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Author: Spinoza, Benedict De
Title: On The Improvement Of The Understanding
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On the Improvement of the Understanding
(Treatise on the Emendation of the Intellect)

by Baruch Spinoza  [Benedict de Spinoza]

Translated by R. H. M. Elwes

August, 1997  [Etext #1016]

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On the Improvement of the Understanding
(Treatise on the Emendation of the Intellect)

by Baruch Spinoza  [Benedict de Spinoza]

Translated by R. H. M. Elwes

TABLE OF CONTENTS:

1   On the Improvement of the Understanding
3   Of the ordinary objects of men's desires
12  Of the true and final good
17  Certain rules of life
19  Of the four modes of perception
25  Of the best mode of perception
33  Of the instruments of the intellect, or true ideas
43  Answers to objections

   
First part of method:

50  Distinction of true ideas from fictitious ideas
64  And from false ideas
77  Of doubt
81  Of memory and forgetfulness
86  Mental hindrances from words - and from the popular confusion
    of ready imagination with distinct understanding. 

Second part of method: 

91  Its object, the acquisition of clear and distinct ideas
94  Its means, good definitions
    Conditions of definition
107 How to define understanding

----------------------------------------------------------------------------

[Notice to the Reader.]
(This notice to the reader was written by the editors of the
Opera Postuma in 1677.  Taken from Curley, Note 3, at end)

*This Treatise on the Emendation of the Intellect etc., which we
give you here, kind reader, in its unfinished [that is, defective]
state, was written by the author many years ago now. He always
intended to finish it. But hindered by other occupations, and
finally snatched away by death, he was unable to bring it to the
desired conclusion. But since it contains many excellent and useful
things, which - we have no doubt - will be of great benefit to
anyone sincerely seeking the truth, we did not wish to deprive you
of them. And so that you would be aware of, and find less difficult
to excuse, the many things that are still obscure, rough, and
unpolished, we wished to warn you of them. Farewell.*

[1]  (1) After experience had taught me that all the usual
surroundings of social life are vain and futile; seeing that none
of the objects of my fears contained in themselves anything either
good or bad, except in so far as the mind is affected by them,
I finally resolved to inquire whether there might be some real
good having power to communicate itself, which would affect the
mind singly, to the exclusion of all else: whether, in fact, there
might be anything of which the discovery and attainment would
enable me to enjoy continuous, supreme, and unending happiness.

[2]  (1) I say "I finally resolved," for at first sight it seemed
unwise willingly to lose hold on what was sure for the sake of
something then uncertain.  (2) I could see the benefits which are
acquired through fame and riches, and that I should be obliged to
abandon the quest of such objects, if I seriously devoted myself
to the search for something different and new.  (3) I perceived
that if true happiness chanced to be placed in the former I should 
necessarily miss it; while if, on the other hand, it were not so
placed, and I gave them my whole attention, I should equally fail. 

[3]  (1) I therefore debated whether it would not be possible to
arrive at the new principle, or at any rate at a certainty
concerning its existence, without changing the conduct and usual
plan of my life; with this end in view I made many efforts,
in vain.  (2) For the ordinary surroundings of life which are
esteemed by men (as their actions testify) to be the highest
good, may be classed under the three heads - Riches, Fame, and
the Pleasures of Sense: with these three the mind is so absorbed
that it has little power to reflect on any different good.

[4]  (1) By sensual pleasure the mind is enthralled to the extent
of quiescence, as if the supreme good were actually attained, so
that it is quite incapable of thinking of any other object; when
such pleasure has been gratified it is followed by extreme
melancholy, whereby the mind, though not enthralled, is disturbed
and dulled.  (2) The pursuit of honors and riches is likewise very
absorbing, especially if such objects be sought simply for their
own sake, [a] inasmuch as they are then supposed to constitute the
highest good.

[5]  (1) In the case of fame the mind is still more absorbed, for fame
is conceived as always good for its own sake, and as the ultimate end
to which all actions are directed.  (2) Further, the attainment of
riches and fame is not followed as in the case of sensual pleasures by
repentance, but, the more we acquire, the greater is our delight, and,
consequently, the more are we incited to increase both the one and the
other; on the other hand, if our hopes happen to be frustrated we are
plunged into the deepest sadness.  (3) Fame has the further drawback
that it compels its votaries to order their lives according to the
opinions of their fellow-men, shunning what they usually shun, and
seeking what they usually seek.

[6]  (1) When I saw that all these ordinary objects of desire would
be obstacles in the way of a search for something different and new -
nay, that they were so opposed thereto, that either they or it would
have to be abandoned, I was forced to inquire which would prove the
most useful to me: for, as I say, I seemed to be willingly losing
hold on a sure good for the sake of something uncertain.  (6:2) However,
after I had reflected on the matter, I came in the first place to the
conclusion that by abandoning the ordinary objects of pursuit, and
betaking myself to a new quest, I should be leaving a good, uncertain
by reason of its own nature, as may be gathered from what has been
said, for the sake of a good not uncertain in its nature (for I sought
for a fixed good), but only in the possibility of its attainment.

[7] (1) Further reflection convinced me that if I could really get
to the root of the matter I should be leaving certain evils for a
certain good.  (2) I thus perceived that I was in a state of great
peril, and I compelled myself to seek with all my strength for a
remedy, however uncertain it might be; as a sick man struggling with
a deadly disease, when he sees that death will surely be upon him
unless a remedy be found, is compelled to seek a remedy with all his
strength, inasmuch as his whole hope lies therein.  (7:3) All the
objects pursued by the multitude not only bring no remedy that tends
to preserve our being, but even act as hindrances, causing the death
not seldom of those who possess them, [b] and always of those who
are possessed by them. 

[8]  (1) There are many examples of men who have suffered persecution
even to death for the sake of their riches, and of men who in pursuit
of wealth have exposed themselves to so many dangers, that they have
paid away their life as a penalty for their folly.  (2) Examples are
no less numerous of men, who have endured the utmost wretchedness for
the sake of gaining or preserving their reputation.  (3) Lastly,
are innumerable cases of men, who have hastened their death through
over-indulgence in sensual pleasure.

[9]  (1) All these evils seem to have arisen from the fact, that
happiness or unhappiness is made wholly dependent on the quality
of the object which we love.  (2) When a thing is not loved, no
quarrels will arise concerning it - no sadness be felt if it
hatred, in short no disturbances of the mind.  (3) All these
arise from the love of what is perishable, such as the objects
already mentioned.

[10]  (1) But love towards a thing eternal and infinite feeds the
mind wholly with joy, and is itself unmingled with any sadness,
wherefore it is greatly to be desired and sought for with all our
strength.  (2) Yet it was not at random that I used the words,
"If I could go to the root of the matter," for, though what I have
urged was perfectly clear to my mind, I could not forthwith lay
aside all love of riches, sensual enjoyment, and fame.

[11]  (1) One thing was evident, namely, that while my mind was
employed with these thoughts it turned away from its former objects
of desire, and seriously considered the search for a new principle;
this state of things was a great comfort to me, for I perceived
that the evils were not such as to resist all remedies.  (11:2) Although
these intervals were at first rare, and of very short duration, yet
afterwards, as the true good became more and more discernible to me,
they became more frequent and more lasting; especially after I had
recognized that the acquisition of wealth, sensual pleasure, or fame,
is only a hindrance, so long as they are sought as ends not as means;
if they be sought as means, they will be under restraint, and, far
from being hindrances, will further not a little the end for which
they are sought, as I will show in due time.

[12]  (1) I will here only briefly state what I mean by true good,
and also what is the nature of the highest good. (2) In order that
this may be rightly understood, we must bear in mind that the terms
good and evil are only applied relatively, so that the same thing
may be called both good and bad according to the relations in view,
in the same way as it may be called perfect or imperfect.
(3) Nothing regarded in its own nature can be called perfect or
imperfect; especially when we are aware that all things which come
to pass, come to pass according to the eternal order and fixed
laws of nature. 

[13]  (1) However, human weakness cannot attain to this order in its
own thoughts, but meanwhile man conceives a human character much more
stable than his own, and sees that there is no reason why he should
not himself acquire such a character.  (2) Thus he is led to seek
for means which will bring him to this pitch of perfection, and
calls everything which will serve as such means a true good.
(13:3) The chief good is that he should arrive, together with other
individuals if possible, at the possession of the aforesaid
character.  (4) What that character is we shall show in due time,
namely, that it is the knowledge of the union existing being
the mind and the whole of nature. [c]

[14]  (1) This, then, is the end for which I strive, to attain to
such a character myself, and to endeavor that many should attain to
it with me.  (2) In other words, it is part of my happiness to lend
a helping hand, that many others may understand even as I do, so
that their understanding and desire may entirely agree with my own.
(3) In order to bring this about, it is necessary to understand as
much of nature as will enable us to attain to the aforesaid character,
and  also to form a social order such as is most conducive to the
attainment of this character by the greatest number with the least
difficulty and danger. 

[15]  (1) We must seek the assistance of Moral Philosophy [d] and
the Theory of Education; further, as health is no insignificant means
for attaining our end, we must also include the whole science of
Medicine, and, as many difficult things are by contrivance rendered
easy, and we can in this way gain much time and convenience, the
science of Mechanics must in no way be despised. 

[16]  (1) But before all things, a means must be devised for
improving the understanding and purifying it, as far as may be at
the outset, so that it may apprehend things without error, and in
the best possible way.  (2) Thus it is apparent to everyone that I
wish to direct all science to one end [e] and aim, so that we may
attain to the supreme human perfection which we have named; and,
therefore, whatsoever in the sciences does not serve to promote
our object will have to be rejected as useless.  (3) To sum up the
matter in a word, all our actions and thoughts must be directed to
this one end. 

