifically different
for each from what it is for the other. One, then, will be in virtue
of its own nature one sort of animal, and the other another, e.g.
one a horse and the other a man. This difference, then, must be an
otherness of the genus. For I give the name of 'difference in the
genus' an otherness which makes the genus itself other.

    This, then, will be a contrariety (as can be shown also by
induction). For all things are divided by opposites, and it has been
proved that contraries are in the same genus. For contrariety was seen
to be complete difference; and all difference in species is a
difference from something in something; so that this is the same for
both and is their genus. (Hence also all contraries which are
different in species and not in genus are in the same line of
predication, and other than one another in the highest degree-for
the difference is complete-, and cannot be present along with one
another.) The difference, then, is a contrariety.

    This, then, is what it is to be 'other in species'-to have a
contrariety, being in the same genus and being indivisible (and
those things are the same in species which have no contrariety,
being indivisible); we say 'being indivisible', for in the process
of division contrarieties arise in the intermediate stages before we
come to the indivisibles. Evidently, therefore, with reference to that
which is called the genus, none of the species-of-a-genus is either
the same as it or other than it in species (and this is fitting; for
the matter is indicated by negation, and the genus is the matter of
that of which it is called the genus, not in the sense in which we
speak of the genus or family of the Heraclidae, but in that in which
the genus is an element in a thing's nature), nor is it so with
reference to things which are not in the same genus, but it will
differ in genus from them, and in species from things in the same
genus. For a thing's difference from that from which it differs in
species must be a contrariety; and this belongs only to things in
the same genus.

                                   9

    One might raise the question, why woman does not differ from man
in species, when female and male are contrary and their difference
is a contrariety; and why a female and a male animal are not different
in species, though this difference belongs to animal in virtue of
its own nature, and not as paleness or darkness does; both 'female'
and 'male' belong to it qua animal. This question is almost the same
as the other, why one contrariety makes things different in species
and another does not, e.g. 'with feet' and 'with wings' do, but
paleness and darkness do not. Perhaps it is because the former are
modifications peculiar to the genus, and the latter are less so. And
since one element is definition and one is matter, contrarieties which
are in the definition make a difference in species, but those which
are in the thing taken as including its matter do not make one. And so
paleness in a man, or darkness, does not make one, nor is there a
difference in species between the pale man and the dark man, not
even if each of them be denoted by one word. For man is here being
considered on his material side, and matter does not create a
difference; for it does not make individual men species of man, though
the flesh and the bones of which this man and that man consist are
other. The concrete thing is other, but not other in species,
because in the definition there is no contrariety. This is the
ultimate indivisible kind. Callias is definition + matter, the pale
man, then, is so also, because it is the individual Callias that is
pale; man, then, is pale only incidentally. Neither do a brazen and
a wooden circle, then, differ in species; and if a brazen triangle and
a wooden circle differ in species, it is not because of the matter,
but because there is a contrariety in the definition. But does the
matter not make things other in species, when it is other in a certain
way, or is there a sense in which it does? For why is this horse other
than this man in species, although their matter is included with their
definitions? Doubtless because there is a contrariety in the
definition. For while there is a contrariety also between pale man and
dark horse, and it is a contrariety in species, it does not depend
on the paleness of the one and the darkness of the other, since even
if both had been pale, yet they would have been other in species.
But male and female, while they are modifications peculiar to
'animal', are so not in virtue of its essence but in the matter, ie.
the body. This is why the same seed becomes female or male by being
acted on in a certain way. We have stated, then, what it is to be
other in species, and why some things differ in species and others
do not.

                                  10

    Since contraries are other in form, and the perishable and the
imperishable are contraries (for privation is a determinate
incapacity), the perishable and the imperishable must be different
in kind.

    Now so far we have spoken of the general terms themselves, so that
it might be thought not to be necessary that every imperishable
thing should be different from every perishable thing in form, just as
not every pale thing is different in form from every dark thing. For
the same thing can be both, and even at the same time if it is a
universal (e.g. man can be both pale and dark), and if it is an
individual it can still be both; for the same man can be, though not
at the same time, pale and dark. Yet pale is contrary to dark.

      But while some contraries belong to certain things by accident
(e.g. both those now mentioned and many others), others cannot, and
among these are 'perishable' and 'imperishable'. For nothing is by
accident perishable. For what is accidental is capable of not being
present, but perishableness is one of the attributes that belong of
necessity to the things to which they belong; or else one and the same
thing may be perishable and imperishable, if perishableness is capable
of not belonging to it. Perishableness then must either be the essence
or be present in the essence of each perishable thing. The same
account holds good for imperishableness also; for both are
attributes which are present of necessity. The characteristics,
then, in respect of which and in direct consequence of which one thing
is perishable and another imperishable, are opposite, so that the
things must be different in kind.

    Evidently, then, there cannot be Forms such as some maintain,
for then one man would be perishable and another imperishable. Yet the
Forms are said to be the same in form with the individuals and not
merely to have the same name; but things which differ in kind are
farther apart than those which differ in form.

                                Book XI

                                   1

    THAT Wisdom is a science of first principles is evident from the
introductory chapters, in which we have raised objections to the
statements of others about the first principles; but one might ask the
question whether Wisdom is to be conceived as one science or as
several. If as one, it may be objected that one science always deals
with contraries, but the first principles are not contrary. If it is
not one, what sort of sciences are those with which it is to be
identified?

    Further, is it the business of one science, or of more than one,
to examine the first principles of demonstration? If of one, why of
this rather than of any other? If of more, what sort of sciences
must these be said to be?

    Further, does Wisdom investigate all substances or not? If not
all, it is hard to say which; but if, being one, it investigates
them all, it is doubtful how the same science can embrace several
subject-matters.

    Further, does it deal with substances only or also with their
attributes? If in the case of attributes demonstration is possible, in
that of substances it is not. But if the two sciences are different,
what is each of them and which is Wisdom? If we think of it as
demonstrative, the science of the attributes is Wisdom, but if as
dealing with what is primary, the science of substances claims the
tide.

    But again the science we are looking for must not be supposed to
deal with the causes which have been mentioned in the Physics. For (A)
it does not deal with the final cause (for that is the nature of the
good, and this is found in the field of action and movement; and it is
the first mover-for that is the nature of the end-but in the case of
things unmovable there is nothing that moved them first), and (B) in
general it is hard to say whether perchance the science we are now
looking for deals with perceptible substances or not with them, but
with certain others. If with others, it must deal either with the
Forms or with the objects of mathematics. Now (a) evidently the
Forms do not exist. (But it is hard to say, even if one suppose them
to exist, why in the world the same is not true of the other things of
which there are Forms, as of the objects of mathematics. I mean that
these thinkers place the objects of mathematics between the Forms
and perceptible things, as a kind of third set of things apart both
from the Forms and from the things in this world; but there is not a
third man or horse besides the ideal and the individuals. If on the
other hand it is not as they say, with what sort of things must the
mathematician be supposed to deal? Certainly not with the things in
this world; for none of these is the sort of thing which the
mathematical sciences demand.) Nor (b) does the science which we are
now seeking treat of the objects of mathematics; for none of them
can exist separately. But again it does not deal with perceptible
substances; for they are perishable.

    In general one might raise the question, to what kind of science
it belongs to discuss the difficulties about the matter of the objects
of mathematics. Neither to physics (because the whole inquiry of the
physicist is about the things that have in themselves a principle.
of movement and rest), nor yet to the science which inquires into
demonstration and science; for this is just the subject which it
investigates. It remains then that it is the philosophy which we
have set before ourselves that treats of those subjects.

    One might discuss the question whether the science we are
seeking should be said to deal with the principles which are by some
called elements; all men suppose these to be present in composite
things. But it might be thought that the science we seek should
treat rather of universals; for every definition and every science
is of universals and not of infimae species, so that as far as this
goes it would deal with the highest genera. These would turn out to be
being and unity; for these might most of all be supposed to contain
all things that are, and to be most like principles because they are
by nature; for if they perish all other things are destroyed with
them; for everything is and is one. But inasmuch as, if one is to
suppose them to be genera, they must be predicable of their
differentiae, and no genus is predicable of any of its differentiae,
in this way it would seem that we should not make them genera nor
principles. Further, if the simpler is more of a principle than the
less simple, and the ultimate members of the genus are simpler than
the genera (for they are indivisible, but the genera are divided
into many and differing species), the species might seem to be the
principles, rather than the genera. But inasmuch as the species are
involved in the destruction of the genera, the genera are more like
principles; for that which involves another in its destruction is a
principle of it. These and others of the kind are the subjects that
involve difficulties.

                                   2

    Further, must we suppose something apart from individual things,
or is it these that the science we are seeking treats of? But these
are infinite in number. Yet the things that are apart from the
individuals are genera or species; but the science we now seek
treats of neither of these. The reason why this is impossible has been
stated. Indeed, it is in general hard to say whether one must assume
that there is a separable substance besides the sensible substances
(i.e. the substances in this world), or that these are the real things
and Wisdom is concerned with them. For we seem to seek another kind of
substance, and this is our problem, i.e. to see if there is
something which can exist apart by itself and belongs to no sensible
thing.-Further, if there is another substance apart from and
corresponding to sensible substances, which kinds of sensible
substance must be supposed to have this corresponding to them? Why
should one suppose men or horses to have it, more than either the
other animals or even all lifeless things? On the other hand to set up
other and eternal substances equal in number to the sensible and
perishable substances would seem to fall beyond the bounds of
probability.-But if the principle we now seek is not separable from
corporeal things, what has a better claim to the name matter? This,
however, does not exist in actuality, but exists in potency. And it
would seem rather that the form or shape is a more important principle
than this; but the form is perishable, so that there is no eternal
substance at all which can exist apart and independent. But this is
paradoxical; for such a principle and substance seems to exist and
is sought by nearly all the most refined thinkers as something that
exists; for how is there to be order unless there is something eternal
and independent and permanent?

    Further, if there is a substance or principle of such a nature
as that which we are now seeking, and if this is one for all things,
and the same for eternal and for perishable things, it is hard to
say why in the world, if there is the same principle, some of the
things that fall under the principle are eternal, and others are not
eternal; this is paradoxical. But if there is one principle of
perishable and another of eternal things, we shall be in a like
difficulty if the principle of perishable things, as well as that of
eternal, is eternal; for why, if the principle is eternal, are not the
things that fall under the principle also eternal? But if it is
perishable another principle is involved to account for it, and
another to account for that, and this will go on to infinity.

    If on the other hand we are to set up what are thought to be the
most unchangeable principles, being and unity, firstly, if each of
these does not indicate a 'this' or substance, how will they be
separable and independent? Yet we expect the eternal and primary
principles to be so. But if each of them does signify a 'this' or
substance, all things that are are substances; for being is predicated
of all things (and unity also of some); but that all things that are
are substance is false. Further, how can they be right who say that
the first principle is unity and this is substance, and generate
number as the first product from unity and from matter, assert that
number is substance? How are we to think of 'two', and each of the
other numbers composed of units, as one? On this point neither do they
say anything nor is it easy to say anything. But if we are to
suppose lines or what comes after these (I mean the primary
surfaces) to be principles, these at least are not separable
substances, but sections and divisions-the former of surfaces, the
latter of bodies (while points are sections and divisions of lines);
and further they are limits of these same things; and all these are in
other things and none is separable. Further, how are we to suppose
that there is a substance of unity and the point? Every substance
comes into being by a gradual process, but a point does not; for the
point is a division.

    A further difficulty is raised by the fact that all knowledge is
of universals and of the 'such', but substance is not a universal, but
is rather a 'this'-a separable thing, so that if there is knowledge
about the first principles, the question arises, how are we to suppose
the first principle to be substance?

    Further, is there anything apart from the concrete thing (by which
I mean the matter and that which is joined with it), or not? If not,
we are met by the objection that all things that are in matter are
perishable. But if there is something, it must be the form or shape.
Now it is hard to determine in which cases this exists apart and in
which it does not; for in some cases the form is evidently not
separable, e.g. in the case of a house.

    Further, are the principles the same in kind or in number? If they
are one in number, all things will be the same.

                                   3

    Since the science of the philosopher treats of being qua being
universally and not in respect of a part of it, and 'being' has many
senses and is not used in one only, it follows that if the word is
used equivocally and in virtue of nothing common to its various
uses, being does not fall under one science (for the meanings of an
equivocal term do not form one genus); but if the word is used in
virtue of something common, being will fall under one science. The
term seems to be used in the way we have mentioned, like 'medical' and
'healthy'. For each of these also we use in many senses. Terms are
used in this way by virtue of some kind of reference, in the one
case to medical science, in the other to health, in others to
something else, but in each case to one identical concept. For a
discussion and a knife are called medical because the former
proceeds from medical science, and the latter is useful to it. And a
thing is called healthy in a similar way; one thing because it is
indicative of health, another because it is productive of it. And
the same is true in the other cases. Everything that is, then, is said
to 'be' in this same way; each thing that is is said to 'be' because
it is a modification of being qua being or a permanent or a
transient state or a movement of it, or something else of the sort.
And since everything that is may be referred to something single and
common, each of the contrarieties also may be referred to the first
differences and contrarieties of being, whether the first
differences of being are plurality and unity, or likeness and
unlikeness, or some other differences; let these be taken as already
discussed. It makes no difference whether that which is be referred to
being or to unity. For even if they are not the same but different, at
least they are convertible; for that which is one is also somehow
being, and that which is being is one.

    But since every pair of contraries falls to be examined by one and
the same science, and in each pair one term is the privative of the
other though one might regarding some contraries raise the question,
how they can be privately related, viz. those which have an
intermediate, e.g. unjust and just-in all such cases one must maintain
that the privation is not of the whole definition, but of the infima
species. if the just man is 'by virtue of some permanent disposition
obedient to the laws', the unjust man will not in every case have
the whole definition denied of him, but may be merely 'in some respect
deficient in obedience to the laws', and in this respect the privation
will attach to him; and similarly in all other cases.

    As the mathematician investigates abstractions (for before
beginning his investigation he strips off all the sensible
qualities, e.g. weight and lightness, hardness and its contrary, and
also heat and cold and the other sensible contrarieties, and leaves
only the quantitative and continuous, sometimes in one, sometimes in
two, sometimes in three dimensions, and the attributes of these qua
quantitative and continuous, and does not consider them in any other
respect, and examines the relative positions of some and the
attributes of these, and the commensurabilities and
incommensurabilities of others, and the ratios of others; but yet we
posit one and the same science of all these things--geometry)--the
same is true with regard to being. For the attributes of this in so
far as it is being, and the contrarieties in it qua being, it is the
business of no other science than philosophy to investigate; for to
physics one would assign the study of things not qua being, but rather
qua sharing in movement; while dialectic and sophistic deal with the
attributes of things that are, but not of things qua being, and not
with being itself in so far as it is being; therefore it remains
that it is the philosopher who studies the things we have named, in so
far as they are being. Since all that is is to 'be' in virtue of
something single and common, though the term has many meanings, and
contraries are in the same case (for they are referred to the first
contrarieties and differences of being), and things of this sort can
fall under one science, the difficulty we stated at the beginning
appears to be solved,-I mean the question how there can be a single
science of things which are many and different in genus.

                                   4

    Since even the mathematician uses the common axioms only in a
special application, it must be the business of first philosophy to
examine the principles of mathematics also. That when equals are taken
from equals the remainders are equal, is common to all quantities, but
mathematics studies a part of its proper matter which it has detached,
e.g. lines or angles or numbers or some other kind of quantity-not,
however, qua being but in so far as each of them is continuous in
one or two or three dimensions; but philosophy does not inquire
about particular subjects in so far as each of them has some attribute
or other, but speculates about being, in so far as each particular
thing is.-Physics is in the same position as mathematics; for
physics studies the attributes and the principles of the things that
are, qua moving and not qua being (whereas the primary science, we
have said, deals with these, only in so far as the underlying subjects
are existent, and not in virtue of any other character); and so both
physics and mathematics must be classed as parts of Wisdom.

                                   5

    There is a principle in things, about which we cannot be deceived,
but must always, on the contrary recognize the truth,-viz. that the
same thing cannot at one and the same time be and not be, or admit any
other similar pair of opposites. About such matters there is no
proof in the full sense, though there is proof ad hominem. For it is
not possible to infer this truth itself from a more certain principle,
yet this is necessary if there is to be completed proof of it in the
full sense. But he who wants to prove to the asserter of opposites
that he is wrong must get from him an admission which shall be
identical with the principle that the same thing cannot be and not
be at one and the same time, but shall not seem to be identical; for
thus alone can his thesis be demonstrated to the man who asserts
that opposite statements can be truly made about the same subject.
Those, then, who are to join in argument with one another must to some
extent understand one another; for if this does not happen how are
they to join in argument with one another? Therefore every word must
be intelligible and indicate something, and not many things but only
one; and if it signifies more than one thing, it must be made plain to
which of these the word is being applied. He, then, who says 'this
is and is not' denies what he affirms, so that what the word
signifies, he says it does not signify; and this is impossible.
Therefore if 'this is' signifies something, one cannot truly assert
its contradictory.

    Further, if the word signifies something and this is asserted
truly, this connexion must be necessary; and it is not possible that
that which necessarily is should ever not be; it is not possible
therefore to make the opposed affirmations and negations truly of
the same subject. Further, if the affirmation is no more true than the
negation, he who says 'man' will be no more right than he who says
'not-man'. It would seem also that in saying the man is not a horse
one would be either more or not less right than in saying he is not
a man, so that one will also be right in saying that the same person
is a horse; for it was assumed to be possible to make opposite
statements equally truly. It follows then that the same person is a
man and a horse, or any other animal.

    While, then, there is no proof of these things in the full
sense, there is a proof which may suffice against one who will make
these suppositions. And perhaps if one had questioned Heraclitus
himself in this way one might have forced him to confess that opposite
statements can never be true of the same subjects. But, as it is, he
adopted this opinion without understanding what his statement
involves. But in any case if what is said by him is true, not even
this itself will be true-viz. that the same thing can at one and the
same time both be and not be. For as, when the statements are
separated, the affirmation is no more true than the negation, in the
same way-the combined and complex statement being like a single
affirmation-the whole taken as an affirmation will be no more true
than the negation. Further, if it is not possible to affirm anything
truly, this itself will be false-the assertion that there is no true
affirmation. But if a true affirmation exists, this appears to
refute what is said by those who raise such objections and utterly
destroy rational discourse.