[17]  (1) Yet, as it is necessary that while we are endeavoring to
attain our purpose, and bring the understanding into the right path
we should carry on our life, we are compelled first of all to lay
down certain rules of life as provisionally good, to wit the
following:-
I.  (2) To speak in a manner intelligible to the multitude, and to
    comply with every general custom that does not hinder the
    attainment of our purpose.  (3) For we can gain from the multitude
    no small advantages, provided that we strive to accommodate
    ourselves to its understanding as far as possible: moreover,
    we shall in this way gain a friendly audience for the reception
    of the truth. 
II. (17:4) To indulge ourselves with pleasures only in so far as they
    are necessary for preserving health. 
III. (5) Lastly, to endeavor to obtain only sufficient money or other
    commodities to enable us to preserve our life and health, and to
    follow such general customs as are consistent with our purpose.

[18]  (1) Having laid down these preliminary rules, I will betake
myself to the first and most important task, namely, the amendment
of the understanding, and the rendering it capable of understanding
things in the manner necessary for attaining our end.  (2) In order
to bring this about, the natural order demands that I should here
recapitulate all the modes of perception, which I have hitherto
employed for affirming or denying anything with certainty, so that
I may choose the best, and at the same time begin to know my own
powers and the nature which I wish to perfect.

[19] (1) Reflection shows that all modes of perception or knowledge
may be reduced to four:-
I. (2) Perception arising from hearsay or from some sign which
   everyone may name as he please. 
II. (3) Perception arising from mere experience - that is, form
   experience not yet classified by the intellect, and only so called
   because the given event has happened to take place, and we have no
   contradictory fact to set against it, so that it therefore remains
   unassailed in our minds.
III. (19:4) Perception arising when the essence of one thing is inferred
   from another thing, but not adequately; this comes when [f] from some
   effect we gather its cause, or when it is inferred from some general
   proposition that some property is  always present.
IV. (5) Lastly, there is the perception arising when a thing is
   perceived solely through its essence, or through the knowledge
   of its proximate cause.

[20] (1) All these kinds of perception I will illustrate by examples.
(2) By hearsay I know the day of my birth, my parentage, and other
matters about which I have never felt any doubt.  (3) By mere
experience I know that I shall die, for this I can affirm from
having seen that others like myself have died, though all did not
live for the same period, or die by the same disease.  (4) I know
by mere experience that oil has the property of feeding fire, and
water of extinguishing it.  (5) In the same way I know that a dog
is a barking animal, man a rational animal, and in fact nearly all
the practical knowledge of life. 

[21]  (1) We deduce one thing from another as follows: when we
clearly perceive that we feel a certain body and no other, we
thence clearly infer that the mind is united [g] to the body,
and that their union is the cause of the given sensation; but
we cannot thence absolutely understand [h] the nature of the
sensation and the union.  (2) Or, after I have become acquainted
with the nature of vision, and know that it has the property of
making one and the same thing appear smaller when far off than
when near, I can infer that the sun is larger than it appears,
and can draw other conclusions of the same kind. 

[22]  (1) Lastly, a thing may be perceived solely through its essence;
when, from the fact of knowing something, I know what it is to know
that thing, or when, from knowing the essence of the mind, I know
that it is united to the body.  (2) By the same kind of knowledge
we know that two and three make five, or that two lines each parallel
to a third, are parallel to one another, &c. (3) The things which I
have been able to know by this kind of knowledge are as yet very few. 

[23]  (1) In order that the whole matter may be put in a clearer
light, I will make use of a single illustration as follows.
(2) Three numbers are given - it is required to find a fourth,
which shall be to the third as the second is to the first.
(23:3) Tradesmen will at once tell us that they know what is required
to find the fourth number, for they have not yet forgotten the rule
which was given to them arbitrarily without proof by their masters;
others construct a universal axiom from their experience with simple
numbers, where the fourth number is self-evident, as in the case of
2, 4, 3, 6; here it is evident that if the second number be
multiplied by the third, and the product divided by the first,
the quotient is 6; when they see that by this process the number
is produced which they knew beforehand to be the proportional,
they infer that the process always holds good for finding a fourth
number proportional. 

[24]  (1) Mathematicians, however, know by the proof of the nineteenth
proposition of the seventh book of Euclid, what numbers are
proportionals, namely, from the nature and property of proportion
it follows that the product of the first and fourth will be equal
to the product of the second and third: still they do not see the
adequate proportionality of the given numbers, or, if they do see it,
they see it not by virtue of Euclid's proposition, but intuitively,
without going through any process. 

[25] (1) In order that from these modes of perception the best may
be selected, it is well that we should briefly enumerate the means
necessary for attaining our end.

I.  (2) To have an exact knowledge of our nature which we desire to
    perfect, and to know as much as is needful of nature in general. 
            
II. To collect in this way the differences, the agreements, and the
    oppositions of things.
            
III. To learn thus exactly how far they can or cannot be modified.
            
IV. To compare this result with the nature and power of man.
    (4) We shall thus discern the highest degree of perfection
    to which man is capable of attaining.

[26] (1) We shall then be in a position to see which mode of
perception we ought to choose.  (2) As to the first mode, it is
evident that from hearsay our knowledge must always be uncertain,
and, moreover, can give us no insight into the essence of a thing,
as is manifest in our illustration; now one can only arrive at
knowledge of a thing through knowledge of its essence, as will
hereafter appear.  (3) We may, therefore clearly conclude that
the certainty arising from hearsay cannot be scientific in its
character.  (4) For simple hearsay cannot affect anyone whose
understanding does not, so to speak, meet it half way.

[27]  (1) The second mode of perception [i] cannot be said to
give us the idea of the proportion of which we are in search.
(2) Moreover its results are very uncertain and indefinite,
for we shall never discover anything in natural phenomena by its
means, except accidental properties, which are never clearly
understood, unless the essence of the things in question be
known first.  (3) Wherefore this mode also must be rejected. 

[28] (1) Of the third mode of perception we may say in a manner
that it gives us the idea of the thing sought, and that it 
us to draw conclusions without risk of error; yet it is not by
itself sufficient to put us in possession of the perfection we
aim at. 

[29] (1) The fourth mode alone apprehends the adequate essence of
a thing without danger of error.  (2) This mode, therefore, must be
the one which we chiefly employ.  (3) How, then, should we avail
ourselves of it so as to gain the fourth kind of knowledge with
the least delay concerning things previously unknown?  (4) I will
proceed to explain. 

[30] (1) Now that we know what kind of knowledge is necessary for
us, we must indicate the way and the method whereby we may gain
the said knowledge concerning the things needful to be known.
(2) In order to accomplish this, we must first take care not to
commit ourselves to a search, going back to infinity - that is,
in order to discover the best method of finding truth, there is
no need of another method to discover such method; nor of a third
method for discovering the second, and so on to infinity.  (3) By
such proceedings, we should never arrive at the knowledge of the
truth, or, indeed, at any knowledge at all.  (30:4) The matter stands
on the same footing as the making of material tools, which might
be argued about in a similar way.  (5) For, in order to work iron,
a hammer is needed, and the hammer cannot be forthcoming unless
it has been made; but, in order to make it, there was need
of another hammer and other tools, and so on to infinity.
(6) We might thus vainly endeavor to prove that men have no
power of working iron.

[31]  (1) But as men at first made use of the instruments supplied
by nature to accomplish very easy pieces of workmanship, laboriously
and imperfectly, and then, when these were finished, wrought other
things more difficult with less labour and greater perfection;
and so gradually mounted from the simplest operations to the making
of tools, and from the making of tools to the making of more complex
tools, and fresh feats of workmanship, till they arrived at making,
complicated mechanisms which they now possess.  (31:2) So, in like
manner, the intellect, by its native strength, [k], makes for itself
intellectual instruments, whereby it acquires strength for performing
other intellectual operations, [l], and from these operations 
again fresh instruments, or the power of pushing its investigations
further, and thus gradually proceeds till it reaches the summit
of wisdom. 

[32]  (1) That this is the path pursued by the understanding may be
readily seen, when we understand the nature of the method for
finding out the truth, and of the natural instruments so necessary
complex instruments, and for the progress of investigation. I thus
proceed with my demonstration. 

[33]  (1) A true idea, [m], (for we possess a true idea) is something
different from its correlate (ideatum); thus a circle is different
from the idea of a circle. (2) The idea of a circle is not something
having a circumference and a center, as a circle has; nor is the idea
of a body that body itself. (3) Now, as it is something different
from its correlate, it is capable of being understood through itself;
in other words, the idea, in so far as its actual essence (essentia
formalis) is concerned, may be the subject of another subjective
essence (essentia objectiva).  [33note1] (4) And, again, this second
subjective essence will, regarded in itself, be something real, 
capable of being understood; and so on, indefinitely. 

[34] (1) For instance, the man Peter is something real; the true
idea of Peter is the reality of Peter represented subjectively,
and is in itself something real, and quite distinct from the
actual Peter.  (2) Now, as this true idea of Peter is in itself
something real, and has its own individual existence, it will
also be capable of being understood - that is, of being the
subject of another idea, which will contain by representation
(objective) all that the idea of Peter contains actually
(formaliter).  (3) And, again, this idea of the idea of Peter
has its own individuality, which may become the subject of yet
another idea; and so on, indefinitely.  (4) This everyone may
make trial of for himself, by reflecting that he knows what
Peter is, and also knows that he knows, and further knows that
he knows that he knows, &c.  (34:5) Hence it is plain that, in
order to understand the actual Peter, it is not necessary first
to understand the idea of Peter, and still less the idea of
the idea of Peter.  (6) This is the same as saying that, in order
to know, there is no need to know that we know, much less to
know that we know that we know.  (7) This is no more necessary
than to know the nature of a circle before knowing the nature of
a triangle. [n].  (8) But, with these ideas, the contrary is the
case: for, in order to know that I know, I must first know. 

[35] (1) Hence it is clear that certainty is nothing else than
the subjective essence of a thing: in other words, the mode in
which we perceive an actual reality is certainty.  (2) Further,
it is also evident that, for the certitude of truth, no further
sign is necessary beyond the possession of a true idea: for,
as I have shown, it is not necessary to know that we know that
we know.  (3) Hence, again, it is clear that no one can know
the nature of the highest certainty, unless he possesses an
adequate idea, or the subjective essence of a thing: 
certainty is identical with such subjective essence. 

[36]  (1) Thus, as the truth needs no sign - it being to possess
the subjective essence of things, or, in other words, the ideas
of them, in order that all doubts may be removed - it follows
that the true method does not consist in seeking for the signs
of truth after the acquisition of the idea, but that the true
method teaches us the order in which we should seek for truth
itself, [o] or the subjective essences of things, or ideas,
for all these expressions are synonymous. 

[37] (1) Again, method must necessarily be concerned with
reasoning or understanding - I mean, method is not identical
with reasoning in the search for causes, still less is it
the comprehension of the causes of things: it is the
discernment of a true idea, by distinguishing it from other
perceptions, and by investigating its nature, in order that
we may so train our mind that it may, by a given standard,
comprehend whatsoever is intelligible, by laying down
certain rules as aids, and by avoiding useless mental
exertion. 

[38]  (1) Whence we may gather that method is nothing else
than reflective knowledge, or the idea of an idea; and that
as there can be no idea of an idea - unless an idea exists
previously, - there can be no method without a pre-existent
idea.  (2) Therefore, that will be a good method which
shows us how the mind should be directed, according to the
standard of the given true idea.  
   (38:3) Again, seeing that the ratio existing between two
ideas the same as the ratio between the actual realities
corresponding to those ideas, it follows that the reflective
knowledge which has for its object the most perfect being is
more excellent than reflective knowledge concerning other
objects - in other words, that method will be most perfect
which affords the standard of the given idea of the most
perfect being whereby we may direct our mind. 

[39] (1) We thus easily understand how, in proportion as it
acquires new ideas, the mind simultaneously acquires fresh
instruments for pursuing its inquiries further. (2) For we
may gather from what has been said, that a true idea must
necessarily first of all exist in us as a natural instrument;
and that when this idea is apprehended by the mind, it enables
us to understand the difference existing between itself and
all other perceptions.  (3) In this, one part of the method
consists. 
    (39:4) Now it is clear that the mind apprehends itself better
in proportion as it understands a greater number of natural
objects; it follows, therefore, that this portion of the method
will be more perfect in proportion as the mind attains to the
comprehension of a greater number of objects, and that it will
be absolutely perfect when the mind gains a knowledge of the
absolutely perfect being, or becomes conscious thereof. 

[40]  (1) Again, the more things the mind knows, the better does
it understand its own strength and the order of nature; by
increased self-knowledge, it can direct itself more easily, and
lay down rules for its own guidance; and, by increased knowledge
of nature, it can more easily avoid what is useless.  (2) And
this is the sum total of method, as we have already stated. 

[41]  (1) We may add that the idea in the world of thought is in
the same case as its correlate in the world of reality.  (2) If,
therefore, there be anything in nature which is without connection
with any other thing, and if we assign to it a subjective essence,
which would in every way correspond to the objective reality,
the subjective essence would have no connection, [p] with any
other ideas - in other words, we could not draw any conclusions
with regard to it.  (41:3) On the other hand, those things which are
connected with others - as all things that exist in nature - will
be understood by the mind, and their subjective essences will
maintain the same mutual relations as their objective realities - 
that is to say, we shall infer from these ideas other ideas, which
will in turn be connected with others, and thus our instruments
for proceeding with our investigation will increase.  (4) This is
what we were endeavoring to prove. 

[42]  (1) Further, from what has just been said - namely, that an
idea must, in all respects, correspond to its correlate in the
world of reality, - it is evident that, in order to reproduce in
every respect the faithful image of nature, our mind must deduce
all its ideas from the idea which represents the origin and source
of the whole of nature, so that it may itself become the source
of other ideas. 

[43]  (1) It may, perhaps, provoke astonishment that, after having
said that the good method is that which teaches us to direct our
mind according to the standard of the given true idea, we should
prove our point by reasoning, which would seem to indicate that it
is not self-evident.  (2) We may, therefore, be questioned as to
the validity of our reasoning.  (3) If our reasoning be sound, we
must take as a starting-point a true idea.  (4) Now, to be certain
that our starting-point is really a true idea, we need proof. 
(5) This first course of reasoning must be supported by a second,
the second by a third, and so on to infinity. 

[44]  (1) To this I make answer that, if by some happy chance anyone
had adopted this method in his investigations of nature - that is,
if he had acquired new ideas in the proper order, according to the
standard of the original true idea, he would never have doubted [q]
of the truth of his knowledge, inasmuch as truth, as we have shown,
makes itself manifest, and all things would flow, as it were,
spontaneously towards him.  (44:2) But as this never, or rarely,
happens, I have been forced so to arrange my proceedings, that we
may acquire by reflection and forethought what we cannot acquire
by chance, and that it may at the same time appear that, for
proving the truth, and for valid reasoning, we need no other means
than the truth and valid reasoning themselves: for by valid
reasoning I have established valid reasoning, and, in like measure,
I seek still to establish it. 

[45]  (1) Moreover, this is the order of thinking adopted by men
in their inward meditations.  (2) The reasons for its rare employment
in investigations of nature are to be found in current misconceptions,
whereof we shall examine the causes hereafter in our philosophy.
(3) Moreover, it demands, as we shall show, a keen and accurate
discernment.  (4) Lastly, it is hindered by the conditions of human
life, which are, as we have already pointed out, extremely changeable.
(5) There are also other obstacles, which we will not here inquire into. 

 
[46]  (1) If anyone asks why I have not at the starting-point set forth
all the truths of nature in their due order, inasmuch as truth is
self-evident, I reply by warning him not to reject as false any
paradoxes he may find here, but to take the trouble to reflect on
the chain of reasoning by which they are supported; he will then
be no longer in doubt that we have attained to the truth.
(2) This is why I have as above. 

[47] (1) If there yet remains some sceptic, who doubts of our
primary truth, and of all deductions we make, taking such truth
as our standard, he must either be arguing in bad faith, or we
must confess that there are men in complete mental blindness
either innate or due to misconceptions - that is, to some external
influence.  (2) Such persons are not conscious of themselves.
(3) If they affirm or doubt anything, they know not that they
affirm or doubt: they say that they know nothing, and they say
that they are ignorant of the very fact of their knowing nothing.
(4) Even this they do not affirm absolutely, they are afraid of
confessing that they exist, so long as they know nothing;
in fact, they ought to remain dumb, for fear of haply supposing
which should smack of truth.

[48]  (1) Lastly, with such persons, one should not speak of
sciences: for, in what relates to life and conduct, they are
compelled by necessity to suppose that they exist, and seek
their own advantage, and often affirm and deny, even with an
oath.  (2) If they deny, grant, or gainsay, they know not that
they deny, grant, or gainsay, so that they ought to be
regarded as automata, utterly devoid of intelligence.

[49] (1) Let us now return to our proposition.  (2) Up to the present,
we have, first, defined the end to which we desire to direct all our
thoughts; secondly, we have determined the mode of perception best
adapted to aid us in attaining our perfection; thirdly, we have
discovered the way which our mind should take, in order to make a good
beginning - namely, that it should use every true idea as a standard in
pursuing its inquiries according to fixed rules.  (49:3) Now, in order
that it may thus proceed, our method must furnish us, first, with a
means of distinguishing a true idea from all other perceptions, and
enabling the mind to avoid the latter; secondly, with rules for
perceiving unknown things according to the standard of the true idea;
thirdly, with an order which enables us to avoid useless labor.
(49:4) When we became acquainted with this method, we saw that,
fourthly, it would be perfect when we had attained to the idea of the
absolutely perfect Being.  (5) This is an observation which should be
made at the outset, in order that we may arrive at the knowledge of
such a being more quickly. 

[50] (1) Let us then make a beginning with the first part of the method,
which is, as we have said, to distinguish and separate the true idea
from other perceptions, and to keep the mind from confusing with true
ideas those which are false, fictitious, and doubtful.  (2) I intend to
dwell on this point at length, partly to keep a distinction so necessary 
before the reader's mind, and also because there are some who doubt of
true ideas, through not having attended to the distinction between a true
perception and all others.  (3) Such persons are like men who, while they
are awake, doubt not that they are awake, but afterwards in a dream, as
often happens, thinking that they are surely awake, and then finding that
they were in error, become doubtful even of being awake.  (4) This state
of mind arises through neglect of the distinction between sleeping and
waking.

[51]  (1) Meanwhile, I give warning that I shall not here give 
essence of every perception, and explain it through its proximate
cause.  (2) Such work lies in the province of philosophy.  (3) I shall
confine myself to what concerns method - that is, to the character of
fictitious, false and doubtful perceptions, and the means of freeing
ourselves therefrom.  (4) Let us then first inquire into the nature of
a fictitious idea. 