                                   6

    The saying of Protagoras is like the views we have mentioned; he
said that man is the measure of all things, meaning simply that that
which seems to each man also assuredly is. If this is so, it follows
that the same thing both is and is not, and is bad and good, and
that the contents of all other opposite statements are true, because
often a particular thing appears beautiful to some and the contrary of
beautiful to others, and that which appears to each man is the
measure. This difficulty may be solved by considering the source of
this opinion. It seems to have arisen in some cases from the
doctrine of the natural philosophers, and in others from the fact that
all men have not the same views about the same things, but a
particular thing appears pleasant to some and the contrary of pleasant
to others.

    That nothing comes to be out of that which is not, but
everything out of that which is, is a dogma common to nearly all the
natural philosophers. Since, then, white cannot come to be if the
perfectly white and in no respect not-white existed before, that which
becomes white must come from that which is not white; so that it
must come to be out of that which is not (so they argue), unless the
same thing was at the beginning white and not-white. But it is not
hard to solve this difficulty; for we have said in our works on
physics in what sense things that come to be come to be from that
which is not, and in what sense from that which is.

    But to attend equally to the opinions and the fancies of disputing
parties is childish; for clearly one of them must be mistaken. And
this is evident from what happens in respect of sensation; for the
same thing never appears sweet to some and the contrary of sweet to
others, unless in the one case the sense-organ which discriminates the
aforesaid flavours has been perverted and injured. And if this is so
the one party must be taken to be the measure, and the other must not.
And say the same of good and bad, and beautiful and ugly, and all
other such qualities. For to maintain the view we are opposing is just
like maintaining that the things that appear to people who put their
finger under their eye and make the object appear two instead of one
must be two (because they appear to be of that number) and again one
(for to those who do not interfere with their eye the one object
appears one).

    In general, it is absurd to make the fact that the things of
this earth are observed to change and never to remain in the same
state, the basis of our judgement about the truth. For in pursuing the
truth one must start from the things that are always in the same state
and suffer no change. Such are the heavenly bodies; for these do not
appear to be now of one nature and again of another, but are
manifestly always the same and share in no change.

    Further, if there is movement, there is also something moved,
and everything is moved out of something and into something; it
follows that that that which is moved must first be in that out of
which it is to be moved, and then not be in it, and move into the
other and come to be in it, and that the contradictory statements
are not true at the same time, as these thinkers assert they are.

    And if the things of this earth continuously flow and move in
respect of quantity-if one were to suppose this, although it is not
true-why should they not endure in respect of quality? For the
assertion of contradictory statements about the same thing seems to
have arisen largely from the belief that the quantity of bodies does
not endure, which, our opponents hold, justifies them in saying that
the same thing both is and is not four cubits long. But essence
depends on quality, and this is of determinate nature, though quantity
is of indeterminate.

    Further, when the doctor orders people to take some particular
food, why do they take it? In what respect is 'this is bread' truer
than 'this is not bread'? And so it would make no difference whether
one ate or not. But as a matter of fact they take the food which is
ordered, assuming that they know the truth about it and that it is
bread. Yet they should not, if there were no fixed constant nature
in sensible things, but all natures moved and flowed for ever.

    Again, if we are always changing and never remain the same, what
wonder is it if to us, as to the sick, things never appear the same?
(For to them also, because they are not in the same condition as
when they were well, sensible qualities do not appear alike; yet,
for all that, the sensible things themselves need not share in any
change, though they produce different, and not identical, sensations
in the sick. And the same must surely happen to the healthy if the
afore-said change takes place.) But if we do not change but remain the
same, there will be something that endures.

    As for those to whom the difficulties mentioned are suggested by
reasoning, it is not easy to solve the difficulties to their
satisfaction, unless they will posit something and no longer demand
a reason for it; for it is only thus that all reasoning and all
proof is accomplished; if they posit nothing, they destroy
discussion and all reasoning. Therefore with such men there is no
reasoning. But as for those who are perplexed by the traditional
difficulties, it is easy to meet them and to dissipate the causes of
their perplexity. This is evident from what has been said.

    It is manifest, therefore, from these arguments that contradictory
statements cannot be truly made about the same subject at one time,
nor can contrary statements, because every contrariety depends on
privation. This is evident if we reduce the definitions of
contraries to their principle.

    Similarly, no intermediate between contraries can be predicated of
one and the same subject, of which one of the contraries is
predicated. If the subject is white we shall be wrong in saying it
is neither black nor white, for then it follows that it is and is
not white; for the second of the two terms we have put together is
true of it, and this is the contradictory of white.

    We could not be right, then, in accepting the views either of
Heraclitus or of Anaxagoras. If we were, it would follow that
contraries would be predicated of the same subject; for when
Anaxagoras says that in everything there is a part of everything, he
says nothing is sweet any more than it is bitter, and so with any
other pair of contraries, since in everything everything is present
not potentially only, but actually and separately. And similarly all
statements cannot be false nor all true, both because of many other
difficulties which might be adduced as arising from this position, and
because if all are false it will not be true to say even this, and
if all are true it will not be false to say all are false.

                                   7

    Every science seeks certain principles and causes for each of
its objects-e.g. medicine and gymnastics and each of the other
sciences, whether productive or mathematical. For each of these
marks off a certain class of things for itself and busies itself about
this as about something existing and real,-not however qua real; the
science that does this is another distinct from these. Of the sciences
mentioned each gets somehow the 'what' in some class of things and
tries to prove the other truths, with more or less precision. Some get
the 'what' through perception, others by hypothesis; so that it is
clear from an induction of this sort that there is no demonstration.
of the substance or 'what'.

    There is a science of nature, and evidently it must be different
both from practical and from productive science. For in the case of
productive science the principle of movement is in the producer and
not in the product, and is either an art or some other faculty. And
similarly in practical science the movement is not in the thing
done, but rather in the doers. But the science of the natural
philosopher deals with the things that have in themselves a
principle of movement. It is clear from these facts, then, that
natural science must be neither practical nor productive, but
theoretical (for it must fall into some one of these classes). And
since each of the sciences must somehow know the 'what' and use this
as a principle, we must not fall to observe how the natural
philosopher should define things and how he should state the
definition of the essence-whether as akin to 'snub' or rather to
'concave'. For of these the definition of 'snub' includes the matter
of the thing, but that of 'concave' is independent of the matter;
for snubness is found in a nose, so that we look for its definition
without eliminating the nose, for what is snub is a concave nose.
Evidently then the definition of flesh also and of the eye and of
the other parts must always be stated without eliminating the matter.

    Since there is a science of being qua being and capable of
existing apart, we must consider whether this is to be regarded as the
same as physics or rather as different. Physics deals with the
things that have a principle of movement in themselves; mathematics is
theoretical, and is a science that deals with things that are at rest,
but its subjects cannot exist apart. Therefore about that which can
exist apart and is unmovable there is a science different from both of
these, if there is a substance of this nature (I mean separable and
unmovable), as we shall try to prove there is. And if there is such
a kind of thing in the world, here must surely be the divine, and this
must be the first and most dominant principle. Evidently, then,
there are three kinds of theoretical sciences-physics, mathematics,
theology. The class of theoretical sciences is the best, and of
these themselves the last named is best; for it deals with the highest
of existing things, and each science is called better or worse in
virtue of its proper object.

    One might raise the question whether the science of being qua
being is to be regarded as universal or not. Each of the
mathematical sciences deals with some one determinate class of things,
but universal mathematics applies alike to all. Now if natural
substances are the first of existing things, physics must be the first
of sciences; but if there is another entity and substance, separable
and unmovable, the knowledge of it must be different and prior to
physics and universal because it is prior.

                                   8

    Since 'being' in general has several senses, of which one is
'being by accident', we must consider first that which 'is' in this
sense. Evidently none of the traditional sciences busies itself
about the accidental. For neither does architecture consider what will
happen to those who are to use the house (e.g. whether they have a
painful life in it or not), nor does weaving, or shoemaking, or the
confectioner's art, do the like; but each of these sciences
considers only what is peculiar to it, i.e. its proper end. And as for
the argument that 'when he who is musical becomes lettered he'll be
both at once, not having been both before; and that which is, not
always having been, must have come to be; therefore he must have at
once become musical and lettered',-this none of the recognized
sciences considers, but only sophistic; for this alone busies itself
about the accidental, so that Plato is not far wrong when he says that
the sophist spends his time on non-being.

    That a science of the accidental is not even possible will be
evident if we try to see what the accidental really is. We say that
everything either is always and of necessity (necessity not in the
sense of violence, but that which we appeal to in demonstrations),
or is for the most part, or is neither for the most part, nor always
and of necessity, but merely as it chances; e.g. there might be cold
in the dogdays, but this occurs neither always and of necessity, nor
for the most part, though it might happen sometimes. The accidental,
then, is what occurs, but not always nor of necessity, nor for the
most part. Now we have said what the accidental is, and it is
obvious why there is no science of such a thing; for all science is of
that which is always or for the most part, but the accidental is in
neither of these classes.

    Evidently there are not causes and principles of the accidental,
of the same kind as there are of the essential; for if there were,
everything would be of necessity. If A is when B is, and B is when C
is, and if C exists not by chance but of necessity, that also of which
C was cause will exist of necessity, down to the last causatum as it
is called (but this was supposed to be accidental). Therefore all
things will be of necessity, and chance and the possibility of a
thing's either occurring or not occurring are removed entirely from
the range of events. And if the cause be supposed not to exist but
to be coming to be, the same results will follow; everything will
occur of necessity. For to-morrow's eclipse will occur if A occurs,
and A if B occurs, and B if C occurs; and in this way if we subtract
time from the limited time between now and to-morrow we shall come
sometime to the already existing condition. Therefore since this
exists, everything after this will occur of necessity, so that all
things occur of necessity.

    As to that which 'is' in the sense of being true or of being by
accident, the former depends on a combination in thought and is an
affection of thought (which is the reason why it is the principles,
not of that which 'is' in this sense, but of that which is outside and
can exist apart, that are sought); and the latter is not necessary but
indeterminate (I mean the accidental); and of such a thing the
causes are unordered and indefinite.

    Adaptation to an end is found in events that happen by nature or
as the result of thought. It is 'luck' when one of these events
happens by accident. For as a thing may exist, so it may be a cause,
either by its own nature or by accident. Luck is an accidental cause
at work in such events adapted to an end as are usually effected in
accordance with purpose. And so luck and thought are concerned with
the same sphere; for purpose cannot exist without thought. The
causes from which lucky results might happen are indeterminate; and so
luck is obscure to human calculation and is a cause by accident, but
in the unqualified sense a cause of nothing. It is good or bad luck
when the result is good or evil; and prosperity or misfortune when the
scale of the results is large.

    Since nothing accidental is prior to the essential, neither are
accidental causes prior. If, then, luck or spontaneity is a cause of
the material universe, reason and nature are causes before it.

                                   9

    Some things are only actually, some potentially, some
potentially and actually, what they are, viz. in one case a particular
reality, in another, characterized by a particular quantity, or the
like. There is no movement apart from things; for change is always
according to the categories of being, and there is nothing common to
these and in no one category. But each of the categories belongs to
all its subjects in either of two ways (e.g. 'this-ness'-for one
kind of it is 'positive form', and the other is 'privation'; and as
regards quality one kind is 'white' and the other 'black', and as
regards quantity one kind is 'complete' and the other 'incomplete',
and as regards spatial movement one is 'upwards' and the other
'downwards', or one thing is 'light' and another 'heavy'); so that
there are as many kinds of movement and change as of being. There
being a distinction in each class of things between the potential
and the completely real, I call the actuality of the potential as
such, movement. That what we say is true, is plain from the
following facts. When the 'buildable', in so far as it is what we mean
by 'buildable', exists actually, it is being built, and this is the
process of building. Similarly with learning, healing, walking,
leaping, ageing, ripening. Movement takes when the complete reality
itself exists, and neither earlier nor later. The complete reality,
then, of that which exists potentially, when it is completely real and
actual, not qua itself, but qua movable, is movement. By qua I mean
this: bronze is potentially a statue; but yet it is not the complete
reality of bronze qua bronze that is movement. For it is not the
same thing to be bronze and to be a certain potency. If it were
absolutely the same in its definition, the complete reality of
bronze would have been a movement. But it is not the same. (This is
evident in the case of contraries; for to be capable of being well and
to be capable of being ill are not the same-for if they were, being
well and being ill would have been the same-it is that which underlies
and is healthy or diseased, whether it is moisture or blood, that is
one and the same.) And since it is not. the same, as colour and the
visible are not the same, it is the complete reality of the potential,
and as potential, that is movement. That it is this, and that movement
takes place when the complete reality itself exists, and neither
earlier nor later, is evident. For each thing is capable of being
sometimes actual, sometimes not, e.g. the buildable qua buildable; and
the actuality of the buildable qua buildable is building. For the
actuality is either this-the act of building-or the house. But when
the house exists, it is no longer buildable; the buildable is what
is being built. The actuality, then, must be the act of building,
and this is a movement. And the same account applies to all other
movements.

    That what we have said is right is evident from what all others
say about movement, and from the fact that it is not easy to define it
otherwise. For firstly one cannot put it in any class. This is evident
from what people say. Some call it otherness and inequality and the
unreal; none of these, however, is necessarily moved, and further,
change is not either to these or from these any more than from their
opposites. The reason why people put movement in these classes is that
it is thought to be something indefinite, and the principles in one of
the two 'columns of contraries' are indefinite because they are
privative, for none of them is either a 'this' or a 'such' or in any
of the other categories. And the reason why movement is thought to
be indefinite is that it cannot be classed either with the potency
of things or with their actuality; for neither that which is capable
of being of a certain quantity, nor that which is actually of a
certain quantity, is of necessity moved, and movement is thought to be
an actuality, but incomplete; the reason is that the potential,
whose actuality it is, is incomplete. And therefore it is hard to
grasp what movement is; for it must be classed either under
privation or under potency or under absolute actuality, but
evidently none of these is possible. Therefore what remains is that it
must be what we said-both actuality and the actuality we have
described-which is hard to detect but capable of existing.

    And evidently movement is in the movable; for it is the complete
realization of this by that which is capable of causing movement.
And the actuality of that which is capable of causing movement is no
other than that of the movable. For it must be the complete reality of
both. For while a thing is capable of causing movement because it
can do this, it is a mover because it is active; but it is on the
movable that it is capable of acting, so that the actuality of both is
one, just as there is the same interval from one to two as from two to
one, and as the steep ascent and the steep descent are one, but the
being of them is not one; the case of the mover and the moved is
similar.

                                  10

    The infinite is either that which is incapable of being
traversed because it is not its nature to be traversed (this
corresponds to the sense in which the voice is 'invisible'), or that
which admits only of incomplete traverse or scarcely admits of
traverse, or that which, though it naturally admits of traverse, is
not traversed or limited; further, a thing may be infinite in
respect of addition or of subtraction, or both. The infinite cannot be
a separate, independent thing. For if it is neither a spatial
magnitude nor a plurality, but infinity itself is its substance and
not an accident of it, it will be indivisible; for the divisible is
either magnitude or plurality. But if indivisible, it is not infinite,
except as the voice is invisible; but people do not mean this, nor are
we examining this sort of infinite, but the infinite as untraversable.
Further, how can an infinite exist by itself, unless number and
magnitude also exist by themselvess-since infinity is an attribute
of these? Further, if the infinite is an accident of something else,
it cannot be qua infinite an element in things, as the invisible is
not an element in speech, though the voice is invisible. And evidently
the infinite cannot exist actually. For then any part of it that might
be taken would be infinite (for 'to be infinite' and 'the infinite'
are the same, if the infinite is substance and not predicated of a
subject). Therefore it is either indivisible, or if it is partible, it
is divisible into infinites; but the same thing cannot be many
infinites (as a part of air is air, so a part of the infinite would be
infinite, if the infinite is substance and a principle). Therefore
it must be impartible and indivisible. But the actually infinite
cannot be indivisible; for it must be of a certain quantity. Therefore
infinity belongs to its subject incidentally. But if so, then (as we
have said) it cannot be it that is a principle, but that of which it
is an accident-the air or the even number.

    This inquiry is universal; but that the infinite is not among
sensible things, is evident from the following argument. If the
definition of a body is 'that which is bounded by planes', there
cannot be an infinite body either sensible or intelligible; nor a
separate and infinite number, for number or that which has a number is
numerable. Concretely, the truth is evident from the following
argument. The infinite can neither be composite nor simple. For (a) it
cannot be a composite body, since the elements are limited in
multitude. For the contraries must be equal and no one of them must be
infinite; for if one of the two bodies falls at all short of the other
in potency, the finite will be destroyed by the infinite. And that
each should be infinite is impossible. For body is that which has
extension in all directions, and the infinite is the boundlessly
extended, so that if the infinite is a body it will be infinite in
every direction. Nor (b) can the infinite body be one and
simple-neither, as some say, something apart from the elements, from
which they generate these (for there is no such body apart from the
elements; for everything can be resolved into that of which it
consists, but no such product of analysis is observed except the
simple bodies), nor fire nor any other of the elements. For apart from
the question how any of them could be infinite, the All, even if it is
finite, cannot either be or become any one of them, as Heraclitus says
all things sometime become fire. The same argument applies to this
as to the One which the natural philosophers posit besides the
elements. For everything changes from contrary to contrary, e.g.
from hot to cold.

    Further, a sensible body is somewhere, and whole and part have the
same proper place, e.g. the whole earth and part of the earth.
Therefore if (a) the infinite body is homogeneous, it will be
unmovable or it will be always moving. But this is impossible; for why
should it rather rest, or move, down, up, or anywhere, rather than
anywhere else? E.g. if there were a clod which were part of an
infinite body, where will this move or rest? The proper place of the
body which is homogeneous with it is infinite. Will the clod occupy
the whole place, then? And how? (This is impossible.) What then is its
rest or its movement? It will either rest everywhere, and then it
cannot move; or it will move everywhere, and then it cannot be
still. But (b) if the All has unlike parts, the proper places of the
parts are unlike also, and, firstly, the body of the All is not one
except by contact, and, secondly, the parts will be either finite or
infinite in variety of kind. Finite they cannot be; for then those
of one kind will be infinite in quantity and those of another will not
(if the All is infinite), e.g. fire or water would be infinite, but
such an infinite element would be destruction to the contrary
elements. But if the parts are infinite and simple, their places
also are infinite and there will be an infinite number of elements;
and if this is impossible, and the places are finite, the All also
must be limited.

    In general, there cannot be an infinite body and also a proper
place for bodies, if every sensible body has either weight or
lightness. For it must move either towards the middle or upwards,
and the infinite either the whole or the half of it-cannot do
either; for how will you divide it? Or how will part of the infinite
be down and part up, or part extreme and part middle? Further, every
sensible body is in a place, and there are six kinds of place, but
these cannot exist in an infinite body. In general, if there cannot be
an infinite place, there cannot be an infinite body; (and there cannot
be an infinite place,) for that which is in a place is somewhere,
and this means either up or down or in one of the other directions,
and each of these is a limit.

    The infinite is not the same in the sense that it is a single
thing whether exhibited in distance or in movement or in time, but the
posterior among these is called infinite in virtue of its relation
to the prior; i.e. a movement is called infinite in virtue of the
distance covered by the spatial movement or alteration or growth,
and a time is called infinite because of the movement which occupies
it.

                                  11

    Of things which change, some change in an accidental sense, like
that in which 'the musical' may be said to walk, and others are
said, without qualification, to change, because something in them
changes, i.e. the things that change in parts; the body becomes
healthy, because the eye does. But there is something which is by
its own nature moved directly, and this is the essentially movable.
The same distinction is found in the case of the mover; for it
causes movement either in an accidental sense or in respect of a
part of itself or essentially. There is something that directly causes
movement; and there is something that is moved, also the time in which
it is moved, and that from which and that into which it is moved.
But the forms and the affections and the place, which are the
terminals of the movement of moving things, are unmovable, e.g.
knowledge or heat; it is not heat that is a movement, but heating.
Change which is not accidental is found not in all things, but between
contraries, and their intermediates, and between contradictories. We
may convince ourselves of this by induction.

    That which changes changes either from positive into positive,
or from negative into negative, or from positive into negative, or
from negative into positive. (By positive I mean that which is
expressed by an affirmative term.) Therefore there must be three
changes; that from negative into negative is not change, because
(since the terms are neither contraries nor contradictories) there
is no opposition. The change from the negative into the positive which
is its contradictory is generation-absolute change absolute
generation, and partial change partial generation; and the change from
positive to negative is destruction-absolute change absolute
destruction, and partial change partial destruction. If, then, 'that
which is not' has several senses, and movement can attach neither to
that which implies putting together or separating, nor to that which
implies potency and is opposed to that which is in the full sense
(true, the not-white or not-good can be moved incidentally, for the
not-white might be a man; but that which is not a particular thing
at all can in no wise be moved), that which is not cannot be moved
(and if this is so, generation cannot be movement; for that which is
not is generated; for even if we admit to the full that its generation
is accidental, yet it is true to say that 'not-being' is predicable of
that which is generated absolutely). Similarly rest cannot be long
to that which is not. These consequences, then, turn out to be
awkward, and also this, that everything that is moved is in a place,
but that which is not is not in a place; for then it would be
somewhere. Nor is destruction movement; for the contrary of movement
is rest, but the contrary of destruction is generation. Since every
movement is a change, and the kinds of change are the three named
above, and of these those in the way of generation and destruction are
not movements, and these are the changes from a thing to its
contradictory, it follows that only the change from positive into
positive is movement. And the positives are either contrary or
intermediate (for even privation must be regarded as contrary), and
are expressed by an affirmative term, e.g. 'naked' or 'toothless' or
'black'.

                                  12

    If the categories are classified as substance, quality, place,
acting or being acted on, relation, quantity, there must be three
kinds of movement-of quality, of quantity, of place. There is no
movement in respect of substance (because there is nothing contrary to
substance), nor of relation (for it is possible that if one of two
things in relation changes, the relative term which was true of the
other thing ceases to be true, though this other does not change at
all,-so that their movement is accidental), nor of agent and
patient, or mover and moved, because there is no movement of
movement nor generation of generation, nor, in general, change of
change. For there might be movement of movement in two senses; (1)
movement might be the subject moved, as a man is moved because he
changes from pale to dark,-so that on this showing movement, too,
may be either heated or cooled or change its place or increase. But
this is impossible; for change is not a subject. Or (2) some other
subject might change from change into some other form of existence
(e.g. a man from disease into health). But this also is not possible
except incidentally. For every movement is change from something
into something. (And so are generation and destruction; only, these
are changes into things opposed in certain ways while the other,
movement, is into things opposed in another way.) A thing changes,
then, at the same time from health into illness, and from this
change itself into another. Clearly, then, if it has become ill, it
will have changed into whatever may be the other change concerned
(though it may be at rest), and, further, into a determinate change
each time; and that new change will be from something definite into
some other definite thing; therefore it will be the opposite change,
that of growing well. We answer that this happens only incidentally;
e.g. there is a change from the process of recollection to that of
forgetting, only because that to which the process attaches is
changing, now into a state of knowledge, now into one of ignorance.

    Further, the process will go on to infinity, if there is to be
change of change and coming to be of coming to be. What is true of the
later, then, must be true of the earlier; e.g. if the simple coming to
be was once coming to be, that which comes to be something was also
once coming to be; therefore that which simply comes to be something
was not yet in existence, but something which was coming to be
coming to be something was already in existence. And this was once
coming to be, so that at that time it was not yet coming to be
something else. Now since of an infinite number of terms there is
not a first, the first in this series will not exist, and therefore no
following term exist. Nothing, then, can either come term wi to be
or move or change. Further, that which is capable of a movement is
also capable of the contrary movement and rest, and that which comes
to be also ceases to be. Therefore that which is coming to be is
ceasing to be when it has come to be coming to be; for it cannot cease
to be as soon as it is coming to be coming to be, nor after it has
come to be; for that which is ceasing to be must be. Further, there
must be a matter underlying that which comes to be and changes. What
will this be, then,-what is it that becomes movement or becoming, as
body or soul is that which suffers alteration? And; again, what is
it that they move into? For it must be the movement or becoming of
something from something into something. How, then, can this condition
be fulfilled? There can be no learning of learning, and therefore no
becoming of becoming. Since there is not movement either of
substance or of relation or of activity and passivity, it remains that
movement is in respect of quality and quantity and place; for each
of these admits of contrariety. By quality I mean not that which is in
the substance (for even the differentia is a quality), but the passive
quality, in virtue of which a thing is said to be acted on or to be
incapable of being acted on. The immobile is either that which is
wholly incapable of being moved, or that which is moved with
difficulty in a long time or begins slowly, or that which is of a
nature to be moved and can be moved but is not moved when and where
and as it would naturally be moved. This alone among immobiles I
describe as being at rest; for rest is contrary to movement, so that
it must be a privation in that which is receptive of movement.

    Things which are in one proximate place are together in place, and
things which are in different places are apart: things whose
extremes are together touch: that at which a changing thing, if it
changes continuously according to its nature, naturally arrives before
it arrives at the extreme into which it is changing, is between.
That which is most distant in a straight line is contrary in place.
That is successive which is after the beginning (the order being
determined by position or form or in some other way) and has nothing
of the same class between it and that which it succeeds, e.g. lines in
the case of a line, units in that of a unit, or a house in that of a
house. (There is nothing to prevent a thing of some other class from
being between.) For the successive succeeds something and is something
later; 'one' does not succeed 'two', nor the first day of the month
the second. That which, being successive, touches, is contiguous.
(Since all change is between opposites, and these are either
contraries or contradictories, and there is no middle term for
contradictories, clearly that which is between is between contraries.)
The continuous is a species of the contiguous. I call two things
continuous when the limits of each, with which they touch and by which
they are kept together, become one and the same, so that plainly the
continuous is found in the things out of which a unity naturally
arises in virtue of their contact. And plainly the successive is the
first of these concepts (for the successive does not necessarily
touch, but that which touches is successive; and if a thing is
continuous, it touches, but if it touches, it is not necessarily
continuous; and in things in which there is no touching, there is no
organic unity); therefore a point is not the same as a unit; for
contact belongs to points, but not to units, which have only
succession; and there is something between two of the former, but
not between two of the latter.

                                Book XII

                                   1

    The subject of our inquiry is substance; for the principles and
the causes we are seeking are those of substances. For if the universe
is of the nature of a whole, substance is its first part; and if it
coheres merely by virtue of serial succession, on this view also
substance is first, and is succeeded by quality, and then by quantity.
At the same time these latter are not even being in the full sense,
but are qualities and movements of it,-or else even the not-white
and the not-straight would be being; at least we say even these are,
e.g. 'there is a not-white'. Further, none of the categories other
than substance can exist apart. And the early philosophers also in
practice testify to the primacy of substance; for it was of
substance that they sought the principles and elements and causes. The
thinkers of the present day tend to rank universals as substances (for
genera are universals, and these they tend to describe as principles
and substances, owing to the abstract nature of their inquiry); but
the thinkers of old ranked particular things as substances, e.g.
fire and earth, not what is common to both, body.

    There are three kinds of substance-one that is sensible (of
which one subdivision is eternal and another is perishable; the latter
is recognized by all men, and includes e.g. plants and animals), of
which we must grasp the elements, whether one or many; and another
that is immovable, and this certain thinkers assert to be capable of
existing apart, some dividing it into two, others identifying the
Forms and the objects of mathematics, and others positing, of these
two, only the objects of mathematics. The former two kinds of
substance are the subject of physics (for they imply movement); but
the third kind belongs to another science, if there is no principle
common to it and to the other kinds.

                                   2

    Sensible substance is changeable. Now if change proceeds from
opposites or from intermediates, and not from all opposites (for the
voice is not-white, (but it does not therefore change to white)),
but from the contrary, there must be something underlying which
changes into the contrary state; for the contraries do not change.
Further, something persists, but the contrary does not persist;
there is, then, some third thing besides the contraries, viz. the
matter. Now since changes are of four kinds-either in respect of the
'what' or of the quality or of the quantity or of the place, and
change in respect of 'thisness' is simple generation and
destruction, and change in quantity is increase and diminution, and
change in respect of an affection is alteration, and change of place
is motion, changes will be from given states into those contrary to
them in these several respects. The matter, then, which changes must
be capable of both states. And since that which 'is' has two senses,
we must say that everything changes from that which is potentially
to that which is actually, e.g. from potentially white to actually
white, and similarly in the case of increase and diminution. Therefore
not only can a thing come to be, incidentally, out of that which is
not, but also all things come to be out of that which is, but is
potentially, and is not actually. And this is the 'One' of Anaxagoras;
for instead of 'all things were together'-and the 'Mixture' of
Empedocles and Anaximander and the account given by Democritus-it is
better to say 'all things were together potentially but not actually'.
Therefore these thinkers seem to have had some notion of matter. Now
all things that change have matter, but different matter; and of
eternal things those which are not generable but are movable in
space have matter-not matter for generation, however, but for motion
from one place to another.

    One might raise the question from what sort of non-being
generation proceeds; for 'non-being' has three senses. If, then, one
form of non-being exists potentially, still it is not by virtue of a
potentiality for any and every thing, but different things come from
different things; nor is it satisfactory to say that 'all things
were together'; for they differ in their matter, since otherwise why
did an infinity of things come to be, and not one thing? For
'reason' is one, so that if matter also were one, that must have
come to be in actuality which the matter was in potency. The causes
and the principles, then, are three, two being the pair of
contraries of which one is definition and form and the other is
privation, and the third being the matter.

                                   3

    Note, next, that neither the matter nor the form comes to be-and I
mean the last matter and form. For everything that changes is
something and is changed by something and into something. That by
which it is changed is the immediate mover; that which is changed, the
matter; that into which it is changed, the form. The process, then,
will go on to infinity, if not only the bronze comes to be round but
also the round or the bronze comes to be; therefore there must be a
stop.

    Note, next, that each substance comes into being out of
something that shares its name. (Natural objects and other things both
rank as substances.) For things come into being either by art or by
nature or by luck or by spontaneity. Now art is a principle of
movement in something other than the thing moved, nature is a
principle in the thing itself (for man begets man), and the other
causes are privations of these two.

    There are three kinds of substance-the matter, which is a 'this'
in appearance (for all things that are characterized by contact and
not, by organic unity are matter and substratum, e.g. fire, flesh,
head; for these are all matter, and the last matter is the matter of
that which is in the full sense substance); the nature, which is a
'this' or positive state towards which movement takes place; and
again, thirdly, the particular substance which is composed of these
two, e.g. Socrates or Callias. Now in some cases the 'this' does not
exist apart from the composite substance, e.g. the form of house
does not so exist, unless the art of building exists apart (nor is
there generation and destruction of these forms, but it is in
another way that the house apart from its matter, and health, and
all ideals of art, exist and do not exist); but if the 'this' exists
apart from the concrete thing, it is only in the case of natural
objects. And so Plato was not far wrong when he said that there are as
many Forms as there are kinds of natural object (if there are Forms
distinct from the things of this earth). The moving causes exist as
things preceding the effects, but causes in the sense of definitions
are simultaneous with their effects. For when a man is healthy, then
health also exists; and the shape of a bronze sphere exists at the
same time as the bronze sphere. (But we must examine whether any
form also survives afterwards. For in some cases there is nothing to
prevent this; e.g. the soul may be of this sort-not all soul but the
reason; for presumably it is impossible that all soul should survive.)
Evidently then there is no necessity, on this ground at least, for the
existence of the Ideas. For man is begotten by man, a given man by
an individual father; and similarly in the arts; for the medical art
is the formal cause of health.

                                   4

    The causes and the principles of different things are in a sense
different, but in a sense, if one speaks universally and analogically,
they are the same for all. For one might raise the question whether
the principles and elements are different or the same for substances
and for relative terms, and similarly in the case of each of the
categories. But it would be paradoxical if they were the same for all.
For then from the same elements will proceed relative terms and
substances. What then will this common element be? For (1) (a) there
is nothing common to and distinct from substance and the other
categories, viz. those which are predicated; but an element is prior
to the things of which it is an element. But again (b) substance is
not an element in relative terms, nor is any of these an element in
substance. Further, (2) how can all things have the same elements? For
none of the elements can be the same as that which is composed of
elements, e.g. b or a cannot be the same as ba. (None, therefore, of
the intelligibles, e.g. being or unity, is an element; for these are
predicable of each of the compounds as well.) None of the elements,
then, will be either a substance or a relative term; but it must be
one or other. All things, then, have not the same elements.

    Or, as we are wont to put it, in a sense they have and in a
sense they have not; e.g. perhaps the elements of perceptible bodies
are, as form, the hot, and in another sense the cold, which is the
privation; and, as matter, that which directly and of itself
potentially has these attributes; and substances comprise both these
and the things composed of these, of which these are the principles,
or any unity which is produced out of the hot and the cold, e.g. flesh
or bone; for the product must be different from the elements. These
things then have the same elements and principles (though specifically
different things have specifically different elements); but all things
have not the same elements in this sense, but only analogically;
i.e. one might say that there are three principles-the form, the
privation, and the matter. But each of these is different for each
class; e.g. in colour they are white, black, and surface, and in day
and night they are light, darkness, and air.

    Since not only the elements present in a thing are causes, but
also something external, i.e. the moving cause, clearly while
'principle' and 'element' are different both are causes, and
'principle' is divided into these two kinds; and that which acts as
producing movement or rest is a principle and a substance. Therefore
analogically there are three elements, and four causes and principles;
but the elements are different in different things, and the
proximate moving cause is different for different things. Health,
disease, body; the moving cause is the medical art. Form, disorder
of a particular kind, bricks; the moving cause is the building art.
And since the moving cause in the case of natural things is-for man,
for instance, man, and in the products of thought the form or its
contrary, there will be in a sense three causes, while in a sense
there are four. For the medical art is in some sense health, and the
building art is the form of the house, and man begets man; further,
besides these there is that which as first of all things moves all
things.

                                   5

    Some things can exist apart and some cannot, and it is the
former that are substances. And therefore all things have the same
causes, because, without substances, modifications and movements do
not exist. Further, these causes will probably be soul and body, or
reason and desire and body.

    And in yet another way, analogically identical things are
principles, i.e. actuality and potency; but these also are not only
different for different things but also apply in different ways to
them. For in some cases the same thing exists at one time actually and
at another potentially, e.g. wine or flesh or man does so. (And
these too fall under the above-named causes. For the form exists
actually, if it can exist apart, and so does the complex of form and
matter, and the privation, e.g. darkness or disease; but the matter
exists potentially; for this is that which can become qualified either
by the form or by the privation.) But the distinction of actuality and
potentiality applies in another way to cases where the matter of cause
and of effect is not the same, in some of which cases the form is
not the same but different; e.g. the cause of man is (1) the
elements in man (viz. fire and earth as matter, and the peculiar
form), and further (2) something else outside, i.e. the father, and
(3) besides these the sun and its oblique course, which are neither
matter nor form nor privation of man nor of the same species with him,
but moving causes.

    Further, one must observe that some causes can be expressed in
universal terms, and some cannot. The proximate principles of all
things are the 'this' which is proximate in actuality, and another
which is proximate in potentiality. The universal causes, then, of
which we spoke do not exist. For it is the individual that is the
originative principle of the individuals. For while man is the
originative principle of man universally, there is no universal man,
but Peleus is the originative principle of Achilles, and your father
of you, and this particular b of this particular ba, though b in
general is the originative principle of ba taken without
qualification.

    Further, if the causes of substances are the causes of all things,
yet different things have different causes and elements, as was
said; the causes of things that are not in the same class, e.g. of
colours and sounds, of substances and quantities, are different except
in an analogical sense; and those of things in the same species are
different, not in species, but in the sense that the causes of
different individuals are different, your matter and form and moving
cause being different from mine, while in their universal definition
they are the same. And if we inquire what are the principles or
elements of substances and relations and qualities-whether they are
the same or different-clearly when the names of the causes are used in
several senses the causes of each are the same, but when the senses
are distinguished the causes are not the same but different, except
that in the following senses the causes of all are the same. They
are (1) the same or analogous in this sense, that matter, form,
privation, and the moving cause are common to all things; and (2)
the causes of substances may be treated as causes of all things in
this sense, that when substances are removed all things are removed;
further, (3) that which is first in respect of complete reality is the
cause of all things. But in another sense there are different first
causes, viz. all the contraries which are neither generic nor
ambiguous terms; and, further, the matters of different things are
different. We have stated, then, what are the principles of sensible
things and how many they are, and in what sense they are the same
and in what sense different.

                                   6

    Since there were three kinds of substance, two of them physical
and one unmovable, regarding the latter we must assert that it is
necessary that there should be an eternal unmovable substance. For
substances are the first of existing things, and if they are all
destructible, all things are destructible. But it is impossible that
movement should either have come into being or cease to be (for it
must always have existed), or that time should. For there could not be
a before and an after if time did not exist. Movement also is
continuous, then, in the sense in which time is; for time is either
the same thing as movement or an attribute of movement. And there is
no continuous movement except movement in place, and of this only that
which is circular is continuous.