[52]  (1) Every perception has for its object either a thing considered
as existing, or solely the essence of a thing.  (2) Now "fiction" is
chiefly occupied with things considered as existing.  (3) I will,
therefore, consider these first - I mean cases where only the existence
of an object is feigned, and the thing thus feigned is understood, or
assumed to be understood.  (4) For instance, I feign that Peter, whom
I know to have gone home, is gone to see me, [r] or something of that
kind.  (5) With what is such an idea concerned?  (6) It is concerned
with things possible, and not with things necessary or impossible. 

[53] (1) I call a thing impossible when its existence would imply a
contradiction; necessary, when its non-existence would imply a
contradiction; possible, when neither its existence nor its
non-existence imply a contradiction, but when the necessity or
impossibility of its nature depends on causes unknown to us, while
we feign that it exists.  (2) If the necessity or impossibility of
its existence depending on external causes were known to us, we
could not form any fictitious hypotheses about it; 

[54] (1) Whence it follows that if there be a God, or omniscient
Being, such an one cannot form fictitious hypotheses.  (2) For,
as regards ourselves, when I know that I exist, [s] I cannot
hypothesize that I exist or do not exist, any more than I can
hypothesize an elephant that can go through the eye of a needle;
nor when I know the nature of God, can I hypothesize that He 
or does not exist. [t]  (54:3) The same thing must be said of the
Chimaera, whereof the nature implies a contradiction.  (4) From
these considerations, it is plain, as I have already stated, that
fiction cannot be concerned with eternal truths. [u]

[55]  (1) But before proceeding further, I must remark, in passing,
that the difference between the essence of one thing and the essence
of another thing is the same as that which exists between the reality
or existence of one thing and the reality or existence of another;
therefore, if we wished to conceive the existence, for example,
of Adam, simply by means of existence in general, it would be the
same as if, in order to conceive his existence, we went back to the
nature of being, so as to define Adam as a being.  (2) Thus, the more
existence is conceived generally, the more is it conceived confusedly
and the more easily can it be ascribed to a given object.
(55:3) Contrariwise, the more it is conceived particularly, the more
is it understood clearly, and the less liable is it to be ascribed,
through negligence of Nature's order, to anything save its proper
object.  (4) This is worthy of remark. 

[56]  (1) We now proceed to consider those cases which are commonly
called fictions, though we clearly understood that the thing is not
as we imagine it.  (2) For instance, I know that the earth is round,
but nothing prevents my telling people that it is a hemisphere,
and that it is like a half apple carved in relief on a dish; or,
that the sun moves round the earth, and so on.  (56:3) However,
examination will show us that there is nothing here inconsistent
with what has been said, provided we first admit that we may have
made mistakes, and be now conscious of them; and, further, that we
can hypothesize, or at least suppose, that others are under the 
same mistake as ourselves, or can, like us, fall under it.  (4) We can,
I repeat, thus hypothesize so long as we see no impossibility.
(56:5) Thus, when I tell anyone that the earth is not round, &c.,
I merely recall the error which I perhaps made myself, or which I
might have fallen into, and afterwards I hypothesize that the person
to whom I tell it, is still, or may still fall under the same mistake.
(6) This I say, I can feign so long as I do not perceive any
impossibility or necessity; if I truly understood either one or the
other I should not be able to feign, and I should be reduced to saying
that I had made the attempt.

[57]  (1) It remains for us to consider hypotheses made in problems,
which sometimes involve impossibilities.  (2) For instance, when we
say - let us assume that this burning candle is not burning, or,
let us assume that it burns in some imaginary space, or where there
are no physical objects.  (3) Such assumptions are freely made,
though the last is clearly seen to be impossible.  (4) But, though
this be so, there is no fiction in the case.  (57:5) For, in the first
case, I have merely recalled to memory, [x] another candle not
burning, or conceived the candle before me as without a flame, and
then I understand as applying to the latter, leaving its flame out
of the question, all that I think of the former.  (6) In the second
case, I have merely to abstract my thoughts from the objects
surrounding the candle, for the mind to devote itself to the
contemplation of the candle singly looked at in itself only; I can
then draw the conclusion that the candle contains in itself no
causes for its own destruction, so that if there were no physical
objects the candle, and even the flame, would remain unchangeable,
and so on.  (7) Thus there is here no fiction, but, [y] true and
bare assertions. 

[58] (1) Let us now pass on to the fictions concerned with essences
only, or with some reality or existence simultaneously.  (2) Of
these we must specially observe that in proportion as the mind's
understanding is smaller, and its experience multiplex, so will its
power of coining fictions be larger, whereas as its understanding
increases, its capacity for entertaining fictitious ideas becomes
less.  (58:3) For instance, in the same way as we are unable, while
we are thinking, to feign that we are thinking or not thinking, so,
also, when we know the nature of body we cannot imagine an infinite
fly; or, when we know the nature of the soul, [z] we cannot imagine
it as square, though anything may be expressed verbally.  (4) But,
as we said above, the less men know of nature the more easily can
they coin fictitious ideas, such as trees speaking, men instantly
changed into stones, or into fountains, ghosts appearing in mirrors,
something issuing from nothing, even gods changed into beasts and men
and infinite other absurdities of the same kind. 

[59] (1) Some persons think, perhaps, that fiction is limited by
fiction, and not by understanding; in other words, after I have
formed some fictitious idea, and have affirmed of my own free will
that it exists under a certain form in nature, I am thereby
precluded from thinking of it under any other form.  (2) For
instance, when I have feigned (to repeat their argument) that the
nature of body is of a certain kind, and have of my own free will
desired to convince myself that it actually exists under this
form, I am no longer able to hypothesize that a fly, for example,
is infinite; so, when I have hypothesized the essence of the soul,
I am not able to think of it as square, &c. 

[60] (1) But these arguments demand further inquiry. (2) First,
their upholders must either grant or deny that we can understand
anything. If they grant it, then necessarily the same must be
said of understanding, as is said of fiction. (3) If they deny
it, let us, who know that we do know something, see what they
mean.  (4) They assert that the soul can be conscious of, and
perceive in a variety of ways, not itself nor things which
exist, but only things which are neither in itself nor anywhere
else, in other words, that the soul can, by its unaided power,
create sensations or ideas unconnected with things.  (5) In fact,
they regard the soul as a sort of god.  (60:6) Further, they assert
that we or our soul have such freedom that we can constrain
ourselves, or our soul, or even our soul's freedom.  (7) For,
after it has formed a fictitious idea, and has given its assent
thereto, it cannot think or feign it in any other manner, but is
constrained by the first fictitious idea to keep all its other
thoughts in harmony therewith.  (8) Our opponents are thus driven
to admit, in support of their fiction, the absurdities which I
have just enumerated; and which are not worthy of rational
refutation. 

[61]  (1) While leaving such persons in their error, we will take
care to derive from our argument with them a truth serviceable for
our purpose, namely, [61a] that the mind, in paying attention to
a thing hypothetical or false, so as to meditate upon it and
understand it, and derive the proper conclusions in due order
therefrom, will readily discover its falsity; and if the thing
hypothetical be in its nature true, and the mind pays attention 
to it, so as to understand it, and deduce the truths which are
derivable from it, the mind will proceed with an uninterrupted
series of apt conclusions; in the same way as it would at once
discover (as we showed just now) the absurdity of a false
hypothesis, and of the conclusions drawn from it. 

[62]  (1) We need, therefore, be in no fear of forming hypotheses,
so long as we have a clear and distinct perception of what is
involved.  (2) For, if we were to assert, haply, that men are
suddenly turned into beasts, the statement would be extremely
general, so general that there would be no conception, that is,
no idea or connection of subject and predicate, in our mind.
(3) If there were such a conception we should at the same time
be aware of the means and the causes whereby the event took place.
(4) Moreover, we pay no attention to the nature of the subject
and the predicate. 

[63]  (1) Now, if the first idea be not fictitious, and if all the
other ideas be deduced therefrom, our hurry to form fictitious ideas
will gradually subside.  (2) Further, as a fictitious idea cannot be
clear and distinct, but is necessarily confused, and as all confusion
arises from the fact that the mind has only partial knowledge of a
thing either simple or complex, and does not distinguish between the
known and the unknown, and, again, that it directs its attention
promiscuously to all parts of an object at once without making
distinctions, it follows, first, that if the idea be of something
very simple, it must necessarily be clear and distinct.  (3) For
a very simple object cannot be known in part, it must either be
known altogether or not at all. 

[64]  (1) Secondly, it follows that if a complex object be divided by
thought into a number of simple component parts, and if each be
regarded separately, all confusion will disappear.  (2) Thirdly, it
follows that fiction cannot be simple, but is made up of the blending
of several confused ideas of diverse objects or actions existent in
nature, or rather is composed of attention directed to all such ideas
at once, [64b] and unaccompanied by any mental assent. 
   (64:3) Now a fiction that was simple would be clear and distinct,
and therefore true, also a fiction composed only of distinct ideas
would be clear and distinct, and therefore true.  (4) For instance,
when we know the nature of the circle and the square, it is
impossible for us to blend together these two figures, and to
hypothesize a square circle, any more than a square soul, or things
of that kind. 