    But if there is something which is capable of moving things or
acting on them, but is not actually doing so, there will not
necessarily be movement; for that which has a potency need not
exercise it. Nothing, then, is gained even if we suppose eternal
substances, as the believers in the Forms do, unless there is to be in
them some principle which can cause change; nay, even this is not
enough, nor is another substance besides the Forms enough; for if it
is not to act, there will be no movement. Further even if it acts,
this will not be enough, if its essence is potency; for there will not
be eternal movement, since that which is potentially may possibly
not be. There must, then, be such a principle, whose very essence is
actuality. Further, then, these substances must be without matter; for
they must be eternal, if anything is eternal. Therefore they must be
actuality.

    Yet there is a difficulty; for it is thought that everything
that acts is able to act, but that not everything that is able to
act acts, so that the potency is prior. But if this is so, nothing
that is need be; for it is possible for all things to be capable of
existing but not yet to exist.

    Yet if we follow the theologians who generate the world from
night, or the natural philosophers who say that 'all things were
together', the same impossible result ensues. For how will there be
movement, if there is no actually existing cause? Wood will surely not
move itself-the carpenter's art must act on it; nor will the menstrual
blood nor the earth set themselves in motion, but the seeds must act
on the earth and the semen on the menstrual blood.

    This is why some suppose eternal actuality-e.g. Leucippus and
Plato; for they say there is always movement. But why and what this
movement is they do say, nor, if the world moves in this way or
that, do they tell us the cause of its doing so. Now nothing is
moved at random, but there must always be something present to move
it; e.g. as a matter of fact a thing moves in one way by nature, and
in another by force or through the influence of reason or something
else. (Further, what sort of movement is primary? This makes a vast
difference.) But again for Plato, at least, it is not permissible to
name here that which he sometimes supposes to be the source of
movement-that which moves itself; for the soul is later, and coeval
with the heavens, according to his account. To suppose potency prior
to actuality, then, is in a sense right, and in a sense not; and we
have specified these senses. That actuality is prior is testified by
Anaxagoras (for his 'reason' is actuality) and by Empedocles in his
doctrine of love and strife, and by those who say that there is always
movement, e.g. Leucippus. Therefore chaos or night did not exist for
an infinite time, but the same things have always existed (either
passing through a cycle of changes or obeying some other law), since
actuality is prior to potency. If, then, there is a constant cycle,
something must always remain, acting in the same way. And if there
is to be generation and destruction, there must be something else
which is always acting in different ways. This must, then, act in
one way in virtue of itself, and in another in virtue of something
else-either of a third agent, therefore, or of the first. Now it
must be in virtue of the first. For otherwise this again causes the
motion both of the second agent and of the third. Therefore it is
better to say 'the first'. For it was the cause of eternal uniformity;
and something else is the cause of variety, and evidently both
together are the cause of eternal variety. This, accordingly, is the
character which the motions actually exhibit. What need then is
there to seek for other principles?

                                   7

    Since (1) this is a possible account of the matter, and (2) if
it were not true, the world would have proceeded out of night and 'all
things together' and out of non-being, these difficulties may be taken
as solved. There is, then, something which is always moved with an
unceasing motion, which is motion in a circle; and this is plain not
in theory only but in fact. Therefore the first heaven must be
eternal. There is therefore also something which moves it. And since
that which moves and is moved is intermediate, there is something
which moves without being moved, being eternal, substance, and
actuality. And the object of desire and the object of thought move
in this way; they move without being moved. The primary objects of
desire and of thought are the same. For the apparent good is the
object of appetite, and the real good is the primary object of
rational wish. But desire is consequent on opinion rather than opinion
on desire; for the thinking is the starting-point. And thought is
moved by the object of thought, and one of the two columns of
opposites is in itself the object of thought; and in this, substance
is first, and in substance, that which is simple and exists
actually. (The one and the simple are not the same; for 'one' means
a measure, but 'simple' means that the thing itself has a certain
nature.) But the beautiful, also, and that which is in itself
desirable are in the same column; and the first in any class is always
best, or analogous to the best.

    That a final cause may exist among unchangeable entities is
shown by the distinction of its meanings. For the final cause is (a)
some being for whose good an action is done, and (b) something at
which the action aims; and of these the latter exists among
unchangeable entities though the former does not. The final cause,
then, produces motion as being loved, but all other things move by
being moved. Now if something is moved it is capable of being
otherwise than as it is. Therefore if its actuality is the primary
form of spatial motion, then in so far as it is subject to change,
in this respect it is capable of being otherwise,-in place, even if
not in substance. But since there is something which moves while
itself unmoved, existing actually, this can in no way be otherwise
than as it is. For motion in space is the first of the kinds of
change, and motion in a circle the first kind of spatial motion; and
this the first mover produces. The first mover, then, exists of
necessity; and in so far as it exists by necessity, its mode of
being is good, and it is in this sense a first principle. For the
necessary has all these senses-that which is necessary perforce
because it is contrary to the natural impulse, that without which
the good is impossible, and that which cannot be otherwise but can
exist only in a single way.

    On such a principle, then, depend the heavens and the world of
nature. And it is a life such as the best which we enjoy, and enjoy
for but a short time (for it is ever in this state, which we cannot
be), since its actuality is also pleasure. (And for this reason are
waking, perception, and thinking most pleasant, and hopes and memories
are so on account of these.) And thinking in itself deals with that
which is best in itself, and that which is thinking in the fullest
sense with that which is best in the fullest sense. And thought thinks
on itself because it shares the nature of the object of thought; for
it becomes an object of thought in coming into contact with and
thinking its objects, so that thought and object of thought are the
same. For that which is capable of receiving the object of thought,
i.e. the essence, is thought. But it is active when it possesses
this object. Therefore the possession rather than the receptivity is
the divine element which thought seems to contain, and the act of
contemplation is what is most pleasant and best. If, then, God is
always in that good state in which we sometimes are, this compels
our wonder; and if in a better this compels it yet more. And God is in
a better state. And life also belongs to God; for the actuality of
thought is life, and God is that actuality; and God's self-dependent
actuality is life most good and eternal. We say therefore that God
is a living being, eternal, most good, so that life and duration
continuous and eternal belong to God; for this is God.

    Those who suppose, as the Pythagoreans and Speusippus do, that
supreme beauty and goodness are not present in the beginning,
because the beginnings both of plants and of animals are causes, but
beauty and completeness are in the effects of these, are wrong in
their opinion. For the seed comes from other individuals which are
prior and complete, and the first thing is not seed but the complete
being; e.g. we must say that before the seed there is a man,-not the
man produced from the seed, but another from whom the seed comes.

    It is clear then from what has been said that there is a substance
which is eternal and unmovable and separate from sensible things. It
has been shown also that this substance cannot have any magnitude, but
is without parts and indivisible (for it produces movement through
infinite time, but nothing finite has infinite power; and, while every
magnitude is either infinite or finite, it cannot, for the above
reason, have finite magnitude, and it cannot have infinite magnitude
because there is no infinite magnitude at all). But it has also been
shown that it is impassive and unalterable; for all the other
changes are posterior to change of place.

                                   8

    It is clear, then, why these things are as they are. But we must
not ignore the question whether we have to suppose one such
substance or more than one, and if the latter, how many; we must
also mention, regarding the opinions expressed by others, that they
have said nothing about the number of the substances that can even
be clearly stated. For the theory of Ideas has no special discussion
of the subject; for those who speak of Ideas say the Ideas are
numbers, and they speak of numbers now as unlimited, now as limited by
the number 10; but as for the reason why there should be just so
many numbers, nothing is said with any demonstrative exactness. We
however must discuss the subject, starting from the presuppositions
and distinctions we have mentioned. The first principle or primary
being is not movable either in itself or accidentally, but produces
the primary eternal and single movement. But since that which is moved
must be moved by something, and the first mover must be in itself
unmovable, and eternal movement must be produced by something
eternal and a single movement by a single thing, and since we see that
besides the simple spatial movement of the universe, which we say
the first and unmovable substance produces, there are other spatial
movements-those of the planets-which are eternal (for a body which
moves in a circle is eternal and unresting; we have proved these
points in the physical treatises), each of these movements also must
be caused by a substance both unmovable in itself and eternal. For the
nature of the stars is eternal just because it is a certain kind of
substance, and the mover is eternal and prior to the moved, and that
which is prior to a substance must be a substance. Evidently, then,
there must be substances which are of the same number as the movements
of the stars, and in their nature eternal, and in themselves
unmovable, and without magnitude, for the reason before mentioned.
That the movers are substances, then, and that one of these is first
and another second according to the same order as the movements of the
stars, is evident. But in the number of the movements we reach a
problem which must be treated from the standpoint of that one of the
mathematical sciences which is most akin to philosophy-viz. of
astronomy; for this science speculates about substance which is
perceptible but eternal, but the other mathematical sciences, i.e.
arithmetic and geometry, treat of no substance. That the movements are
more numerous than the bodies that are moved is evident to those who
have given even moderate attention to the matter; for each of the
planets has more than one movement. But as to the actual number of
these movements, we now-to give some notion of the subject-quote
what some of the mathematicians say, that our thought may have some
definite number to grasp; but, for the rest, we must partly
investigate for ourselves, Partly learn from other investigators,
and if those who study this subject form an opinion contrary to what
we have now stated, we must esteem both parties indeed, but follow the
more accurate.

    Eudoxus supposed that the motion of the sun or of the moon
involves, in either case, three spheres, of which the first is the
sphere of the fixed stars, and the second moves in the circle which
runs along the middle of the zodiac, and the third in the circle which
is inclined across the breadth of the zodiac; but the circle in
which the moon moves is inclined at a greater angle than that in which
the sun moves. And the motion of the planets involves, in each case,
four spheres, and of these also the first and second are the same as
the first two mentioned above (for the sphere of the fixed stars is
that which moves all the other spheres, and that which is placed
beneath this and has its movement in the circle which bisects the
zodiac is common to all), but the poles of the third sphere of each
planet are in the circle which bisects the zodiac, and the motion of
the fourth sphere is in the circle which is inclined at an angle to
the equator of the third sphere; and the poles of the third sphere are
different for each of the other planets, but those of Venus and
Mercury are the same.

    Callippus made the position of the spheres the same as Eudoxus
did, but while he assigned the same number as Eudoxus did to Jupiter
and to Saturn, he thought two more spheres should be added to the
sun and two to the moon, if one is to explain the observed facts;
and one more to each of the other planets.

    But it is necessary, if all the spheres combined are to explain
the observed facts, that for each of the planets there should be other
spheres (one fewer than those hitherto assigned) which counteract
those already mentioned and bring back to the same position the
outermost sphere of the star which in each case is situated below
the star in question; for only thus can all the forces at work produce
the observed motion of the planets. Since, then, the spheres
involved in the movement of the planets themselves are--eight for
Saturn and Jupiter and twenty-five for the others, and of these only
those involved in the movement of the lowest-situated planet need
not be counteracted the spheres which counteract those of the
outermost two planets will be six in number, and the spheres which
counteract those of the next four planets will be sixteen; therefore
the number of all the spheres--both those which move the planets and
those which counteract these--will be fifty-five. And if one were
not to add to the moon and to the sun the movements we mentioned,
the whole set of spheres will be forty-seven in number.

    Let this, then, be taken as the number of the spheres, so that the
unmovable substances and principles also may probably be taken as just
so many; the assertion of necessity must be left to more powerful
thinkers. But if there can be no spatial movement which does not
conduce to the moving of a star, and if further every being and
every substance which is immune from change and in virtue of itself
has attained to the best must be considered an end, there can be no
other being apart from these we have named, but this must be the
number of the substances. For if there are others, they will cause
change as being a final cause of movement; but there cannot he other
movements besides those mentioned. And it is reasonable to infer
this from a consideration of the bodies that are moved; for if
everything that moves is for the sake of that which is moved, and
every movement belongs to something that is moved, no movement can
be for the sake of itself or of another movement, but all the
movements must be for the sake of the stars. For if there is to be a
movement for the sake of a movement, this latter also will have to
be for the sake of something else; so that since there cannot be an
infinite regress, the end of every movement will be one of the
divine bodies which move through the heaven.

    (Evidently there is but one heaven. For if there are many
heavens as there are many men, the moving principles, of which each
heaven will have one, will be one in form but in number many. But
all things that are many in number have matter; for one and the same
definition, e.g. that of man, applies to many things, while Socrates
is one. But the primary essence has not matter; for it is complete
reality. So the unmovable first mover is one both in definition and in
number; so too, therefore, is that which is moved always and
continuously; therefore there is one heaven alone.) Our forefathers in
the most remote ages have handed down to their posterity a
tradition, in the form of a myth, that these bodies are gods, and that
the divine encloses the whole of nature. The rest of the tradition has
been added later in mythical form with a view to the persuasion of the
multitude and to its legal and utilitarian expediency; they say
these gods are in the form of men or like some of the other animals,
and they say other things consequent on and similar to these which
we have mentioned. But if one were to separate the first point from
these additions and take it alone-that they thought the first
substances to be gods, one must regard this as an inspired
utterance, and reflect that, while probably each art and each
science has often been developed as far as possible and has again
perished, these opinions, with others, have been preserved until the
present like relics of the ancient treasure. Only thus far, then, is
the opinion of our ancestors and of our earliest predecessors clear to
us.

                                   9

    The nature of the divine thought involves certain problems; for
while thought is held to be the most divine of things observed by
us, the question how it must be situated in order to have that
character involves difficulties. For if it thinks of nothing, what
is there here of dignity? It is just like one who sleeps. And if it
thinks, but this depends on something else, then (since that which
is its substance is not the act of thinking, but a potency) it
cannot be the best substance; for it is through thinking that its
value belongs to it. Further, whether its substance is the faculty
of thought or the act of thinking, what does it think of? Either of
itself or of something else; and if of something else, either of the
same thing always or of something different. Does it matter, then,
or not, whether it thinks of the good or of any chance thing? Are
there not some things about which it is incredible that it should
think? Evidently, then, it thinks of that which is most divine and
precious, and it does not change; for change would be change for the
worse, and this would be already a movement. First, then, if 'thought'
is not the act of thinking but a potency, it would be reasonable to
suppose that the continuity of its thinking is wearisome to it.
Secondly, there would evidently be something else more precious than
thought, viz. that which is thought of. For both thinking and the
act of thought will belong even to one who thinks of the worst thing
in the world, so that if this ought to be avoided (and it ought, for
there are even some things which it is better not to see than to see),
the act of thinking cannot be the best of things. Therefore it must be
of itself that the divine thought thinks (since it is the most
excellent of things), and its thinking is a thinking on thinking.

    But evidently knowledge and perception and opinion and
understanding have always something else as their object, and
themselves only by the way. Further, if thinking and being thought
of are different, in respect of which does goodness belong to thought?
For to he an act of thinking and to he an object of thought are not
the same thing. We answer that in some cases the knowledge is the
object. In the productive sciences it is the substance or essence of
the object, matter omitted, and in the theoretical sciences the
definition or the act of thinking is the object. Since, then,
thought and the object of thought are not different in the case of
things that have not matter, the divine thought and its object will be
the same, i.e. the thinking will be one with the object of its
thought.

    A further question is left-whether the object of the divine
thought is composite; for if it were, thought would change in
passing from part to part of the whole. We answer that everything
which has not matter is indivisible-as human thought, or rather the
thought of composite beings, is in a certain period of time (for it
does not possess the good at this moment or at that, but its best,
being something different from it, is attained only in a whole
period of time), so throughout eternity is the thought which has
itself for its object.

                                  10

    We must consider also in which of two ways the nature of the
universe contains the good, and the highest good, whether as something
separate and by itself, or as the order of the parts. Probably in both
ways, as an army does; for its good is found both in its order and
in its leader, and more in the latter; for he does not depend on the
order but it depends on him. And all things are ordered together
somehow, but not all alike,-both fishes and fowls and plants; and
the world is not such that one thing has nothing to do with another,
but they are connected. For all are ordered together to one end, but
it is as in a house, where the freemen are least at liberty to act
at random, but all things or most things are already ordained for
them, while the slaves and the animals do little for the common
good, and for the most part live at random; for this is the sort of
principle that constitutes the nature of each. I mean, for instance,
that all must at least come to be dissolved into their elements, and
there are other functions similarly in which all share for the good of
the whole.

    We must not fail to observe how many impossible or paradoxical
results confront those who hold different views from our own, and what
are the views of the subtler thinkers, and which views are attended by
fewest difficulties. All make all things out of contraries. But
neither 'all things' nor 'out of contraries' is right; nor do these
thinkers tell us how all the things in which the contraries are
present can be made out of the contraries; for contraries are not
affected by one another. Now for us this difficulty is solved
naturally by the fact that there is a third element. These thinkers
however make one of the two contraries matter; this is done for
instance by those who make the unequal matter for the equal, or the
many matter for the one. But this also is refuted in the same way; for
the one matter which underlies any pair of contraries is contrary to
nothing. Further, all things, except the one, will, on the view we are
criticizing, partake of evil; for the bad itself is one of the two
elements. But the other school does not treat the good and the bad
even as principles; yet in all things the good is in the highest
degree a principle. The school we first mentioned is right in saying
that it is a principle, but how the good is a principle they do not
say-whether as end or as mover or as form.

    Empedocles also has a paradoxical view; for he identifies the good
with love, but this is a principle both as mover (for it brings things
together) and as matter (for it is part of the mixture). Now even if
it happens that the same thing is a principle both as matter and as
mover, still the being, at least, of the two is not the same. In which
respect then is love a principle? It is paradoxical also that strife
should be imperishable; the nature of his 'evil' is just strife.

    Anaxagoras makes the good a motive principle; for his 'reason'
moves things. But it moves them for an end, which must be something
other than it, except according to our way of stating the case; for,
on our view, the medical art is in a sense health. It is paradoxical
also not to suppose a contrary to the good, i.e. to reason. But all
who speak of the contraries make no use of the contraries, unless we
bring their views into shape. And why some things are perishable and
others imperishable, no one tells us; for they make all existing
things out of the same principles. Further, some make existing
things out of the nonexistent; and others to avoid the necessity of
this make all things one.

    Further, why should there always be becoming, and what is the
cause of becoming?-this no one tells us. And those who suppose two
principles must suppose another, a superior principle, and so must
those who believe in the Forms; for why did things come to
participate, or why do they participate, in the Forms? And all other
thinkers are confronted by the necessary consequence that there is
something contrary to Wisdom, i.e. to the highest knowledge; but we
are not. For there is nothing contrary to that which is primary; for
all contraries have matter, and things that have matter exist only
potentially; and the ignorance which is contrary to any knowledge
leads to an object contrary to the object of the knowledge; but what
is primary has no contrary.

    Again, if besides sensible things no others exist, there will be
no first principle, no order, no becoming, no heavenly bodies, but
each principle will have a principle before it, as in the accounts
of the theologians and all the natural philosophers. But if the
Forms or the numbers are to exist, they will be causes of nothing;
or if not that, at least not of movement. Further, how is extension,
i.e. a continuum, to be produced out of unextended parts? For number
will not, either as mover or as form, produce a continuum. But again
there cannot be any contrary that is also essentially a productive
or moving principle; for it would be possible for it not to be. Or
at least its action would be posterior to its potency. The world,
then, would not be eternal. But it is; one of these premisses, then,
must be denied. And we have said how this must be done. Further, in
virtue of what the numbers, or the soul and the body, or in general
the form and the thing, are one-of this no one tells us anything;
nor can any one tell, unless he says, as we do, that the mover makes
them one. And those who say mathematical number is first and go on
to generate one kind of substance after another and give different
principles for each, make the substance of the universe a mere
series of episodes (for one substance has no influence on another by
its existence or nonexistence), and they give us many governing
principles; but the world refuses to be governed badly.

          'The rule of many is not good; one ruler let there be.'

                                Book XIII

                                   1

    WE have stated what is the substance of sensible things, dealing
in the treatise on physics with matter, and later with the substance
which has actual existence. Now since our inquiry is whether there
is or is not besides the sensible substances any which is immovable
and eternal, and, if there is, what it is, we must first consider what
is said by others, so that, if there is anything which they say
wrongly, we may not be liable to the same objections, while, if
there is any opinion common to them and us, we shall have no private
grievance against ourselves on that account; for one must be content
to state some points better than one's predecessors, and others no
worse.

    Two opinions are held on this subject; it is said that the objects
of mathematics-i.e. numbers and lines and the like-are substances, and
again that the Ideas are substances. And (1) since some recognize
these as two different classes-the Ideas and the mathematical numbers,
and (2) some recognize both as having one nature, while (3) some
others say that the mathematical substances are the only substances,
we must consider first the objects of mathematics, not qualifying them
by any other characteristic-not asking, for instance, whether they are
in fact Ideas or not, or whether they are the principles and
substances of existing things or not, but only whether as objects of
mathematics they exist or not, and if they exist, how they exist. Then
after this we must separately consider the Ideas themselves in a
general way, and only as far as the accepted mode of treatment
demands; for most of the points have been repeatedly made even by
the discussions outside our school, and, further, the greater part
of our account must finish by throwing light on that inquiry, viz.
when we examine whether the substances and the principles of
existing things are numbers and Ideas; for after the discussion of the
Ideas this remans as a third inquiry.

    If the objects of mathematics exist, they must exist either in
sensible objects, as some say, or separate from sensible objects
(and this also is said by some); or if they exist in neither of
these ways, either they do not exist, or they exist only in some
special sense. So that the subject of our discussion will be not
whether they exist but how they exist.

                                   2

    That it is impossible for mathematical objects to exist in
sensible things, and at the same time that the doctrine in question is
an artificial one, has been said already in our discussion of
difficulties we have pointed out that it is impossible for two
solids to be in the same place, and also that according to the same
argument the other powers and characteristics also should exist in
sensible things and none of them separately. This we have said
already. But, further, it is obvious that on this theory it is
impossible for any body whatever to be divided; for it would have to
be divided at a plane, and the plane at a line, and the line at a
point, so that if the point cannot be divided, neither can the line,
and if the line cannot, neither can the plane nor the solid. What
difference, then, does it make whether sensible things are such
indivisible entities, or, without being so themselves, have
indivisible entities in them? The result will be the same; if the
sensible entities are divided the others will be divided too, or
else not even the sensible entities can be divided.

    But, again, it is not possible that such entities should exist
separately. For if besides the sensible solids there are to be other
solids which are separate from them and prior to the sensible
solids, it is plain that besides the planes also there must be other
and separate planes and points and lines; for consistency requires
this. But if these exist, again besides the planes and lines and
points of the mathematical solid there must be others which are
separate. (For incomposites are prior to compounds; and if there
are, prior to the sensible bodies, bodies which are not sensible, by
the same argument the planes which exist by themselves must be prior
to those which are in the motionless solids. Therefore these will be
planes and lines other than those that exist along with the
mathematical solids to which these thinkers assign separate existence;
for the latter exist along with the mathematical solids, while the
others are prior to the mathematical solids.) Again, therefore,
there will be, belonging to these planes, lines, and prior to them
there will have to be, by the same argument, other lines and points;
and prior to these points in the prior lines there will have to be
other points, though there will be no others prior to these. Now (1)
the accumulation becomes absurd; for we find ourselves with one set of
solids apart from the sensible solids; three sets of planes apart from
the sensible planes-those which exist apart from the sensible
planes, and those in the mathematical solids, and those which exist
apart from those in the mathematical solids; four sets of lines, and
five sets of points. With which of these, then, will the
mathematical sciences deal? Certainly not with the planes and lines
and points in the motionless solid; for science always deals with what
is prior. And (the same account will apply also to numbers; for
there will be a different set of units apart from each set of
points, and also apart from each set of realities, from the objects of
sense and again from those of thought; so that there will be various
classes of mathematical numbers.

    Again, how is it possible to solve the questions which we have
already enumerated in our discussion of difficulties? For the
objects of astronomy will exist apart from sensible things just as the
objects of geometry will; but how is it possible that a heaven and its
parts-or anything else which has movement-should exist apart?
Similarly also the objects of optics and of harmonics will exist
apart; for there will be both voice and sight besides the sensible
or individual voices and sights. Therefore it is plain that the
other senses as well, and the other objects of sense, will exist
apart; for why should one set of them do so and another not? And if
this is so, there will also be animals existing apart, since there
will be senses.

    Again, there are certain mathematical theorems that are universal,
extending beyond these substances. Here then we shall have another
intermediate substance separate both from the Ideas and from the
intermediates,-a substance which is neither number nor points nor
spatial magnitude nor time. And if this is impossible, plainly it is
also impossible that the former entities should exist separate from
sensible things.

    And, in general, conclusion contrary alike to the truth and to the
usual views follow, if one is to suppose the objects of mathematics to
exist thus as separate entities. For because they exist thus they must
be prior to sensible spatial magnitudes, but in truth they must be
posterior; for the incomplete spatial magnitude is in the order of
generation prior, but in the order of substance posterior, as the
lifeless is to the living.

    Again, by virtue of what, and when, will mathematical magnitudes
be one? For things in our perceptible world are one in virtue of soul,
or of a part of soul, or of something else that is reasonable
enough; when these are not present, the thing is a plurality, and
splits up into parts. But in the case of the subjects of
mathematics, which are divisible and are quantities, what is the cause
of their being one and holding together?

    Again, the modes of generation of the objects of mathematics
show that we are right. For the dimension first generated is length,
then comes breadth, lastly depth, and the process is complete. If,
then, that which is posterior in the order of generation is prior in
the order of substantiality, the solid will be prior to the plane
and the line. And in this way also it is both more complete and more
whole, because it can become animate. How, on the other hand, could
a line or a plane be animate? The supposition passes the power of
our senses.

    Again, the solid is a sort of substance; for it already has in a
sense completeness. But how can lines be substances? Neither as a form
or shape, as the soul perhaps is, nor as matter, like the solid; for
we have no experience of anything that can be put together out of
lines or planes or points, while if these had been a sort of
material substance, we should have observed things which could be
put together out of them.

    Grant, then, that they are prior in definition. Still not all
things that are prior in definition are also prior in
substantiality. For those things are prior in substantiality which
when separated from other things surpass them in the power of
independent existence, but things are prior in definition to those
whose definitions are compounded out of their definitions; and these
two properties are not coextensive. For if attributes do not exist
apart from the substances (e.g. a 'mobile' or a pale'), pale is
prior to the pale man in definition, but not in substantiality. For it
cannot exist separately, but is always along with the concrete
thing; and by the concrete thing I mean the pale man. Therefore it
is plain that neither is the result of abstraction prior nor that
which is produced by adding determinants posterior; for it is by
adding a determinant to pale that we speak of the pale man.

    It has, then, been sufficiently pointed out that the objects of
mathematics are not substances in a higher degree than bodies are, and
that they are not prior to sensibles in being, but only in definition,
and that they cannot exist somewhere apart. But since it was not
possible for them to exist in sensibles either, it is plain that
they either do not exist at all or exist in a special sense and
therefore do not 'exist' without qualification. For 'exist' has many
senses.

                                   3

    For just as the universal propositions of mathematics deal not
with objects which exist separately, apart from extended magnitudes
and from numbers, but with magnitudes and numbers, not however qua
such as to have magnitude or to be divisible, clearly it is possible
that there should also be both propositions and demonstrations about
sensible magnitudes, not however qua sensible but qua possessed of
certain definite qualities. For as there are many propositions about
things merely considered as in motion, apart from what each such thing
is and from their accidents, and as it is not therefore necessary that
there should be either a mobile separate from sensibles, or a distinct
mobile entity in the sensibles, so too in the case of mobiles there
will be propositions and sciences, which treat them however not qua
mobile but only qua bodies, or again only qua planes, or only qua
lines, or qua divisibles, or qua indivisibles having position, or only
qua indivisibles. Thus since it is true to say without qualification
that not only things which are separable but also things which are
inseparable exist (for instance, that mobiles exist), it is true
also to say without qualification that the objects of mathematics
exist, and with the character ascribed to them by mathematicians.
And as it is true to say of the other sciences too, without
qualification, that they deal with such and such a subject-not with
what is accidental to it (e.g. not with the pale, if the healthy thing
is pale, and the science has the healthy as its subject), but with
that which is the subject of each science-with the healthy if it
treats its object qua healthy, with man if qua man:-so too is it
with geometry; if its subjects happen to be sensible, though it does
not treat them qua sensible, the mathematical sciences will not for
that reason be sciences of sensibles-nor, on the other hand, of
other things separate from sensibles. Many properties attach to things
in virtue of their own nature as possessed of each such character;
e.g. there are attributes peculiar to the animal qua female or qua
male (yet there is no 'female' nor 'male' separate from animals); so
that there are also attributes which belong to things merely as
lengths or as planes. And in proportion as we are dealing with
things which are prior in definition and simpler, our knowledge has
more accuracy, i.e. simplicity. Therefore a science which abstracts
from spatial magnitude is more precise than one which takes it into
account; and a science is most precise if it abstracts from
movement, but if it takes account of movement, it is most precise if
it deals with the primary movement, for this is the simplest; and of
this again uniform movement is the simplest form.

    The same account may be given of harmonics and optics; for neither
considers its objects qua sight or qua voice, but qua lines and
numbers; but the latter are attributes proper to the former. And
mechanics too proceeds in the same way. Therefore if we suppose
attributes separated from their fellow attributes and make any inquiry
concerning them as such, we shall not for this reason be in error, any
more than when one draws a line on the ground and calls it a foot long
when it is not; for the error is not included in the premisses.

    Each question will be best investigated in this way-by setting
up by an act of separation what is not separate, as the
arithmetician and the geometer do. For a man qua man is one
indivisible thing; and the arithmetician supposed one indivisible
thing, and then considered whether any attribute belongs to a man
qua indivisible. But the geometer treats him neither qua man nor qua
indivisible, but as a solid. For evidently the properties which
would have belonged to him even if perchance he had not been
indivisible, can belong to him even apart from these attributes. Thus,
then, geometers speak correctly; they talk about existing things,
and their subjects do exist; for being has two forms-it exists not
only in complete reality but also materially.

    Now since the good and the beautiful are different (for the former
always implies conduct as its subject, while the beautiful is found
also in motionless things), those who assert that the mathematical
sciences say nothing of the beautiful or the good are in error. For
these sciences say and prove a great deal about them; if they do not
expressly mention them, but prove attributes which are their results
or their definitions, it is not true to say that they tell us
nothing about them. The chief forms of beauty are order and symmetry
and definiteness, which the mathematical sciences demonstrate in a
special degree. And since these (e.g. order and definiteness) are
obviously causes of many things, evidently these sciences must treat
this sort of causative principle also (i.e. the beautiful) as in
some sense a cause. But we shall speak more plainly elsewhere about
these matters.

                                   4

    So much then for the objects of mathematics; we have said that
they exist and in what sense they exist, and in what sense they are
prior and in what sense not prior. Now, regarding the Ideas, we must
first examine the ideal theory itself, not connecting it in any way
with the nature of numbers, but treating it in the form in which it
was originally understood by those who first maintained the
existence of the Ideas. The supporters of the ideal theory were led to
it because on the question about the truth of things they accepted the
Heraclitean sayings which describe all sensible things as ever passing
away, so that if knowledge or thought is to have an object, there must
be some other and permanent entities, apart from those which are
sensible; for there could be no knowledge of things which were in a
state of flux. But when Socrates was occupying himself with the
excellences of character, and in connexion with them became the
first to raise the problem of universal definition (for of the
physicists Democritus only touched on the subject to a small extent,
and defined, after a fashion, the hot and the cold; while the
Pythagoreans had before this treated of a few things, whose
definitions-e.g. those of opportunity, justice, or marriage-they
connected with numbers; but it was natural that Socrates should be
seeking the essence, for he was seeking to syllogize, and 'what a
thing is' is the starting-point of syllogisms; for there was as yet
none of the dialectical power which enables people even without
knowledge of the essence to speculate about contraries and inquire
whether the same science deals with contraries; for two things may
be fairly ascribed to Socrates-inductive arguments and universal
definition, both of which are concerned with the starting-point of
science):-but Socrates did not make the universals or the
definitions exist apart: they, however, gave them separate
existence, and this was the kind of thing they called Ideas. Therefore
it followed for them, almost by the same argument, that there must
be Ideas of all things that are spoken of universally, and it was
almost as if a man wished to count certain things, and while they were
few thought he would not be able to count them, but made more of
them and then counted them; for the Forms are, one may say, more
numerous than the particular sensible things, yet it was in seeking
the causes of these that they proceeded from them to the Forms. For to
each thing there answers an entity which has the same name and
exists apart from the substances, and so also in the case of all other
groups there is a one over many, whether these be of this world or
eternal.

    Again, of the ways in which it is proved that the Forms exist,
none is convincing; for from some no inference necessarily follows,
and from some arise Forms even of things of which they think there are
no Forms. For according to the arguments from the sciences there
will be Forms of all things of which there are sciences, and according
to the argument of the 'one over many' there will be Forms even of
negations, and according to the argument that thought has an object
when the individual object has perished, there will be Forms of
perishable things; for we have an image of these. Again, of the most
accurate arguments, some lead to Ideas of relations, of which they say
there is no independent class, and others introduce the 'third man'.

    And in general the arguments for the Forms destroy things for
whose existence the believers in Forms are more zealous than for the
existence of the Ideas; for it follows that not the dyad but number is
first, and that prior to number is the relative, and that this is
prior to the absolute-besides all the other points on which certain
people, by following out the opinions held about the Forms, came
into conflict with the principles of the theory.

    Again, according to the assumption on the belief in the Ideas
rests, there will be Forms not only of substances but also of many
other things; for the concept is single not only in the case of
substances, but also in that of non-substances, and there are sciences
of other things than substance; and a thousand other such difficulties
confront them. But according to the necessities of the case and the
opinions about the Forms, if they can be shared in there must be Ideas
of substances only. For they are not shared in incidentally, but
each Form must be shared in as something not predicated of a
subject. (By 'being shared in incidentally' I mean that if a thing
shares in 'double itself', it shares also in 'eternal', but
incidentally; for 'the double' happens to be eternal.) Therefore the
Forms will be substance. But the same names indicate substance in this
and in the ideal world (or what will be the meaning of saying that
there is something apart from the particulars-the one over many?). And
if the Ideas and the things that share in them have the same form,
there will be something common: for why should '2' be one and the same
in the perishable 2's, or in the 2's which are many but eternal, and
not the same in the '2 itself' as in the individual 2? But if they
have not the same form, they will have only the name in common, and it
is as if one were to call both Callias and a piece of wood a 'man',
without observing any community between them.

    But if we are to suppose that in other respects the common
definitions apply to the Forms, e.g. that 'plane figure' and the other
parts of the definition apply to the circle itself, but 'what really
is' has to be added, we must inquire whether this is not absolutely
meaningless. For to what is this to be added? To 'centre' or to
'plane' or to all the parts of the definition? For all the elements in
the essence are Ideas, e.g. 'animal' and 'two-footed'. Further,
there must be some Ideal answering to 'plane' above, some nature which
will be present in all the Forms as their genus.

                                   5

    Above all one might discuss the question what in the world the
Forms contribute to sensible things, either to those that are
eternal or to those that come into being and cease to be; for they
cause neither movement nor any change in them. But again they help
in no wise either towards the knowledge of other things (for they
are not even the substance of these, else they would have been in
them), or towards their being, if they are not in the individuals
which share in them; though if they were, they might be thought to
be causes, as white causes whiteness in a white object by entering
into its composition. But this argument, which was used first by
Anaxagoras, and later by Eudoxus in his discussion of difficulties and
by certain others, is very easily upset; for it is easy to collect
many and insuperable objections to such a view.

    But, further, all other things cannot come from the Forms in any
of the usual senses of 'from'. And to say that they are patterns and
the other things share in them is to use empty words and poetical
metaphors. For what is it that works, looking to the Ideas? And any
thing can both be and come into being without being copied from
something else, so that, whether Socrates exists or not, a man like
Socrates might come to be. And evidently this might be so even if
Socrates were eternal. And there will be several patterns of the
same thing, and therefore several Forms; e.g. 'animal' and
'two-footed', and also 'man-himself', will be Forms of man. Again, the
Forms are patterns not only of sensible things, but of Forms
themselves also; i.e. the genus is the pattern of the various
forms-of-a-genus; therefore the same thing will be pattern and copy.

    Again, it would seem impossible that substance and that whose
substance it is should exist apart; how, therefore, could the Ideas,
being the substances of things, exist apart?