[65] (1) Let us shortly come to our conclusion, and again repeat
that we need have no fear of confusing with true ideas that which
is only a fiction.  (2) As for the first sort of fiction of which
we have already spoken, when a thing is clearly conceived, we saw
that if the existence of a that thing is in itself an eternal trut
fiction can have no part in it; but if the existence of the 
conceived be not an eternal truth, we have only to be careful 
such existence be compared to the thing's essence, and to
consider the order of nature. (64:3) As for the second sort of
fiction, which we stated to be the result of simultaneously
directing the attention, without the assent of the intellect,
to different confused ideas representing different things and
actions existing in nature, we have seen that an absolutely
simple thing cannot be feigned, but must be understood, and that
a complex thing is in the same case if we regard separately the
simple parts whereof it is composed; we shall not even be able
to hypothesize any untrue action concerning such objects, for we
shall be obliged to consider at the same time the causes and manner
of such action.

[66]  (1) These matters being thus understood, let us pass on to
consider the false idea, observing the objects with which it is
concerned, and the means of guarding ourselves from falling into
false perceptions.  (2) Neither of these tasks will present much
difficulty, after our inquiry concerning fictitious ideas.
(3) The false idea only differs from the fictitious idea in the
fact of implying a mental assent - that is, as we have already
remarked, while the representations are occurring, there are no
causes present to us, wherefrom, as in fiction, we can conclude
that such representations do not arise from external objects:
in fact, it is much the same as dreaming with our eyes open,
or while awake.  (67:4) Thus, a false idea is concerned with, or
(to speak more correctly) is attributable to, the existence of
a thing whereof the essence is known, or the essence itself, in
the same way as a fictitious idea. 

[67]  (1) If attributable to the existence of the thing, it is
corrected in the same way as a fictitious idea under similar
circumstances.  (2) If attributable to the essence, it is
likewise corrected in the same way as a fictitious idea.
(67:3) For if the nature of the thing known implies necessary
existence, we cannot possible be in error with regard to its
existence; but if the nature of the thing be not an eternal
truth, like its essence, but contrariwise the necessity or
impossibility of its existence depends on external causes,
then we must follow the same course as we adopted in the 
of fiction, for it is corrected in the same manner. 

[68]  (1) As for false ideas concerned with essences, or even
with actions, such perceptions are necessarily always confused,
being compounded of different confused perceptions of things
existing in nature, as, for instance, when men are persuaded
that deities are present in woods, in statues, in brute beasts,
and the like; that there are bodies which, by their composition
alone, give rise to intellect; that corpses reason, walk about,
and speak; that God is deceived, and so on.  (68:2) But ideas which
are clear and distinct can never be false: for ideas of things
clearly and distinctly conceived are either very simple
themselves, or are compounded from very simple ideas, that is,
are deduced therefrom.  (3) The impossibility of a very simple
idea being false is evident to everyone who understands the nature
of truth or understanding and of falsehood. 

[69]  (1) As regards that which constitutes the reality of truth,
it is certain that a true idea is distinguished from a false one,
not so much by its extrinsic object as by its intrinsic nature.
(2) If an architect conceives a building properly constructed,
though such a building may never have existed, and amy never exist,
nevertheless the idea is true; and the idea remains the same,
whether it be put into execution or not.  (69:3) On the other hand,
if anyone asserts, for instance, that Peter exists, without
knowing whether Peter really exists or not, the assertion, as far
as its asserter is concerned, is false, or not true, even though
Peter actually does exist.  (4) The assertion that Peter exists is
true only with regard to him who knows for certain that Peter does
exist. 

[70]  (1) Whence it follows that there is in ideas something real,
whereby the true are distinguished from the false.  (2) This reality
must be inquired into, if we are to find the best standard of truth
(we have said that we ought to determine our thoughts by the given
standard of a true idea, and that method is reflective knowledge),
and to know the properties of our understanding.  (70:3) Neither must
we say that the difference between true and false arises from the
fact, that true knowledge consists in knowing things through their
primary causes, wherein it is totally different from false knowledge,
as I have just explained it: for thought is said to be true, if
it involves subjectively the essence of any principle which has no
cause, and is known through itself and in itself. 

[71]  (1) Wherefore the reality (forma) of true thought must exist
in the thought itself, without reference to other thoughts; it does
not acknowledge the object as its cause, but must depend on the
actual power and nature of the understanding.  (2) For, if we
suppose that the understanding has perceived some new entity which
has never existed, as some conceive the understanding of God before
He created thing (a perception which certainly could not arise 
any object), and has legitimately deduced other thoughts from said
perception, all such thoughts would be true, without being
determined by any external object; they would depend solely on the
power and nature of the understanding.  (71:3) Thus, that which
constitutes the reality of a true thought must be sought in the
thought itself, and deduced from the nature of the understanding.

[72]  (1) In order to pursue our investigation, let us confront
ourselves with some true idea, whose object we know for
certain to be dependent on our power of thinking, and to have
nothing corresponding to it in nature.  (2) With an idea of this
kind before us, we shall, as appears from what has just been said,
be more easily able to carry on the research we have in view.
(72:3) For instance, in order to form the conception of a sphere,
I invent a cause at my pleasure - namely, a semicircle revolving
round its center, and thus producing a sphere.  (4) This is
indisputably a true idea; and, although we know that no sphere in
nature has ever actually been so formed, the perception remains
true, and is the easiest manner of conceiving a sphere.
(72:5) We must observe that this perception asserts the rotation
of a semicircle - which assertion would be false, if it were not
associated with the conception of a sphere, or of a cause
determining a motion of the kind, or absolutely, if the assertion
were isolated.  (6) The mind would then only tend to the
affirmation of the sole motion of a semicircle, which is not
contained in the conception of a semicircle, and does not arise
from the conception of any cause capable of producing such motion.
    (72:7) Thus falsity consists only in this, that something is
affirmed of a thing, which is not contained in the conception
we have formed of that thing, as motion or rest of a semicircle.
(8) Whence it follows that simple ideas cannot be other than
true - e.g., the simple idea of a semicircle, of motion, of rest,
of quantity, &c.
    (72:9) Whatsoever affirmation such ideas contain is equal to the
concept formed, and does not extend further.  (10) Wherefore we
form as many simple ideas as we please, without any fear of error.

[73]  (1) It only remains for us to inquire by what power our mind
can form true ideas, and how far such power extends.  (2) It is
certain that such power cannot extend itself infinitely.  (3) For
when we affirm somewhat of a thing, which is not contained in the
concept we have formed of that thing, such an affirmation shows a
defect of our perception, or that we have formed fragmentary or
mutilated ideas.  (4) Thus we have seen that the notion of a
semicircle is false when it is isolated in the mind, but true when
it is associated with the concept of a sphere, or of some cause
determining such a motion.  (73:5) But if it be the nature of a
thinking being, as seems, prima facie, to be the case, to form true
or adequate thoughts, it is plain that inadequate ideas arise in us
only because we are parts of a thinking being, whose thoughts - some
in their entirety, others in fragments only - constitute our mind.

[74]  (1) But there is another point to be considered, which was not
worth raising in the case of fiction, but which give rise to complete
deception - namely, that certain things presented to the imagination
also exist in the understanding - in other words, are conceived
clearly and distinctly.  (2) Hence, so long as we do not separate that
which is distinct from that which is confused, certainty, or the true
idea, becomes mixed with indistinct ideas.  (3) For instance, certain
Stoics heard, perhaps, the term "soul," and also that the soul is
immortal, yet imagined it only confusedly; they imaged, also, and
understood that very subtle bodies penetrate all others, and are
penetrated by none.  (74:4) By combining these ideas, and being at the
same time certain of the truth of the axiom, they forthwith became
convinced that the mind consists of very subtle bodies; that these
very subtle bodies cannot be divided &c.

[75]  (1) But we are freed from mistakes of this kind, so long as we
endeavor to examine all our perceptions by the standard of the given
true idea.  (2) We must take care, as has been said, to separate such
perceptions from all those which arise from hearsay or unclassified
experience.  (3) Moreover, such mistakes arise from things being
conceived too much in the abstract; for it is sufficiently self-evident
that what I conceive as in its true object I cannot apply to anything
else.  (75:4) Lastly, they arise from a want of understanding of the
primary elements of nature as a whole; whence we proceed without due
order, and confound nature with abstract rules, which, although they
be true enough in their sphere, yet, when misapplied, confound
themselves, and pervert the order of nature.  (5) However, if we
proceed with as little abstraction as possible, and begin from primary
elements - that is, from the source and origin of nature, as far back
as we can reach, - we need not fear any deceptions of this kind.

[76] (1) As far as the knowledge of the origin of nature is concerned,
there is no danger of our confounding it with abstractions.  (2) For
when a thing is conceived in the abstract, as are all universal
notions, the said universal notions are always more extensive in the
mind than the number of individuals forming their contents really
existing in nature.  (3) Again, there are many things in nature, the
difference between which is so slight as to be hardly perceptible to
the understanding; so that it may readily happen that such things are
confounded together, if they be conceived abstractedly.  (4) But since
the first principle of nature cannot (as we shall see hereafter) be
conceived abstractedly or universally, and cannot extend further in
the understanding than it does in reality, and has no likeness to
mutable things, no confusion need be feared in respect to the idea of
it, provided (as before shown) that we possess a standard of truth.
(5) This is, in fact, a being single and infinite [76z] ; in other
words, it is the sum total of being, beyond which there is no being
found. [76a]

[77]  (1) Thus far we have treated of the false idea. We have now
to investigate the doubtful idea - that is, to inquire what can
cause us to doubt, and how doubt may be removed.  (2) I speak of
real doubt existing in the mind, not of such doubt as we see
exemplified when a man says that he doubts, though his mind does
not really hesitate.  (77:3) The cure of the latter does not fall
within the province of method, it belongs rather to inquiries
concerning obstinacy and its cure.