    In the Phaedo the case is stated in this way-that the Forms are
causes both of being and of becoming. Yet though the Forms exist,
still things do not come into being, unless there is something to
originate movement; and many other things come into being (e.g. a
house or a ring) of which they say there are no Forms. Clearly
therefore even the things of which they say there are Ideas can both
be and come into being owing to such causes as produce the things just
mentioned, and not owing to the Forms. But regarding the Ideas it is
possible, both in this way and by more abstract and accurate
arguments, to collect many objections like those we have considered.

                                    6

    Since we have discussed these points, it is well to consider again
the results regarding numbers which confront those who say that
numbers are separable substances and first causes of things. If number
is an entity and its substance is nothing other than just number, as
some say, it follows that either (1) there is a first in it and a
second, each being different in species,-and either (a) this is true
of the units without exception, and any unit is inassociable with
any unit, or (b) they are all without exception successive, and any of
them are associable with any, as they say is the case with
mathematical number; for in mathematical number no one unit is in
any way different from another. Or (c) some units must be associable
and some not; e.g. suppose that 2 is first after 1, and then comes 3
and then the rest of the number series, and the units in each number
are associable, e.g. those in the first 2 are associable with one
another, and those in the first 3 with one another, and so with the
other numbers; but the units in the '2-itself' are inassociable with
those in the '3-itself'; and similarly in the case of the other
successive numbers. And so while mathematical number is counted
thus-after 1, 2 (which consists of another 1 besides the former 1),
and 3 which consists of another 1 besides these two), and the other
numbers similarly, ideal number is counted thus-after 1, a distinct
2 which does not include the first 1, and a 3 which does not include
the 2 and the rest of the number series similarly. Or (2) one kind
of number must be like the first that was named, one like that which
the mathematicians speak of, and that which we have named last must be
a third kind.

    Again, these kinds of numbers must either be separable from
things, or not separable but in objects of perception (not however
in the way which we first considered, in the sense that objects of
perception consists of numbers which are present in them)-either one
kind and not another, or all of them.

    These are of necessity the only ways in which the numbers can
exist. And of those who say that the 1 is the beginning and
substance and element of all things, and that number is formed from
the 1 and something else, almost every one has described number in one
of these ways; only no one has said all the units are inassociable.
And this has happened reasonably enough; for there can be no way
besides those mentioned. Some say both kinds of number exist, that
which has a before and after being identical with the Ideas, and
mathematical number being different from the Ideas and from sensible
things, and both being separable from sensible things; and others
say mathematical number alone exists, as the first of realities,
separate from sensible things. And the Pythagoreans, also, believe
in one kind of number-the mathematical; only they say it is not
separate but sensible substances are formed out of it. For they
construct the whole universe out of numbers-only not numbers
consisting of abstract units; they suppose the units to have spatial
magnitude. But how the first 1 was constructed so as to have
magnitude, they seem unable to say.

    Another thinker says the first kind of number, that of the
Forms, alone exists, and some say mathematical number is identical
with this.

    The case of lines, planes, and solids is similar. For some think
that those which are the objects of mathematics are different from
those which come after the Ideas; and of those who express
themselves otherwise some speak of the objects of mathematics and in a
mathematical way-viz. those who do not make the Ideas numbers nor
say that Ideas exist; and others speak of the objects of
mathematics, but not mathematically; for they say that neither is
every spatial magnitude divisible into magnitudes, nor do any two
units taken at random make 2. All who say the 1 is an element and
principle of things suppose numbers to consist of abstract units,
except the Pythagoreans; but they suppose the numbers to have
magnitude, as has been said before. It is clear from this statement,
then, in how many ways numbers may be described, and that all the ways
have been mentioned; and all these views are impossible, but some
perhaps more than others.

                                   7

    First, then, let us inquire if the units are associable or
inassociable, and if inassociable, in which of the two ways we
distinguished. For it is possible that any unity is inassociable
with any, and it is possible that those in the 'itself' are
inassociable with those in the 'itself', and, generally, that those in
each ideal number are inassociable with those in other ideal
numbers. Now (1) all units are associable and without difference, we
get mathematical number-only one kind of number, and the Ideas
cannot be the numbers. For what sort of number will man-himself or
animal-itself or any other Form be? There is one Idea of each thing
e.g. one of man-himself and another one of animal-itself; but the
similar and undifferentiated numbers are infinitely many, so that
any particular 3 is no more man-himself than any other 3. But if the
Ideas are not numbers, neither can they exist at all. For from what
principles will the Ideas come? It is number that comes from the 1 and
the indefinite dyad, and the principles or elements are said to be
principles and elements of number, and the Ideas cannot be ranked as
either prior or posterior to the numbers.

    But (2) if the units are inassociable, and inassociable in the
sense that any is inassociable with any other, number of this sort
cannot be mathematical number; for mathematical number consists of
undifferentiated units, and the truths proved of it suit this
character. Nor can it be ideal number. For 2 will not proceed
immediately from 1 and the indefinite dyad, and be followed by the
successive numbers, as they say '2,3,4' for the units in the ideal are
generated at the same time, whether, as the first holder of the theory
said, from unequals (coming into being when these were equalized) or
in some other way-since, if one unit is to be prior to the other, it
will be prior also to 2 the composed of these; for when there is one
thing prior and another posterior, the resultant of these will be
prior to one and posterior to the other.  Again, since the 1-itself is
first, and then there is a particular 1 which is first among the
others and next after the 1-itself, and again a third which is next
after the second and next but one after the first 1,-so the units must
be prior to the numbers after which they are named when we count them;
e.g. there will be a third unit in 2 before 3 exists, and a fourth and
a fifth in 3 before the numbers 4 and 5 exist.-Now none of these
thinkers has said the units are inassociable in this way, but
according to their principles it is reasonable that they should be
so even in this way, though in truth it is impossible. For it is
reasonable both that the units should have priority and posteriority
if there is a first unit or first 1, and also that the 2's should if
there is a first 2; for after the first it is reasonable and necessary
that there should be a second, and if a second, a third, and so with
the others successively. (And to say both things at the same time,
that a unit is first and another unit is second after the ideal 1, and
that a 2 is first after it, is impossible.) But they make a first unit
or 1, but not also a second and a third, and a first 2, but not also a
second and a third. Clearly, also, it is not possible, if all the
units are inassociable, that there should be a 2-itself and a
3-itself; and so with the other numbers. For whether the units are
undifferentiated or different each from each, number must be counted
by addition, e.g. 2 by adding another 1 to the one, 3 by adding
another 1 to the two, and similarly. This being so, numbers cannot
be generated as they generate them, from the 2 and the 1; for 2
becomes part of 3 and 3 of 4 and the same happens in the case of the
succeeding numbers, but they say 4 came from the first 2 and the
indefinite which makes it two 2's other than the 2-itself; if not, the
2-itself will be a part of 4 and one other 2 will be added. And
similarly 2 will consist of the 1-itself and another 1; but if this is
so, the other element cannot be an indefinite 2; for it generates
one unit, not, as the indefinite 2 does, a definite 2.

    Again, besides the 3-itself and the 2-itself how can there be
other 3's and 2's? And how do they consist of prior and posterior
units? All this is absurd and fictitious, and there cannot be a
first 2 and then a 3-itself. Yet there must, if the 1 and the
indefinite dyad are to be the elements. But if the results are
impossible, it is also impossible that these are the generating
principles.

    If the units, then, are differentiated, each from each, these
results and others similar to these follow of necessity. But (3) if
those in different numbers are differentiated, but those in the same
number are alone undifferentiated from one another, even so the
difficulties that follow are no less. E.g. in the 10-itself their
are ten units, and the 10 is composed both of them and of two 5's. But
since the 10-itself is not any chance number nor composed of any
chance 5's--or, for that matter, units--the units in this 10 must
differ. For if they do not differ, neither will the 5's of which the
10 consists differ; but since these differ, the units also will
differ. But if they differ, will there be no other 5's in the 10 but
only these two, or will there be others? If there are not, this is
paradoxical; and if there are, what sort of 10 will consist of them?
For there is no other in the 10 but the 10 itself. But it is
actually necessary on their view that the 4 should not consist of
any chance 2's; for the indefinite as they say, received the
definite 2 and made two 2's; for its nature was to double what it
received.

    Again, as to the 2 being an entity apart from its two units, and
the 3 an entity apart from its three units, how is this possible?
Either by one's sharing in the other, as 'pale man' is different
from 'pale' and 'man' (for it shares in these), or when one is a
differentia of the other, as 'man' is different from 'animal' and
'two-footed'.

    Again, some things are one by contact, some by intermixture,
some by position; none of which can belong to the units of which the 2
or the 3 consists; but as two men are not a unity apart from both,
so must it be with the units. And their being indivisible will make no
difference to them; for points too are indivisible, but yet a pair
of them is nothing apart from the two.

    But this consequence also we must not forget, that it follows that
there are prior and posterior 2 and similarly with the other
numbers. For let the 2's in the 4 be simultaneous; yet these are prior
to those in the 8 and as the 2 generated them, they generated the
4's in the 8-itself. Therefore if the first 2 is an Idea, these 2's
also will be Ideas of some kind. And the same account applies to the
units; for the units in the first 2 generate the four in 4, so that
all the units come to be Ideas and an Idea will be composed of
Ideas. Clearly therefore those things also of which these happen to be
the Ideas will be composite, e.g. one might say that animals are
composed of animals, if there are Ideas of them.

    In general, to differentiate the units in any way is an
absurdity and a fiction; and by a fiction I mean a forced statement
made to suit a hypothesis. For neither in quantity nor in quality do
we see unit differing from unit, and number must be either equal or
unequal-all number but especially that which consists of abstract
units-so that if one number is neither greater nor less than
another, it is equal to it; but things that are equal and in no wise
differentiated we take to be the same when we are speaking of numbers.
If not, not even the 2 in the 10-itself will be undifferentiated,
though they are equal; for what reason will the man who alleges that
they are not differentiated be able to give?

    Again, if every unit + another unit makes two, a unit from the
2-itself and one from the 3-itself will make a 2. Now (a) this will
consist of differentiated units; and will it be prior to the 3 or
posterior? It rather seems that it must be prior; for one of the units
is simultaneous with the 3 and the other is simultaneous with the 2.
And we, for our part, suppose that in general 1 and 1, whether the
things are equal or unequal, is 2, e.g. the good and the bad, or a man
and a horse; but those who hold these views say that not even two
units are 2.

    If the number of the 3-itself is not greater than that of the 2,
this is surprising; and if it is greater, clearly there is also a
number in it equal to the 2, so that this is not different from the
2-itself. But this is not possible, if there is a first and a second
number.

    Nor will the Ideas be numbers. For in this particular point they
are right who claim that the units must be different, if there are
to be Ideas; as has been said before. For the Form is unique; but if
the units are not different, the 2's and the 3's also will not be
different. This is also the reason why they must say that when we
count thus-'1,2'-we do not proceed by adding to the given number;
for if we do, neither will the numbers be generated from the
indefinite dyad, nor can a number be an Idea; for then one Idea will
be in another, and all Forms will be parts of one Form. And so with
a view to their hypothesis their statements are right, but as a
whole they are wrong; for their view is very destructive, since they
will admit that this question itself affords some
difficulty-whether, when we count and say -1,2,3-we count by
addition or by separate portions. But we do both; and so it is
absurd to reason back from this problem to so great a difference of
essence.

                                   8

    First of all it is well to determine what is the differentia of
a number-and of a unit, if it has a differentia. Units must differ
either in quantity or in quality; and neither of these seems to be
possible. But number qua number differs in quantity. And if the
units also did differ in quantity, number would differ from number,
though equal in number of units. Again, are the first units greater or
smaller, and do the later ones increase or diminish? All these are
irrational suppositions. But neither can they differ in quality. For
no attribute can attach to them; for even to numbers quality is said
to belong after quantity. Again, quality could not come to them either
from the 1 or the dyad; for the former has no quality, and the
latter gives quantity; for this entity is what makes things to be
many. If the facts are really otherwise, they should state this
quite at the beginning and determine if possible, regarding the
differentia of the unit, why it must exist, and, failing this, what
differentia they mean.

    Evidently then, if the Ideas are numbers, the units cannot all
be associable, nor can they be inassociable in either of the two ways.
But neither is the way in which some others speak about numbers
correct. These are those who do not think there are Ideas, either
without qualification or as identified with certain numbers, but think
the objects of mathematics exist and the numbers are the first of
existing things, and the 1-itself is the starting-point of them. It is
paradoxical that there should be a 1 which is first of 1's, as they
say, but not a 2 which is first of 2's, nor a 3 of 3's; for the same
reasoning applies to all. If, then, the facts with regard to number
are so, and one supposes mathematical number alone to exist, the 1
is not the starting-point (for this sort of 1 must differ from
the-other units; and if this is so, there must also be a 2 which is
first of 2's, and similarly with the other successive numbers). But if
the 1 is the starting-point, the truth about the numbers must rather
be what Plato used to say, and there must be a first 2 and 3 and
numbers must not be associable with one another. But if on the other
hand one supposes this, many impossible results, as we have said,
follow. But either this or the other must be the case, so that if
neither is, number cannot exist separately.

    It is evident, also, from this that the third version is the
worst,-the view ideal and mathematical number is the same. For two
mistakes must then meet in the one opinion. (1) Mathematical number
cannot be of this sort, but the holder of this view has to spin it out
by making suppositions peculiar to himself. And (2) he must also admit
all the consequences that confront those who speak of number in the
sense of 'Forms'.

    The Pythagorean version in one way affords fewer difficulties than
those before named, but in another way has others peculiar to
itself. For not thinking of number as capable of existing separately
removes many of the impossible consequences; but that bodies should be
composed of numbers, and that this should be mathematical number, is
impossible. For it is not true to speak of indivisible spatial
magnitudes; and however much there might be magnitudes of this sort,
units at least have not magnitude; and how can a magnitude be composed
of indivisibles? But arithmetical number, at least, consists of units,
while these thinkers identify number with real things; at any rate
they apply their propositions to bodies as if they consisted of
those numbers.

    If, then, it is necessary, if number is a self-subsistent real
thing, that it should exist in one of these ways which have been
mentioned, and if it cannot exist in any of these, evidently number
has no such nature as those who make it separable set up for it.

    Again, does each unit come from the great and the small,
equalized, or one from the small, another from the great? (a) If the
latter, neither does each thing contain all the elements, nor are
the units without difference; for in one there is the great and in
another the small, which is contrary in its nature to the great.
Again, how is it with the units in the 3-itself? One of them is an odd
unit. But perhaps it is for this reason that they give 1-itself the
middle place in odd numbers. (b) But if each of the two units consists
of both the great and the small, equalized, how will the 2 which is
a single thing, consist of the great and the small? Or how will it
differ from the unit? Again, the unit is prior to the 2; for when it
is destroyed the 2 is destroyed. It must, then, be the Idea of an Idea
since it is prior to an Idea, and it must have come into being
before it. From what, then? Not from the indefinite dyad, for its
function was to double.

    Again, number must be either infinite or finite; for these
thinkers think of number as capable of existing separately, so that it
is not possible that neither of those alternatives should be true.
Clearly it cannot be infinite; for infinite number is neither odd
nor even, but the generation of numbers is always the generation
either of an odd or of an even number; in one way, when 1 operates
on an even number, an odd number is produced; in another way, when 2
operates, the numbers got from 1 by doubling are produced; in
another way, when the odd numbers operate, the other even numbers
are produced. Again, if every Idea is an Idea of something, and the
numbers are Ideas, infinite number itself will be an Idea of
something, either of some sensible thing or of something else. Yet
this is not possible in view of their thesis any more than it is
reasonable in itself, at least if they arrange the Ideas as they do.

    But if number is finite, how far does it go? With regard to this
not only the fact but the reason should be stated. But if number
goes only up to 10 as some say, firstly the Forms will soon run short;
e.g. if 3 is man-himself, what number will be the horse-itself? The
series of the numbers which are the several things-themselves goes
up to 10. It must, then, be one of the numbers within these limits;
for it is these that are substances and Ideas. Yet they will run
short; for the various forms of animal will outnumber them. At the
same time it is clear that if in this way the 3 is man-himself, the
other 3's are so also (for those in identical numbers are similar), so
that there will be an infinite number of men; if each 3 is an Idea,
each of the numbers will be man-himself, and if not, they will at
least be men. And if the smaller number is part of the greater
(being number of such a sort that the units in the same number are
associable), then if the 4-itself is an Idea of something, e.g. of
'horse' or of 'white', man will be a part of horse, if man is It is
paradoxical also that there should be an Idea of 10 but not of 11, nor
of the succeeding numbers. Again, there both are and come to be
certain things of which there are no Forms; why, then, are there not
Forms of them also? We infer that the Forms are not causes. Again,
it is paradoxical-if the number series up to 10 is more of a real
thing and a Form than 10 itself. There is no generation of the
former as one thing, and there is of the latter. But they try to
work on the assumption that the series of numbers up to 10 is a
complete series. At least they generate the derivatives-e.g. the void,
proportion, the odd, and the others of this kind-within the decade.
For some things, e.g. movement and rest, good and bad, they assign
to the originative principles, and the others to the numbers. This
is why they identify the odd with 1; for if the odd implied 3 how
would 5 be odd? Again, spatial magnitudes and all such things are
explained without going beyond a definite number; e.g. the first,
the indivisible, line, then the 2 &c.; these entities also extend only
up to 10.

    Again, if number can exist separately, one might ask which is
prior- 1, or 3 or 2? Inasmuch as the number is composite, 1 is prior,
but inasmuch as the universal and the form is prior, the number is
prior; for each of the units is part of the number as its matter,
and the number acts as form. And in a sense the right angle is prior
to the acute, because it is determinate and in virtue of its
definition; but in a sense the acute is prior, because it is a part
and the right angle is divided into acute angles. As matter, then, the
acute angle and the element and the unit are prior, but in respect
of the form and of the substance as expressed in the definition, the
right angle, and the whole consisting of the matter and the form,
are prior; for the concrete thing is nearer to the form and to what is
expressed in the definition, though in generation it is later. How
then is 1 the starting-point? Because it is not divisiable, they
say; but both the universal, and the particular or the element, are
indivisible. But they are starting-points in different ways, one in
definition and the other in time. In which way, then, is 1 the
starting-point? As has been said, the right angle is thought to be
prior to the acute, and the acute to the right, and each is one.
Accordingly they make 1 the starting-point in both ways. But this is
impossible. For the universal is one as form or substance, while the
element is one as a part or as matter. For each of the two is in a
sense one-in truth each of the two units exists potentially (at
least if the number is a unity and not like a heap, i.e. if
different numbers consist of differentiated units, as they say), but
not in complete reality; and the cause of the error they fell into
is that they were conducting their inquiry at the same time from the
standpoint of mathematics and from that of universal definitions, so
that (1) from the former standpoint they treated unity, their first
principle, as a point; for the unit is a point without position.
They put things together out of the smallest parts, as some others
also have done. Therefore the unit becomes the matter of numbers and
at the same time prior to 2; and again posterior, 2 being treated as a
whole, a unity, and a form. But (2) because they were seeking the
universal they treated the unity which can be predicated of a
number, as in this sense also a part of the number. But these
characteristics cannot belong at the same time to the same thing.

    If the 1-itself must be unitary (for it differs in nothing from
other 1's except that it is the starting-point), and the 2 is
divisible but the unit is not, the unit must be liker the 1-itself
than the 2 is. But if the unit is liker it, it must be liker to the
unit than to the 2; therefore each of the units in 2 must be prior
to the 2. But they deny this; at least they generate the 2 first.
Again, if the 2-itself is a unity and the 3-itself is one also, both
form a 2. From what, then, is this 2 produced?

                                   9

    Since there is not contact in numbers, but succession, viz.
between the units between which there is nothing, e.g. between those
in 2 or in 3 one might ask whether these succeed the 1-itself or
not, and whether, of the terms that succeed it, 2 or either of the
units in 2 is prior.

    Similar difficulties occur with regard to the classes of things
posterior to number,-the line, the plane, and the solid. For some
construct these out of the species of the 'great and small'; e.g.
lines from the 'long and short', planes from the 'broad and narrow',
masses from the 'deep and shallow'; which are species of the 'great
and small'. And the originative principle of such things which answers
to the 1 different thinkers describe in different ways, And in these
also the impossibilities, the fictions, and the contradictions of
all probability are seen to be innumerable. For (i) geometrical
classes are severed from one another, unless the principles of these
are implied in one another in such a way that the 'broad and narrow'
is also 'long and short' (but if this is so, the plane will be line
and the solid a plane; again, how will angles and figures and such
things be explained?). And (ii) the same happens as in regard to
number; for 'long and short', &c., are attributes of magnitude, but
magnitude does not consist of these, any more than the line consists
of 'straight and curved', or solids of 'smooth and rough'.

    (All these views share a difficulty which occurs with regard to
species-of-a-genus, when one posits the universals, viz. whether it is
animal-itself or something other than animal-itself that is in the
particular animal. True, if the universal is not separable from
sensible things, this will present no difficulty; but if the 1 and the
numbers are separable, as those who express these views say, it is not
easy to solve the difficulty, if one may apply the words 'not easy' to
the impossible. For when we apprehend the unity in 2, or in general in
a number, do we apprehend a thing-itself or something else?).

    Some, then, generate spatial magnitudes from matter of this
sort, others from the point -and the point is thought by them to be
not 1 but something like 1-and from other matter like plurality, but
not identical with it; about which principles none the less the same
difficulties occur. For if the matter is one, line and plane-and
soli will be the same; for from the same elements will come one and
the same thing. But if the matters are more than one, and there is one
for the line and a second for the plane and another for the solid,
they either are implied in one another or not, so that the same
results will follow even so; for either the plane will not contain a
line or it will he a line.

    Again, how number can consist of the one and plurality, they
make no attempt to explain; but however they express themselves, the
same objections arise as confront those who construct number out of
the one and the indefinite dyad. For the one view generates number
from the universally predicated plurality, and not from a particular
plurality; and the other generates it from a particular plurality, but
the first; for 2 is said to be a 'first plurality'. Therefore there is
practically no difference, but the same difficulties will follow,-is
it intermixture or position or blending or generation? and so on.
Above all one might press the question 'if each unit is one, what does
it come from?' Certainly each is not the one-itself. It must, then,
come from the one itself and plurality, or a part of plurality. To say
that the unit is a plurality is impossible, for it is indivisible; and
to generate it from a part of plurality involves many other
objections; for (a) each of the parts must be indivisible (or it
will be a plurality and the unit will be divisible) and the elements
will not be the one and plurality; for the single units do not come
from plurality and the one. Again, (,the holder of this view does
nothing but presuppose another number; for his plurality of
indivisibles is a number. Again, we must inquire, in view of this
theory also, whether the number is infinite or finite. For there was
at first, as it seems, a plurality that was itself finite, from
which and from the one comes the finite number of units. And there
is another plurality that is plurality-itself and infinite
plurality; which sort of plurality, then, is the element which
co-operates with the one? One might inquire similarly about the point,
i.e. the element out of which they make spatial magnitudes. For surely
this is not the one and only point; at any rate, then, let them say
out of what each of the points is formed. Certainly not of some
distance + the point-itself. Nor again can there be indivisible
parts of a distance, as the elements out of which the units are said
to be made are indivisible parts of plurality; for number consists
of indivisibles, but spatial magnitudes do not.

    All these objections, then, and others of the sort make it evident
that number and spatial magnitudes cannot exist apart from things.
Again, the discord about numbers between the various versions is a
sign that it is the incorrectness of the alleged facts themselves that
brings confusion into the theories. For those who make the objects
of mathematics alone exist apart from sensible things, seeing the
difficulty about the Forms and their fictitiousness, abandoned ideal
number and posited mathematical. But those who wished to make the
Forms at the same time also numbers, but did not see, if one assumed
these principles, how mathematical number was to exist apart from
ideal, made ideal and mathematical number the same-in words, since
in fact mathematical number has been destroyed; for they state
hypotheses peculiar to themselves and not those of mathematics. And he
who first supposed that the Forms exist and that the Forms are numbers
and that the objects of mathematics exist, naturally separated the
two. Therefore it turns out that all of them are right in some
respect, but on the whole not right. And they themselves confirm this,
for their statements do not agree but conflict. The cause is that
their hypotheses and their principles are false. And it is hard to
make a good case out of bad materials, according to Epicharmus: 'as
soon as 'tis said, 'tis seen to be wrong.'

    But regarding numbers the questions we have raised and the
conclusions we have reached are sufficient (for while he who is
already convinced might be further convinced by a longer discussion,
one not yet convinced would not come any nearer to conviction);
regarding the first principles and the first causes and elements,
the views expressed by those who discuss only sensible substance
have been partly stated in our works on nature, and partly do not
belong to the present inquiry; but the views of those who assert
that there are other substances besides the sensible must be
considered next after those we have been mentioning. Since, then, some
say that the Ideas and the numbers are such substances, and that the
elements of these are elements and principles of real things, we
must inquire regarding these what they say and in what sense they
say it.

    Those who posit numbers only, and these mathematical, must be
considered later; but as regards those who believe in the Ideas one
might survey at the same time their way of thinking and the difficulty
into which they fall. For they at the same time make the Ideas
universal and again treat them as separable and as individuals. That
this is not possible has been argued before. The reason why those
who described their substances as universal combined these two
characteristics in one thing, is that they did not make substances
identical with sensible things. They thought that the particulars in
the sensible world were a state of flux and none of them remained, but
that the universal was apart from these and something different. And
Socrates gave the impulse to this theory, as we said in our earlier
discussion, by reason of his definitions, but he did not separate
universals from individuals; and in this he thought rightly, in not
separating them. This is plain from the results; for without the
universal it is not possible to get knowledge, but the separation is
the cause of the objections that arise with regard to the Ideas. His
successors, however, treating it as necessary, if there are to be
any substances besides the sensible and transient substances, that
they must be separable, had no others, but gave separate existence
to these universally predicated substances, so that it followed that
universals and individuals were almost the same sort of thing. This in
itself, then, would be one difficulty in the view we have mentioned.

                                  10

    Let us now mention a point which presents a certain difficulty
both to those who believe in the Ideas and to those who do not, and
which was stated before, at the beginning, among the problems. If we
do not suppose substances to be separate, and in the way in which
individual things are said to be separate, we shall destroy
substance in the sense in which we understand 'substance'; but if we
conceive substances to be separable, how are we to conceive their
elements and their principles?

    If they are individual and not universal, (a) real things will
be just of the same number as the elements, and (b) the elements
will not be knowable. For (a) let the syllables in speech be
substances, and their elements elements of substances; then there must
be only one 'ba' and one of each of the syllables, since they are
not universal and the same in form but each is one in number and a
'this' and not a kind possessed of a common name (and again they
suppose that the 'just what a thing is' is in each case one). And if
the syllables are unique, so too are the parts of which they
consist; there will not, then, be more a's than one, nor more than one
of any of the other elements, on the same principle on which an
identical syllable cannot exist in the plural number. But if this is
so, there will not be other things existing besides the elements,
but only the elements.

    (b) Again, the elements will not be even knowable; for they are
not universal, and knowledge is of universals. This is clear from
demonstrations and from definitions; for we do not conclude that
this triangle has its angles equal to two right angles, unless every
triangle has its angles equal to two right angles, nor that this man
is an animal, unless every man is an animal.

    But if the principles are universal, either the substances
composed of them are also universal, or non-substance will be prior to
substance; for the universal is not a substance, but the element or
principle is universal, and the element or principle is prior to the
things of which it is the principle or element.

    All these difficulties follow naturally, when they make the
Ideas out of elements and at the same time claim that apart from the
substances which have the same form there are Ideas, a single separate
entity. But if, e.g. in the case of the elements of speech, the a's
and the b's may quite well be many and there need be no a-itself and
b-itself besides the many, there may be, so far as this goes, an
infinite number of similar syllables. The statement that an
knowledge is universal, so that the principles of things must also
be universal and not separate substances, presents indeed, of all
the points we have mentioned, the greatest difficulty, but yet the
statement is in a sense true, although in a sense it is not. For
knowledge, like the verb 'to know', means two things, of which one
is potential and one actual. The potency, being, as matter,
universal and indefinite, deals with the universal and indefinite; but
the actuality, being definite, deals with a definite object, being a
'this', it deals with a 'this'. But per accidens sight sees
universal colour, because this individual colour which it sees is
colour; and this individual a which the grammarian investigates is
an a. For if the principles must be universal, what is derived from
them must also be universal, as in demonstrations; and if this is
so, there will be nothing capable of separate existence-i.e. no
substance. But evidently in a sense knowledge is universal, and in a
sense it is not.

                                Book XIV

                                   1

    REGARDING this kind of substance, what we have said must be
taken as sufficient. All philosophers make the first principles
contraries: as in natural things, so also in the case of
unchangeable substances. But since there cannot be anything prior to
the first principle of all things, the principle cannot be the
principle and yet be an attribute of something else. To suggest this
is like saying that the white is a first principle, not qua anything
else but qua white, but yet that it is predicable of a subject, i.e.
that its being white presupposes its being something else; this is
absurd, for then that subject will be prior. But all things which
are generated from their contraries involve an underlying subject; a
subject, then, must be present in the case of contraries, if anywhere.
All contraries, then, are always predicable of a subject, and none can
exist apart, but just as appearances suggest that there is nothing
contrary to substance, argument confirms this. No contrary, then, is
the first principle of all things in the full sense; the first
principle is something different.

    But these thinkers make one of the contraries matter, some
making the unequal which they take to be the essence of
plurality-matter for the One, and others making plurality matter for
the One. (The former generate numbers out of the dyad of the
unequal, i.e. of the great and small, and the other thinker we have
referred to generates them out of plurality, while according to both
it is generated by the essence of the One.) For even the philosopher
who says the unequal and the One are the elements, and the unequal
is a dyad composed of the great and small, treats the unequal, or
the great and the small, as being one, and does not draw the
distinction that they are one in definition, but not in number. But
they do not describe rightly even the principles which they call
elements, for some name the great and the small with the One and treat
these three as elements of numbers, two being matter, one the form;
while others name the many and few, because the great and the small
are more appropriate in their nature to magnitude than to number;
and others name rather the universal character common to these-'that
which exceeds and that which is exceeded'. None of these varieties
of opinion makes any difference to speak of, in view of some of the
consequences; they affect only the abstract objections, which these
thinkers take care to avoid because the demonstrations they themselves
offer are abstract,-with this exception, that if the exceeding and the
exceeded are the principles, and not the great and the small,
consistency requires that number should come from the elements
before does; for number is more universal than as the exceeding and
the exceeded are more universal than the great and the small. But as
it is, they say one of these things but do not say the other. Others
oppose the different and the other to the One, and others oppose
plurality to the One. But if, as they claim, things consist of
contraries, and to the One either there is nothing contrary, or if
there is to be anything it is plurality, and the unequal is contrary
to the equal, and the different to the same, and the other to the
thing itself, those who oppose the One to plurality have most claim to
plausibility, but even their view is inadequate, for the One would
on their view be a few; for plurality is opposed to fewness, and the
many to the few.

    'The one' evidently means a measure. And in every case there is
some underlying thing with a distinct nature of its own, e.g. in the
scale a quarter-tone, in spatial magnitude a finger or a foot or
something of the sort, in rhythms a beat or a syllable; and
similarly in gravity it is a definite weight; and in the same way in
all cases, in qualities a quality, in quantities a quantity (and the
measure is indivisible, in the former case in kind, and in the
latter to the sense); which implies that the one is not in itself
the substance of anything. And this is reasonable; for 'the one' means
the measure of some plurality, and 'number' means a measured plurality
and a plurality of measures. (Thus it is natural that one is not a
number; for the measure is not measures, but both the measure and
the one are starting-points.) The measure must always be some
identical thing predicable of all the things it measures, e.g. if
the things are horses, the measure is 'horse', and if they are men,
'man'. If they are a man, a horse, and a god, the measure is perhaps
'living being', and the number of them will be a number of living
beings. If the things are 'man' and 'pale' and 'walking', these will
scarcely have a number, because all belong to a subject which is one
and the same in number, yet the number of these will be a number of
'kinds' or of some such term.

    Those who treat the unequal as one thing, and the dyad as an
indefinite compound of great and small, say what is very far from
being probable or possible. For (a) these are modifications and
accidents, rather than substrata, of numbers and magnitudes-the many
and few of number, and the great and small of magnitude-like even
and odd, smooth and rough, straight and curved. Again, (b) apart
from this mistake, the great and the small, and so on, must be
relative to something; but what is relative is least of all things a
kind of entity or substance, and is posterior to quality and quantity;
and the relative is an accident of quantity, as was said, not its
matter, since something with a distinct nature of its own must serve
as matter both to the relative in general and to its parts and
kinds. For there is nothing either great or small, many or few, or, in
general, relative to something else, which without having a nature
of its own is many or few, great or small, or relative to something
else. A sign that the relative is least of all a substance and a
real thing is the fact that it alone has no proper generation or
destruction or movement, as in respect of quantity there is increase
and diminution, in respect of quality alteration, in respect of
place locomotion, in respect of substance simple generation and
destruction. In respect of relation there is no proper change; for,
without changing, a thing will be now greater and now less or equal,
if that with which it is compared has changed in quantity. And (c) the
matter of each thing, and therefore of substance, must be that which
is potentially of the nature in question; but the relative is
neither potentially nor actually substance. It is strange, then, or
rather impossible, to make not-substance an element in, and prior
to, substance; for all the categories are posterior to substance.
Again, (d) elements are not predicated of the things of which they are
elements, but many and few are predicated both apart and together of
number, and long and short of the line, and both broad and narrow
apply to the plane. If there is a plurality, then, of which the one
term, viz. few, is always predicated, e.g. 2 (which cannot be many,
for if it were many, 1 would be few), there must be also one which
is absolutely many, e.g. 10 is many (if there is no number which is
greater than 10), or 10,000. How then, in view of this, can number
consist of few and many? Either both ought to be predicated of it,
or neither; but in fact only the one or the other is predicated.

                                   2

    We must inquire generally, whether eternal things can consist of
elements. If they do, they will have matter; for everything that
consists of elements is composite. Since, then, even if a thing exists
for ever, out of that of which it consists it would necessarily
also, if it had come into being, have come into being, and since
everything comes to be what it comes to be out of that which is it
potentially (for it could not have come to be out of that which had
not this capacity, nor could it consist of such elements), and since
the potential can be either actual or not,-this being so, however
everlasting number or anything else that has matter is, it must be
capable of not existing, just as that which is any number of years old
is as capable of not existing as that which is a day old; if this is
capable of not existing, so is that which has lasted for a time so
long that it has no limit. They cannot, then, be eternal, since that
which is capable of not existing is not eternal, as we had occasion to
show in another context. If that which we are now saying is true
universally-that no substance is eternal unless it is actuality-and if
the elements are matter that underlies substance, no eternal substance
can have elements present in it, of which it consists.

    There are some who describe the element which acts with the One as
an indefinite dyad, and object to 'the unequal', reasonably enough,
because of the ensuing difficulties; but they have got rid only of
those objections which inevitably arise from the treatment of the
unequal, i.e. the relative, as an element; those which arise apart
from this opinion must confront even these thinkers, whether it is
ideal number, or mathematical, that they construct out of those
elements.

    There are many causes which led them off into these
explanations, and especially the fact that they framed the
difficulty in an obsolete form. For they thought that all things
that are would be one (viz. Being itself), if one did not join issue
with and refute the saying of Parmenides:

      'For never will this he proved, that things that are not are.'

    They thought it necessary to prove that that which is not is;
for only thus-of that which is and something else-could the things
that are be composed, if they are many.

    But, first, if 'being' has many senses (for it means sometimes
substance, sometimes that it is of a certain quality, sometimes that
it is of a certain quantity, and at other times the other categories),
what sort of 'one', then, are all the things that are, if non-being is
to be supposed not to be? Is it the substances that are one, or the
affections and similarly the other categories as well, or all
together-so that the 'this' and the 'such' and the 'so much' and the
other categories that indicate each some one class of being will all
be one? But it is strange, or rather impossible, that the coming
into play of a single thing should bring it about that part of that
which is is a 'this', part a 'such', part a 'so much', part a 'here'.

    Secondly, of what sort of non-being and being do the things that
are consist? For 'nonbeing' also has many senses, since 'being' has;
and 'not being a man' means not being a certain substance, 'not
being straight' not being of a certain quality, 'not being three
cubits long' not being of a certain quantity. What sort of being and
non-being, then, by their union pluralize the things that are? This
thinker means by the non-being the union of which with being
pluralizes the things that are, the false and the character of
falsity. This is also why it used to be said that we must assume
something that is false, as geometers assume the line which is not a
foot long to be a foot long. But this cannot be so. For neither do
geometers assume anything false (for the enunciation is extraneous
to the inference), nor is it non-being in this sense that the things
that are are generated from or resolved into. But since 'non-being'
taken in its various cases has as many senses as there are categories,
and besides this the false is said not to be, and so is the potential,
it is from this that generation proceeds, man from that which is not
man but potentially man, and white from that which is not white but
potentially white, and this whether it is some one thing that is
generated or many.