[78]  (1) Real doubt is never produced in the mind by the thing
doubted of.  (2) In other words, if there were only one idea in
the mind, whether that idea were true or false, there would be no
doubt or certainty present, only a certain sensation.  (3) For an
idea is in itself nothing else than a certain sensation. (4) But
doubt will arise through another idea, not clear and distinct
enough for us to be able to draw any certain conclusions with
regard to the matter under consideration; that is, the idea which
causes us to doubt is not clear and distinct. (5) To take an example.
(78:6) Supposing that a man has never reflected, taught by experience
or by any other means, that our senses sometimes deceive us, he will
never doubt whether the sun be greater or less than it appears.
(7) Thus rustics are generally astonished when they hear that the
sun is much larger than the earth. (8) But from reflection on the
deceitfulness of the senses [78a] doubt arises, and if, after
doubting, we acquire a true knowledge of the senses, and how things
at a distance are represented through their instrumentality, doubt
is again removed. 

[79]  (1) Hence we cannot cast doubt on true ideas by the supposition
that there is a deceitful Deity, who leads us astray even in what is
most certain.  (2) We can only hold such an hypothesis so long as we
have no clear and distinct idea - in other words, until we reflect 
the knowledge which we have of the first principle of all things, and
find that which teaches us that God is not a deceiver, and until we
know this with the same certainty as we know from reflecting on the
are equal to two right angles.  (3) But if we have a knowledge of God
equal to that which we have of a triangle, all doubt is removed.
(79:4) In the same way as we can arrive at the said knowledge of a
triangle, though not absolutely sure that there is not some
arch-deceiver leading us astray, so can we come to a like knowledge
of God under the like condition, and when we have attained to it,
it is sufficient, as I said before, to remove every doubt which we can
possess concerning clear and distinct ideas. 

[80]  (1) Thus, if a man proceeded with our investigations in due
order, inquiring first into those things which should first be
inquired into, never passing over a link in the chain of association,
and with knowledge how to define his questions before seeking to
answer them, he will never have any ideas save such as are very
certain, or, in other words, clear and distinct; for doubt is only a
suspension of the spirit concerning some affirmation or negation
which it would pronounce upon unhesitatingly if it were not in
ignorance of something, without which the knowledge of the matter in
hand must needs be imperfect.  (2) We may, therefore, conclude that
doubt always proceeds from want of due order in investigation.

[81]  (1) These are the points I promised to discuss in the first part
of my treatise on method.  (2) However, in order not to omit anything
which can conduce to the knowledge of the understanding and its
faculties, I will add a few words on the subject of memory and
forgetfulness.
   (81:3) The point most worthy of attention is, that memory is
strengthened both with and without the aid of the understanding.
(4) For the more intelligible a thing is, the more easily is it
remembered, and the less intelligible it is, the more easily do we
forget it.  (5) For instance, a number of unconnected words is much
more difficult to remember than the same number in the form of a
narration.

[82]  (1) The memory is also strengthened without the aid of the
understanding by means of the power wherewith the imagination or
the sense called common, is affected by some particular physical
object.  (2) I say particular, for the imagination is only affected
by particular objects.  (3) If we read, for instance, a single romantic
comedy, we shall remember it very well, so long as we do not read
many others of the same kind, for it will reign alone in the memory
(4) If, however, we read several others of the same kind, we shall
think of them altogether, and easily confuse one with another.
(82:5) I say also, physical.  (6) For the imagination is only
affected by physical objects.  (7) As, then, the memory is
strengthened both with and without the aid of the understanding,
we may conclude that it is different from the understanding,
and that in the latter considered in itself there is neither
memory nor forgetfulness. 

[83] (1) What, then, is memory? (2) It is nothing else than the
actual sensation of impressions on the brain, accompanied with the
thought of a definite duration, [83d] of the sensation.  (3) This
is also shown by reminiscence.  (4) For then we think of the
sensation, but without the notion of continuous duration; thus the
idea of that sensation is not the actual duration of the sensation
or actual memory.  (83:5) Whether ideas are or are not subject to
corruption will be seen in philosophy.  (6) If this seems too
absurd to anyone, it will be sufficient for our purpose, if he
reflect on the fact that a thing is more easily remembered in
proportion to its singularity, as appears from the example of
the comedy just cited.  (83:7) Further, a thing is remembered more
easily in proportion to its intelligibility; therefore we cannot
help remember that which is extremely singular and sufficiently
intelligible.
 

[84]  (1) Thus, then, we have distinguished between a true idea and
other perceptions, and shown that ideas fictitious, false, and the
rest, originate in the imagination - that is, in certain sensations
fortuitous (so to speak) and disconnected, arising not from the power
of the mind, but from external causes, according as the body,
sleeping or waking, receives various motions.
   (2) But one may take any view one likes of the imagination so long
as one acknowledges that it is different from the understanding, and
that the soul is passive with regard to it.  (3) The view taken is
immaterial, if we know that the imagination is something indefinite,
with regard to which the soul is passive, and that we can by some
means or other free ourselves therefrom with the help of the
understanding.  (4) Let no one then be astonished that before proving
the existence of body, and other necessary things, I speak of
imagination of body, and of its composition.  (5) The view taken is,
I repeat, immaterial, so long as we know that imagination is something
indefinite, &c. 

[85] (1) As regards as a true idea, we have shown that it is simple
or compounded of simple ideas; that it shows how and why something
is or has been made; and that its subjective effects in the soul
correspond to the actual reality of its object.  (2) This conclusion
is identical with the saying of the ancients, that true proceeds
from cause to effect; though the ancients, so far as I know,
never formed the conception put forward here that the soul acts
according to fixed laws, and is as it were an immaterial automaton. 

[86]  (1) Hence, as far as is possible at the outset, we have
acquired a knowledge of our understanding, and such a standard of
a true idea that we need no longer fear confounding truth with
falsehood and fiction.  (2) Neither shall we wonder why we
understand some things which in nowise fall within the scope of
the imagination, while other things are in the imagination but
wholly opposed to the understanding, or others, again, which
agree therewith.  (3) We now know that the operations, whereby the
effects of imagination are produced, take place under other laws
quite different from the laws of the understanding, and that the
mind is entirely passive with regard to them. 

[87]  (1) Whence we may also see how easily men may fall into grave
errors through not distinguishing accurately between the imagination
and the understanding; such as believing that extension must be
localized, that it must be finite, that its parts are really distinct
one from the other, that it is the primary and single foundation of
all things, that it occupies more space at one time than at another
and other similar doctrines, all entirely opposed to truth, as we
shall duly show. 

[88] (1) Again, since words are a part of the imagination - that is,
since we form many conceptions in accordance with confused
arrangements of words in the memory, dependent on particular bodily
conditions, - there is no doubt that words may, equally with the
imagination, be the cause of many and great errors, unless we 
strictly on our guard. 

[89] (1) Moreover, words are formed according to popular fancy and
intelligence, and are, therefore, signs of things as existing in the
imagination, not as existing in the understanding.  (2) This is
evident from the fact that to all such things as exist only in the
understanding, not in the imagination, negative names are often
given, such as incorporeal, infinite, &c.  (3) So, also, many
conceptions really affirmative are expressed negatively, and vice
versa, such as uncreate, independent, infinite, immortal, &c.,
inasmuch as their contraries are much more easily imagined, and,
therefore, occurred first to men, and usurped positive names.
(89:4) Many things we affirm and deny, because the nature of words
allows us to do so, though the nature of things does not.  (5) While
we remain unaware of this fact, we may easily mistake falsehood for
truth.

[90] (1) Let us also beware of another great cause of confusion,
which prevents the understanding from reflecting on itself.
(2) Sometimes, while making no distinction between the imagination
and the intellect, we think that what we more readily imagine is
clearer to us; and also we think that what we imagine we understand.
(3) Thus, we put first that which should be last: the true order of
progression is reversed, and no legitimate conclusion is drawn. 

[91]  [91e] (1) Now, in order at length to pass on to the second
part of this method, I shall first set forth the object aimed at,
and next the means for its attainment.  (2) The object aimed at
is the acquisition of clear and distinct ideas, such as are
produced by the pure intellect, and not by chance physical motions.
(3) In order that all ideas may be reduced to unity, we shall
endeavor so to associate and arrange them that our mind may, as far
as possible, reflect subjectively the reality of nature, both as
a whole and as parts. 

[92] (1) As for the first point, it is necessary (as we have said)
for our purpose that everything should be conceived, either solely
through its essence, or through its proximate cause.  (2) If the
thing be self-existent, or, as is commonly said, the cause of
itself, it must be understood through its essence only; if it be
not self-existent, but requires a cause for its existence, it must
be understood through its proximate cause.  (3) For, in reality,
the knowledge, [92f] of an effect is nothing else than the
acquisition of more perfect knowledge of its cause. 

[93] (1) Therefore, we may never, while we are concerned with
inquiries into actual things, draw any conclusion from
abstractions; we shall be extremely careful not to confound that
which is only in the understanding with that which is in the
thing itself. (2) The best basis for drawing a conclusion will
be either some particular affirmative essence, or a true and
legitimate definition.  (93:3) For the understanding cannot descend
from universal axioms by themselves to particular things, since
axioms are of infinite extent, and do not determine the
understanding to contemplate one particular thing more than
another. 

[94] (1) Thus the true method of discovery is to form thoughts
from some given definition.  (2) This process will be the
more fruitful and easy in proportion as the thing given be
better defined.  (3) Wherefore, the cardinal point of all this
second part of method consists in the knowledge of the conditions
of good definition, and the means of finding them.  (4) I will
first treat of the conditions of definition.

[95]  (1) A definition, if it is to be called perfect, must
explain the inmost essence of a thing, and must take care not
to substitute for this any of its properties.  (2) In order
to illustrate my meaning, without taking an example which
would seem to show a desire to expose other people's errors,
I will choose the case of something abstract, the definition
of which is of little moment.  (95:3) Such is a circle.  (4) If
a circle be defined as a figure, such that all straight lines
drawn from the center to the circumference are equal, every
one can see that such a definition does not in the least
explain the essence of a circle, but solely one of its
properties.  (5) Though, as I have said, this is of no
importance in the case of figures and other abstractions,
it is of great importance in the case of physical beings
and realities: for the properties of things are not understood
so long as their essences are unknown. (6) If the latter be
passed over, there is necessarily a perversion of the
succession of ideas which should reflect the succession of
nature, and we go far astray from our object.

[96]  In order to be free from this fault, the following rules
should be observed in definition:-
I.  (1) If the thing in question be created, the definition
   must (as we have said) comprehend the proximate cause.
   (2) For instance, a circle should, according to this rule,
   be defined as follows: the figure described by any line
   whereof one end is fixed and the other free.  (3) This
   definition clearly comprehends the proximate cause.
II.  (4) A conception or definition of a thing should be such
   that all the properties of that thing, in so far as it is
   considered by itself, and not in conjunction with other
   things, can be deduced from it, as may be seen in the
   definition given of a circle: for from that it clearly follows
   that all straight lines drawn from the center to the
   circumference are equal.  (5) That this is a necessary
   characteristic of a definition is so clear to anyone, who
   reflects on the matter, that there is no need to spend time
   in proving it, or in showing that, owing to this second
   condition, every definition should be affirmative.  (6) I
   speak of intellectual affirmation, giving little thought to
   verbal affirmations which, owing to the poverty of language,
   must sometimes, perhaps, be expressed negatively, though
   the idea contained is affirmative.

[97]  The rules for the definition of an uncreated thing
are as follows:--
I.  The exclusion of all idea of cause - that is, the thing
   must not need explanation by Anything outside itself.
II. When the definition of the thing has been given, there must
   be no room for doubt as to whether the thing exists or not.
III. It must contain, as far as the mind is concerned, no
   substantives which could be put into an adjectival form;
   in other words, the object defined must not be explained
   through abstractions.
IV. Lastly, though this is not absolutely necessary, it should
   be possible to deduce from the definition all the properties
   of the thing defined.
All these rules become obvious to anyone giving strict
attention to the matter.

[98]  (1) I have also stated that the best basis for drawing a
conclusion is a particular affirmative essence.  (2) The more
specialized the idea is, the more it is distinct, and therefore
clear.  (3) Wherefore a knowledge of particular things should
be sought for as diligently as possible.

[99]  (1) As regards the order of our perceptions, and the manner
in which they should be arranged and united, it is necessary that,
as soon as is possible and rational, we should inquire whether
there be any being (and, if so, what being), that is the cause
of all things, so that its essence, represented in thought, may
be the cause of all our ideas, and then our mind will to the
utmost possible extent reflect nature. (2) For it will possess,
subjectively, nature's essence, order, and union.  (3) Thus we
can see that it is before all things necessary for us to deduce
all our ideas from physical things - that is, from real entities,
proceeding, as far as may be, according to the series of causes,
from one real entity to another real entity, never passing to
universals and abstractions, either for the purpose of deducing
some real entity from them, or deducing them from some real
entity.  (4) Either of these processes interrupts the true
progress of the understanding.

[100]  (1) But it must be observed that, by the series of causes
and real entities, I do not here mean the series of particular
and mutable things, but only the series of fixed and eternal
things. (2) It would be impossible for human infirmity to follow
up the series of particular mutable things, both on account
their multitude, surpassing all calculation, and on account of
the infinitely diverse circumstances surrounding one and the same
thing, any one of which may be the cause of its existence or
non-existence.  (3) Indeed, their existence has no connection
with their essence, or (as we have said already) is not an
eternal truth.

[101] (1) Neither is there any need that we should understand
their series, for the essences of particular mutable things are
not to be gathered from their series or order of existence,
which would furnish us with nothing beyond their extrinsic
denominations, their relations, or, at most, their circumstances,
all of which are very different from their inmost essence.
(101:2) This inmost essence must be sought solely from fixed and
eternal things, and from the laws, inscribed (so to speak) in
those things as in their true codes, according to which all
particular things take place and are arranged; nay, these mutable
particular things depend so intimately and essentially (so to
phrase it) upon the fixed things, that they cannot either be
conceived without them.

[102]  (1) But, though this be so, there seems to be no small
difficulty in arriving at the knowledge of these particular things,
for to conceive them all at once would far surpass the powers of
the human understanding.  (2) The arrangement whereby one thing is
understood, before another, as we have stated, should not be sought
from their series of existence, nor from eternal things.  (3) For
the latter are all by nature simultaneous.  (4) Other aids are
therefore needed besides those employed for understanding eternal
things and their laws.  (5) However, this is not the place to recount
such aids, nor is there any need to do so, until we have acquired a
sufficient knowledge of eternal things and their infallible laws,
and until the nature of our senses has become plain to us.

[103]  (1) Before betaking ourselves to seek knowledge of particular
things, it will be seasonable to speak of such aids, as all tend to
teach us the mode of employing our senses, and to make certain
experiments under fixed rules and arrangements which may suffice to
determine the object of our inquiry, so that we may therefrom infer
what laws of eternal things it has been produced under, and may gain
an insight into its inmost nature, as I will duly show.  (2) Here,
to return to my purpose, I will only endeavor to set forth what seems
necessary for enabling us to attain to knowledge of eternal things,
and to define them under the conditions laid down above.

[104]  (1) With this end, we must bear in mind what has already been
stated, namely, that when the mind devotes itself to any thought, so
as to examine it, and to deduce therefrom in due order all the
legitimate conclusions possible, any falsehood which may lurk in the
thought will be detected; but if the thought be true, the mind will
readily proceed without interruption to deduce truths from it.
(104:2) This, I say, is necessary for our purpose, for our thoughts
may be brought to a close by the absence of a foundation.

[105]  (1) If, therefore, we wish to investigate the first thing of
all, it will be necessary to supply some foundation which may direct
our thoughts thither.  (2) Further, since method is reflective
knowledge, the foundation which must direct our thoughts can be
nothing else than the knowledge of that which constitutes the reality
of truth, and the knowledge of the understanding, its properties, and
powers.  (3) When this has been acquired we shall possess a foundation
wherefrom we can deduce our thoughts, and a path whereby the intellect,
according to its capacity, may attain the knowledge of eternal things,
allowance being made for the extent of the intellectual powers.

[106]  (1) If, as I stated in the first part, it belongs to the nature
of thought to form true ideas, we must here inquire what is meant by
the faculties and power of the understanding.  (2) The chief part of
our method is to understand as well as possible the powers of the
intellect, and its nature; we are, therefore, compelled (by the
considerations advanced in the second part of the method) necessarily
to draw these conclusions from the definition itself of thought and
understanding.

[107]  (1) But, so far as we have not got any rules for finding
definitions, and, as we cannot set forth such rules without a
previous knowledge of nature, that is without a definition of the
understanding and its power, it follows either that the definition
of the understanding must be clear in itself, or that we can
understand nothing.  (2) Nevertheless this definition is not
absolutely clear in itself; however, since its properties, like
all things that we possess through the understanding, cannot be
known clearly and distinctly, unless its nature be known previously,
understanding makes itself manifest, if we pay attention to its
properties, which we know clearly and distinctly.  (3) Let us,
then, enumerate here the properties of the understanding, let us
examine them, and begin by discussing the instruments for research
which we find innate in us. See [31]

[108]  (1) The properties of the understanding which I have chiefly
remarked, and which I clearly understand, are the following:-
I. (2) It involves certainty - in other words, it knows that a thing
   exists in reality as it is reflected subjectively.
II. (108:3) That it perceives certain things, or forms some ideas
   absolutely, some ideas from others.  (4) Thus it forms the
   idea of quantity absolutely, without reference to any other
   thoughts; but ideas of motion it only forms after taking into
   consideration the idea of quantity.
III. (108:5) Those ideas which the understanding forms absolutely
   express infinity; determinate ideas are derived from other
   ideas.  (6) Thus in the idea of quantity, perceived by means
   of a cause, the quantity is determined, as when a body is
   perceived to be formed by the motion of a plane, a plane by
   the motion of a line, or, again, a line by the motion of a
   point.  (7) All these are perceptions which do not serve
   towards understanding quantity, but only towards determining
   it.  (108:8) This is proved by the fact that we conceive them
   as formed as it were by motion, yet this motion is not perceived
   unless the quantity be perceived also; we can even prolong the
   motion to form an infinite line, which we certainly could not do
   unless we had an idea of infinite quantity.
IV. (9) The understanding forms positive ideas before forming
   negative ideas.
V. (108:10) It perceives things not so much under the condition
   of duration as under a certain form of eternity, and in an
   infinite number; or rather in perceiving things it does not
   consider either their number or duration, whereas, in imagining
   them, it perceives them in a determinate number, duration, and
   quantity.
VI. (108:11) The ideas which we form as clear and distinct, seem
   to follow from the sole necessity of our nature, that they
   appear to depend absolutely on our sole power; with confused
   ideas the contrary is the case.  (12) They are often formed
   against our will.
VII. (108:13) The mind can determine in many ways the ideas of things,
which the understanding forms from other ideas: thus, for instance,
in order to define the plane of an ellipse, it supposes a point
adhering to a cord to be moved around two centers, or, again, it
conceives an infinity of points, always in the same fixed relation
to a given straight line, angle of the vertex of the cone, or in an
infinity of other ways.
VIII. (108:14) The more ideas express perfection of any object,
the more perfect are they themselves; for we do not admire the
architect who has planned a chapel so much as the architect who
has planned a splendid temple.