    The question evidently is, how being, in the sense of 'the
substances', is many; for the things that are generated are numbers
and lines and bodies. Now it is strange to inquire how being in the
sense of the 'what' is many, and not how either qualities or
quantities are many. For surely the indefinite dyad or 'the great
and the small' is not a reason why there should be two kinds of
white or many colours or flavours or shapes; for then these also would
be numbers and units. But if they had attacked these other categories,
they would have seen the cause of the plurality in substances also;
for the same thing or something analogous is the cause. This
aberration is the reason also why in seeking the opposite of being and
the one, from which with being and the one the things that are
proceed, they posited the relative term (i.e. the unequal), which is
neither the contrary nor the contradictory of these, and is one kind
of being as 'what' and quality also are.

    They should have asked this question also, how relative terms
are many and not one. But as it is, they inquire how there are many
units besides the first 1, but do not go on to inquire how there are
many unequals besides the unequal. Yet they use them and speak of
great and small, many and few (from which proceed numbers), long and
short (from which proceeds the line), broad and narrow (from which
proceeds the plane), deep and shallow (from which proceed solids); and
they speak of yet more kinds of relative term. What is the reason,
then, why there is a plurality of these?

    It is necessary, then, as we say, to presuppose for each thing
that which is it potentially; and the holder of these views further
declared what that is which is potentially a 'this' and a substance
but is not in itself being-viz. that it is the relative (as if he
had said 'the qualitative'), which is neither potentially the one or
being, nor the negation of the one nor of being, but one among beings.
And it was much more necessary, as we said, if he was inquiring how
beings are many, not to inquire about those in the same category-how
there are many substances or many qualities-but how beings as a
whole are many; for some are substances, some modifications, some
relations. In the categories other than substance there is yet another
problem involved in the existence of plurality. Since they are not
separable from substances, qualities and quantities are many just
because their substratum becomes and is many; yet there ought to be
a matter for each category; only it cannot be separable from
substances. But in the case of 'thises', it is possible to explain how
the 'this' is many things, unless a thing is to be treated as both a
'this' and a general character. The difficulty arising from the
facts about substances is rather this, how there are actually many
substances and not one.

    But further, if the 'this' and the quantitative are not the
same, we are not told how and why the things that are are many, but
how quantities are many. For all 'number' means a quantity, and so
does the 'unit', unless it means a measure or the quantitatively
indivisible. If, then, the quantitative and the 'what' are
different, we are not told whence or how the 'what' is many; but if
any one says they are the same, he has to face many inconsistencies.

    One might fix one's attention also on the question, regarding
the numbers, what justifies the belief that they exist. To the
believer in Ideas they provide some sort of cause for existing things,
since each number is an Idea, and the Idea is to other things
somehow or other the cause of their being; for let this supposition be
granted them. But as for him who does not hold this view because he
sees the inherent objections to the Ideas (so that it is not for
this reason that he posits numbers), but who posits mathematical
number, why must we believe his statement that such number exists, and
of what use is such number to other things? Neither does he who says
it exists maintain that it is the cause of anything (he rather says it
is a thing existing by itself), nor is it observed to be the cause
of anything; for the theorems of arithmeticians will all be found true
even of sensible things, as was said before.

                                   3

    As for those, then, who suppose the Ideas to exist and to be
numbers, by their assumption in virtue of the method of setting out
each term apart from its instances-of the unity of each general term
they try at least to explain somehow why number must exist. Since
their reasons, however, are neither conclusive nor in themselves
possible, one must not, for these reasons at least, assert the
existence of number. Again, the Pythagoreans, because they saw many
attributes of numbers belonging te sensible bodies, supposed real
things to be numbers-not separable numbers, however, but numbers of
which real things consist. But why? Because the attributes of
numbers are present in a musical scale and in the heavens and in
many other things. Those, however, who say that mathematical number
alone exists cannot according to their hypotheses say anything of this
sort, but it used to be urged that these sensible things could not
be the subject of the sciences. But we maintain that they are, as we
said before. And it is evident that the objects of mathematics do
not exist apart; for if they existed apart their attributes would
not have been present in bodies. Now the Pythagoreans in this point
are open to no objection; but in that they construct natural bodies
out of numbers, things that have lightness and weight out of things
that have not weight or lightness, they seem to speak of another
heaven and other bodies, not of the sensible. But those who make
number separable assume that it both exists and is separable because
the axioms would not be true of sensible things, while the
statements of mathematics are true and 'greet the soul'; and similarly
with the spatial magnitudes of mathematics. It is evident, then,
both that the rival theory will say the contrary of this, and that the
difficulty we raised just now, why if numbers are in no way present in
sensible things their attributes are present in sensible things, has
to be solved by those who hold these views.

    There are some who, because the point is the limit and extreme
of the line, the line of the plane, and the plane of the solid,
think there must be real things of this sort. We must therefore
examine this argument too, and see whether it is not remarkably
weak. For (i) extremes are not substances, but rather all these things
are limits. For even walking, and movement in general, has a limit, so
that on their theory this will be a 'this' and a substance. But that
is absurd. Not but what (ii) even if they are substances, they will
all be the substances of the sensible things in this world; for it
is to these that the argument applied. Why then should they be capable
of existing apart?

    Again, if we are not too easily satisfied, we may, regarding all
number and the objects of mathematics, press this difficulty, that
they contribute nothing to one another, the prior to the posterior;
for if number did not exist, none the less spatial magnitudes would
exist for those who maintain the existence of the objects of
mathematics only, and if spatial magnitudes did not exist, soul and
sensible bodies would exist. But the observed facts show that nature
is not a series of episodes, like a bad tragedy. As for the
believers in the Ideas, this difficulty misses them; for they
construct spatial magnitudes out of matter and number, lines out of
the number planes doubtless out of solids out of or they use other
numbers, which makes no difference. But will these magnitudes be
Ideas, or what is their manner of existence, and what do they
contribute to things? These contribute nothing, as the objects of
mathematics contribute nothing. But not even is any theorem true of
them, unless we want to change the objects of mathematics and invent
doctrines of our own. But it is not hard to assume any random
hypotheses and spin out a long string of conclusions. These
thinkers, then, are wrong in this way, in wanting to unite the objects
of mathematics with the Ideas. And those who first posited two kinds
of number, that of the Forms and that which is mathematical, neither
have said nor can say how mathematical number is to exist and of
what it is to consist. For they place it between ideal and sensible
number. If (i) it consists of the great and small, it will be the same
as the other-ideal-number (he makes spatial magnitudes out of some
other small and great). And if (ii) he names some other element, he
will be making his elements rather many. And if the principle of
each of the two kinds of number is a 1, unity will be something common
to these, and we must inquire how the one is these many things,
while at the same time number, according to him, cannot be generated
except from one and an indefinite dyad.

    All this is absurd, and conflicts both with itself and with the
probabilities, and we seem to see in it Simonides 'long rigmarole' for
the long rigmarole comes into play, like those of slaves, when men
have nothing sound to say. And the very elements-the great and the
small-seem to cry out against the violence that is done to them; for
they cannot in any way generate numbers other than those got from 1 by
doubling.

    It is strange also to attribute generation to things that are
eternal, or rather this is one of the things that are impossible.
There need be no doubt whether the Pythagoreans attribute generation
to them or not; for they say plainly that when the one had been
constructed, whether out of planes or of surface or of seed or of
elements which they cannot express, immediately the nearest part of
the unlimited began to be constrained and limited by the limit. But
since they are constructing a world and wish to speak the language
of natural science, it is fair to make some examination of their
physical theorics, but to let them off from the present inquiry; for
we are investigating the principles at work in unchangeable things, so
that it is numbers of this kind whose genesis we must study.

                                   4

    These thinkers say there is no generation of the odd number, which
evidently implies that there is generation of the even; and some
present the even as produced first from unequals-the great and the
small-when these are equalized. The inequality, then, must belong to
them before they are equalized. If they had always been equalized,
they would not have been unequal before; for there is nothing before
that which is always. Therefore evidently they are not giving their
account of the generation of numbers merely to assist contemplation of
their nature.

    A difficulty, and a reproach to any one who finds it no
difficulty, are contained in the question how the elements and the
principles are related to the good and the beautiful; the difficulty
is this, whether any of the elements is such a thing as we mean by the
good itself and the best, or this is not so, but these are later in
origin than the elements. The theologians seem to agree with some
thinkers of the present day, who answer the question in the
negative, and say that both the good and the beautiful appear in the
nature of things only when that nature has made some progress. (This
they do to avoid a real objection which confronts those who say, as
some do, that the one is a first principle. The objection arises not
from their ascribing goodness to the first principle as an
attribute, but from their making the one a principle-and a principle
in the sense of an element-and generating number from the one.) The
old poets agree with this inasmuch as they say that not those who
are first in time, e.g. Night and Heaven or Chaos or Ocean, reign
and rule, but Zeus. These poets, however, are led to speak thus only
because they think of the rulers of the world as changing; for those
of them who combine the two characters in that they do not use
mythical language throughout, e.g. Pherecydes and some others, make
the original generating agent the Best, and so do the Magi, and some
of the later sages also, e.g. both Empedocles and Anaxagoras, of
whom one made love an element, and the other made reason a
principle. Of those who maintain the existence of the unchangeable
substances some say the One itself is the good itself; but they
thought its substance lay mainly in its unity.

    This, then, is the problem,-which of the two ways of speaking is
right. It would be strange if to that which is primary and eternal and
most self-sufficient this very quality--self-sufficiency and
self-maintenance--belongs primarily in some other way than as a
good. But indeed it can be for no other reason indestructible or
self-sufficient than because its nature is good. Therefore to say that
the first principle is good is probably correct; but that this
principle should be the One or, if not that, at least an element,
and an element of numbers, is impossible. Powerful objections arise,
to avoid which some have given up the theory (viz. those who agree
that the One is a first principle and element, but only of
mathematical number). For on this view all the units become
identical with species of good, and there is a great profusion of
goods. Again, if the Forms are numbers, all the Forms are identical
with species of good. But let a man assume Ideas of anything he
pleases. If these are Ideas only of goods, the Ideas will not be
substances; but if the Ideas are also Ideas of substances, all animals
and plants and all individuals that share in Ideas will be good.

    These absurdities follow, and it also follows that the contrary
element, whether it is plurality or the unequal, i.e. the great and
small, is the bad-itself. (Hence one thinker avoided attaching the
good to the One, because it would necessarily follow, since generation
is from contraries, that badness is the fundamental nature of
plurality; while others say inequality is the nature of the bad.) It
follows, then, that all things partake of the bad except one--the
One itself, and that numbers partake of it in a more undiluted form
than spatial magnitudes, and that the bad is the space in which the
good is realized, and that it partakes in and desires that which tends
to destroy it; for contrary tends to destroy contrary. And if, as we
were saying, the matter is that which is potentially each thing,
e.g. that of actual fire is that which is potentially fire, the bad
will be just the potentially good.

    All these objections, then, follow, partly because they make every
principle an element, partly because they make contraries
principles, partly because they make the One a principle, partly
because they treat the numbers as the first substances, and as capable
of existing apart, and as Forms.

                                   5

    If, then, it is equally impossible not to put the good among the
first principles and to put it among them in this way, evidently the
principles are not being correctly described, nor are the first
substances. Nor does any one conceive the matter correctly if he
compares the principles of the universe to that of animals and plants,
on the ground that the more complete always comes from the
indefinite and incomplete-which is what leads this thinker to say that
this is also true of the first principles of reality, so that the
One itself is not even an existing thing. This is incorrect, for
even in this world of animals and plants the principles from which
these come are complete; for it is a man that produces a man, and
the seed is not first.

    It is out of place, also, to generate place simultaneously with
the mathematical solids (for place is peculiar to the individual
things, and hence they are separate in place; but mathematical objects
are nowhere), and to say that they must be somewhere, but not say what
kind of thing their place is.

    Those who say that existing things come from elements and that the
first of existing things are the numbers, should have first
distinguished the senses in which one thing comes from another, and
then said in which sense number comes from its first principles.

    By intermixture? But (1) not everything is capable of
intermixture, and (2) that which is produced by it is different from
its elements, and on this view the one will not remain separate or a
distinct entity; but they want it to be so.

    By juxtaposition, like a syllable? But then (1) the elements
must have position; and (2) he who thinks of number will be able to
think of the unity and the plurality apart; number then will be this-a
unit and plurality, or the one and the unequal.

    Again, coming from certain things means in one sense that these
are still to be found in the product, and in another that they are
not; which sense does number come from these elements? Only things
that are generated can come from elements which are present in them.
Does number come, then, from its elements as from seed? But nothing
can be excreted from that which is indivisible. Does it come from
its contrary, its contrary not persisting? But all things that come in
this way come also from something else which does persist. Since,
then, one thinker places the 1 as contrary to plurality, and another
places it as contrary to the unequal, treating the 1 as equal,
number must be being treated as coming from contraries. There is,
then, something else that persists, from which and from one contrary
the compound is or has come to be. Again, why in the world do the
other things that come from contraries, or that have contraries,
perish (even when all of the contrary is used to produce them),
while number does not? Nothing is said about this. Yet whether present
or not present in the compound the contrary destroys it, e.g. 'strife'
destroys the 'mixture' (yet it should not; for it is not to that
that is contrary).

    Once more, it has not been determined at all in which way
numbers are the causes of substances and of being-whether (1) as
boundaries (as points are of spatial magnitudes). This is how
Eurytus decided what was the number of what (e.g. one of man and
another of horse), viz. by imitating the figures of living things with
pebbles, as some people bring numbers into the forms of triangle and
square. Or (2) is it because harmony is a ratio of numbers, and so
is man and everything else? But how are the attributes-white and sweet
and hot-numbers? Evidently it is not the numbers that are the
essence or the causes of the form; for the ratio is the essence, while
the number the causes of the form; for the ratio is the essence, while
the number is the matter. E.g. the essence of flesh or bone is
number only in this way, 'three parts of fire and two of earth'. And a
number, whatever number it is, is always a number of certain things,
either of parts of fire or earth or of units; but the essence is
that there is so much of one thing to so much of another in the
mixture; and this is no longer a number but a ratio of mixture of
numbers, whether these are corporeal or of any other kind.

    Number, then, whether it be number in general or the number
which consists of abstract units, is neither the cause as agent, nor
the matter, nor the ratio and form of things. Nor, of course, is it
the final cause.

                                   6

    One might also raise the question what the good is that things get
from numbers because their composition is expressible by a number,
either by one which is easily calculable or by an odd number. For in
fact honey-water is no more wholesome if it is mixed in the proportion
of three times three, but it would do more good if it were in no
particular ratio but well diluted than if it were numerically
expressible but strong. Again, the ratios of mixtures are expressed by
the adding of numbers, not by mere numbers; e.g. it is 'three parts to
two', not 'three times two'. For in any multiplication the genus of
the things multiplied must be the same; therefore the product 1X2X3
must be measurable by 1, and 4X5X6 by 4 and therefore all products
into which the same factor enters must be measurable by that factor.
The number of fire, then, cannot be 2X5X3X6 and at the same time
that of water 2X3.

    If all things must share in number, it must follow that many
things are the same, and the same number must belong to one thing
and to another. Is number the cause, then, and does the thing exist
because of its number, or is this not certain? E.g. the motions of the
sun have a number, and again those of the moon,-yes, and the life
and prime of each animal. Why, then, should not some of these
numbers be squares, some cubes, and some equal, others double? There
is no reason why they should not, and indeed they must move within
these limits, since all things were assumed to share in number. And it
was assumed that things that differed might fall under the same
number. Therefore if the same number had belonged to certain things,
these would have been the same as one another, since they would have
had the same form of number; e.g. sun and moon would have been the
same. But why need these numbers be causes? There are seven vowels,
the scale consists of seven strings, the Pleiades are seven, at
seven animals lose their teeth (at least some do, though some do not),
and the champions who fought against Thebes were seven. Is it then
because the number is the kind of number it is, that the champions
were seven or the Pleiad consists of seven stars? Surely the champions
were seven because there were seven gates or for some other reason,
and the Pleiad we count as seven, as we count the Bear as twelve,
while other peoples count more stars in both. Nay they even say that
X, Ps and Z are concords and that because there are three concords,
the double consonants also are three. They quite neglect the fact that
there might be a thousand such letters; for one symbol might be
assigned to GP. But if they say that each of these three is equal to
two of the other letters, and no other is so, and if the cause is that
there are three parts of the mouth and one letter is in each applied
to sigma, it is for this reason that there are only three, not because
the concords are three; since as a matter of fact the concords are
more than three, but of double consonants there cannot be more.

    These people are like the old-fashioned Homeric scholars, who
see small resemblances but neglect great ones. Some say that there are
many such cases, e.g. that the middle strings are represented by
nine and eight, and that the epic verse has seventeen syllables, which
is equal in number to the two strings, and that the scansion is, in
the right half of the line nine syllables, and in the left eight.
And they say that the distance in the letters from alpha to omega is
equal to that from the lowest note of the flute to the highest, and
that the number of this note is equal to that of the whole choir of
heaven. It may be suspected that no one could find difficulty either
in stating such analogies or in finding them in eternal things,
since they can be found even in perishable things.

    But the lauded characteristics of numbers, and the contraries of
these, and generally the mathematical relations, as some describe
them, making them causes of nature, seem, when we inspect them in this
way, to vanish; for none of them is a cause in any of the senses
that have been distinguished in reference to the first principles.
In a sense, however, they make it plain that goodness belongs to
numbers, and that the odd, the straight, the square, the potencies
of certain numbers, are in the column of the beautiful. For the
seasons and a particular kind of number go together; and the other
agreements that they collect from the theorems of mathematics all have
this meaning. Hence they are like coincidences. For they are
accidents, but the things that agree are all appropriate to one
another, and one by analogy. For in each category of being an
analogous term is found-as the straight is in length, so is the
level in surface, perhaps the odd in number, and the white in colour.

    Again, it is not the ideal numbers that are the causes of
musical phenomena and the like (for equal ideal numbers differ from
one another in form; for even the units do); so that we need not
assume Ideas for this reason at least.

    These, then, are the results of the theory, and yet more might
be brought together. The fact that our opponnts have much trouble with
the generation of numbers and can in no way make a system of them,
seems to indicate that the objects of mathematics are not separable
from sensible things, as some say, and that they are not the first
principles.

                                   -THE END-
.

Colophon

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