[109] (1) I do not stop to consider the rest of what is referred
to thought, such as love, joy, &c.  (2) They are nothing to our
present purpose, and cannot even be conceived unless the
understanding be perceived previously. (3) When perception is
removed, all these go with it.

[110] (1) False and fictitious ideas have nothing positive about
them (as we have abundantly shown), which causes them to be called
false or fictitious; they are only considered as such through the
defectiveness of knowledge.  (2) Therefore, false and fictitious
ideas as such can teach us nothing concerning the essence of thought;
this must be sought from the positive properties just enumerated;
in other words, we must lay down some common basis from which these
properties necessarily follow, so that when this is given, the
properties are necessarily given also, and when it is removed,
they too vanish with it.

The rest of the treatise is wanting.

----------------------------------------------------------------------------
Spinoza's Endnotes: Marks as per Curley, see Note 5 above.
[a] (1) This might be explained more at large and more clearly:
    I mean by distinguishing riches according as they are pursued for
    their own sake, in or furtherance of fame, or sensual pleasure,
    or the advancement of science and art. (2) But this subject is
    reserved to its own place, for it is not here proper to
    investigate the matter more accurately.
[b] These considerations should be set forth more precisely.
[c] These matters are explained more at length elsewhere.
[d] N.B. I do no more here than enumerate the sciences necessary
    for our purpose; I lay no stress on their order.
[e] There is for the sciences but one end, to which they should
    all be directed.
[f] (1) In this case we do not understand anything of the cause
    from the consideration of it in the effect.  (2) This is
    sufficiently evident from the fact that the cause is only
    spoken of in very general terms, such as - there exists then
    something; there exists then some power, &c.; or from the
    that we only express it in a negative manner - it is not
    or that, &c.  (3) In the second case something is ascribed
    to the cause because of the effect, as we shall show in an
    example, but only a property, never an essence.
[g] (1) From this example may be clearly seen what I have just
    drawn attention to.  (2) For through this union we understand
    nothing beyond the sensation, the effect, to wit, from which
    we inferred the cause of which we understand nothing.
[h] (1) A conclusion of this sort, though it be certain, is yet
    not to be relied on without great caution; for unless we are
    exceedingly careful we shall forthwith fall into error.
    (2) When things are conceived thus abstractedly, and not
    through their true essence, they are apt to be confused by the
    imagination.  (3) For that which is in itself one, men imagine
    to be multiplex.  (4) To those things which are conceived
    abstractedly, apart, and confusedly, terms are applied which are
    apt to become wrested from their strict meaning, and bestowed on
    things more familiar; whence it results that these latter are
    imagined in the same way as the former to which the terms were
    originally given.
[i] I shall here treat a little more in detail of experience,
    and shall examine the method adopted by the Empirics,
    and by recent philosophers.
[k] By native strength, I mean that not bestowed on us by external
    causes, as I shall afterwards explain in my philosophy.
[l] Here I term them operations: I shall explain their nature
    in my philosophy.
[m] I shall take care not only to demonstrate what I have just
    advanced, but also that we have hitherto proceeded rightly,
    and other things needful to be known.
[33note1] (1) In modern language, "the idea may become the
    subject of another presentation."  (2) Objectivus generally
    corresponds to the modern "subjective," formalis to the
    modern "objective." [Trans.- Note 1]
[n] (1) Observe that we are not here inquiring how the first
    subjective essence is innate in us.  (2) This belongs to an
    investigation into nature, where all these matters are amply
    explained, and it is shown that without ideas neither
    affirmation, nor negation, nor volition are possible.
[o] The nature of mental search is explained in my philosophy.
[p] To be connected with other things is to be produced by them,
    or to produce them.
[q] In the same way as we have here no doubt of the truth of
    our knowledge.
[r] See below the note on hypotheses, whereof we have a clear
    understanding; the fiction consists in saying that such
    hypotheses exist in heavenly bodies.
[s] (1) As a thing, when once it is understood, manifests itself,
    we have need only of an example without further proof.
    (2) In the same way the contrary has only to be presented to
    our minds to be recognized as false, as will forthwith appear
    when we come to discuss fiction concerning essences.
[t] Observe, that although many assert that they doubt whether God
    exists, they have nought but his name in their minds, or else
    some fiction which they call God: this fiction is not in
    harmony with God's real nature, as we will duly show.
[u] (1) I shall presently show that no fiction can concern eternal
    truths. By an eternal truth, I mean that which being positive
    could never become negative.  (2) Thus it is a primary and
    eternal truth that God exists, but it is not an eternal truth
    that Adam thinks.  (3) That the Chimaera does not exist is an
    eternal truth, that Adam does not think is not so.
[x] (1) Afterwards, when we come to speak of fiction that is
    concerned with essences, it will be evident that fiction never
    creates or furnishes the mind with anything new; only such things
    as are already in the brain or imagination are recalled to the
    memory, when the attention is directed to them confusedly and all
    at once.  (2) For instance, we have remembrance of spoken words
    and of a tree; when the mind directs itself to them confusedly,
    it forms the notion of a tree speaking.  (3) The same may be said
    of existence, especially when it is conceived quite generally as
    an entity; it is then readily applied to all things together in
    the memory.  (4) This is specially worthy of remark.
[y] We must understand as much in the case of hypotheses put forward
    to explain certain movements accompanying celestial phenomena;
    but from these, when applied to the celestial motions, we any
    draw conclusions as to the nature of the heavens, whereas this
    last may be quite different, especially as many other causes are
    conceivable which would account for such motions.
[z] (1) It often happens that a man recalls to mind this word soul,
    and forms at the same time some corporeal image: as the two
    representations are simultaneous, he easily thinks that he
    imagines and feigns a corporeal soul: thus confusing the name
    with the thing itself.  (2) I here beg that my readers will not
    be in a hurry to refute this proposition; they will, I hope,
    have no mind to do so, if they pay close attention to the
    examples given and to what follows.
[61a] (1) Though I seem to deduce this from experience, some
    may deny its cogency because I have given no formal proof.
    (2) I therefore append the following for those who may
    desire it.  (3) As there can be nothing in nature contrary
    to nature's laws, since all things come to pass by fixed
    laws, so that each thing must irrefragably produce its own
    proper effect, it follows that the soul, as soon as it
    possesses the true conception of a thing, proceeds to
    reproduce in thought that thing's effects.  (4) See below,
    where I speak of the false idea.
[64b] (1) Observe that fiction regarded in itself, only differs
    from dreams in that in the latter we do not perceive the
    external causes which we perceive through the senses while
    awake.  (2) It has hence been inferred that representations
    occurring in sleep have no connection with objects external
    to us.  (3) We shall presently see that error is the dreaming
    of a waking man: if it reaches a certain pitch it becomes delirium.
[76z] These are not attributes of God displaying His essence,
    as I will show in my philosophy.
[76a] (1) This has been shown already.  (2) For if such a being
    did not exist it would never be produced; therefore the mind
    would be able to understand more than nature could furnish;
    and this has been shown above to be false.
[78a] (1) That is, it is known that the senses sometimes deceive us.
    (2) But it is only known confusedly, for it is not known how
    they deceive us.
[83d] (1) If the duration be indefinite, the recollection is
    imperfect; this everyone seems to have learnt from nature.
    (2) For we often ask, to strengthen our belief in something
    we hear of, when and where it happened; though ideas
    themselves have their own duration in the mind, yet, as we
    are wont to determine duration by the aid of some measure
    of motion which, again, takes place by aid of imagination,
    we preserve no memory connected with pure intellect.
[91e] The chief rule of this part is, as appears from the first
    part, to review all the ideas coming to us through pure
    intellect, so as to distinguish them from such as we imagine:
    the distinction will be shown through the properties of each,
    namely, of the imagination and of the understanding.
[92f] Observe that it is thereby manifest that we cannot understand
    anything of nature without at the same time increasing our
    knowledge of the first cause, or God.

End of "On the Improvement of the Understanding."

Notes by Volunteer.

1. Used, in part, with kind permission from:
   http://www.physics.wisc.edu/~shalizi/Spinoza/TIE/

2. The text is that of the translation of the Tractatus de Intellectus
   Emendatione by R. H. M. Elwes, as printed by Dover Publications
   (NY):1955), ISBN 0-486-20250-X.  This text is "an unabridged and
   unaltered republication of the Bohn Library edition originally
   published by George Bell and Sons in 1883."

3. Paragraph Numbers, shown thus [1], are from Edwin Curley's
   translation in his "The Collected Works of Spinoza", Volume 1, 1985,
   Princeton University Press; ISBN 0-691-07222-1.

4. Sentence Numbers, shown thus (1), have been added by volunteer.

5. Spinoza's endnotes are shown thus [a]. The letter is taken from
   Curley, see Note 3.

6. Search strings are enclosed in square brackets; include brackets.

7. HTML versions of "On the Improvement of the Understanding" are
   published in the Books On-Line Web Pages;
   ttp://www.cs.cmu.edu/books.html and they include:
       http://www.physics.wisc.edu/~shalizi/Spinoza/TIE/
       http://www.erols.com/jyselman/teielwes.htm

End of Project Gutenberg's Etext On the Improvement of the Understanding
(Treatise on the Emendation of the Intellect), by Baruch Spinoza


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