The Ethics

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PROP. XXXIII. There is nothing positive in ideas, which causes
them to be called false.
Proof.-If this be denied, conceive, if possible, a positive
mode of thinking, which should constitute the distinctive quality
of falsehood. Such a mode of thinking cannot be in God (II.
xxxii.) ; external to God it cannot be or be conceived (I. xv.).
Therefore there is nothing positive in ideas which causes them to
be called false. Q.E.D.

PROP. XXXIV. Every idea, which in us is absolute or adequate and
perfect, is true.
Proof.-When we say that an idea in us is adequate and
perfect, we say, in other words (II. xi. Coroll.), that the idea
is adequate and perfect in God, in so far as he constitutes the
essence of our mind ; consequently (II. xxxii.), we say that such
an idea is true. Q.E.D.

PROP. XXXV. Falsity consists in the privation of knowledge,
which inadequate, fragmentary, or confused ideas involve.
Proof.-There is nothing positive in ideas, which causes them
to be called false (II. xxxiii.) ; but falsity cannot consist in
simple privation (for minds, not bodies, are said to err and to
be mistaken), neither can it consist in absolute ignorance, for
ignorance and error are not identical ; wherefore it consists in
the privation of knowledge, which inadequate, fragmentary, or
confused ideas involve. Q.E.D.
Note.-In the note to II. xvii. I explained how error consists
in the privation of knowledge, but in order to throw more light
on the subject I will give an example. For instance, men are
mistaken in thinking themselves free ; their opinion is made up
of consciousness of their own actions, and ignorance of the
causes by which they are conditioned. Their idea of freedom,
therefore, is simply their ignorance of any cause for their
actions. As for their saying that human actions depend on the
will, this is a mere phrase without any idea to correspond
thereto. What the will is, and how it moves the body, they none
of them know ; those who boast of such knowledge, and feign
dwellings and habitations for the soul, are wont to provoke
either laughter or disgust. So, again, when we look at the sun,
we imagine that it is distant from us about two hundred feet ;
this error does not lie solely in this fancy, but in the fact
that, while we thus imagine, we do not know the sun's true
distance or the cause of the fancy. For although we afterwards
learn, that the sun is distant from us more than six hundred of
the earth's diameters, we none the less shall fancy it to be near
; for we do not imagine the sun as near us, because we are
ignorant of its true distance, but because the modification of
our body involves the essence of the sun, in so far as our said
body is affected thereby.

PROP. XXXVI. Inadequate and confused ideas follow by the same
necessity, as adequate or clear and distinct ideas.
Proof.-All ideas are in God (I. xv.), and in so far as they
are referred to God are true (II. xxxii.) and (II. vii. Coroll.)
adequate ; therefore there are no ideas confused or inadequate,
except in respect to a particular mind (cf. II. xxiv. and
xxviii.) ; therefore all ideas, whether adequate or inadequate,
follow by the same necessity (II. vi.). Q.E.D.

PROP. XXXVII. That which is common to all (cf. Lemma II.,
above), and which is equally in a part and in the whole, does not
constitute the essence of any particular thing.
Proof.-If this be denied, conceive, if possible, that it
constitutes the essence of some particular thing ; for instance,
the essence of B. Then (II. Def. ii.) it cannot without B either
exist or be conceived ; but this is against our hypothesis.
Therefore it does not appertain to B's essence, nor does it
constitute the essence of any particular thing. Q.E.D.

PROP. XXXVIII. Those things, which are common to all, and which
are equally in a part and in the whole, cannot be conceived
except adequately.
Proof.-Let A be something, which is common to all bodies, and
which is equally present in the part of any given body and in the
whole. I say A cannot be conceived except adequately. For the
idea thereof in God will necessarily be adequate (II. vii.
Coroll.), both in so far as God has the idea of the human body,
and also in so far as he has the idea of the modifications of the
human body, which (II. xvi., xxv., xxvii.) involve in part the
nature of the human body and the nature of external bodies ; that
is (II. xii., xiii.), the idea in God will necessarily be
adequate, both in so far as he constitutes the human mind, and in
so far as he has the ideas, which are in the human mind.
Therefore the mind (II. xi. Coroll.) necessarily perceives A
adequately, and has this adequate perception, both in so far as
it perceives itself, and in so far as it perceives its own or any
external body, nor can A be conceived in any other manner.
Q.E.D.
Corollary-Hence it follows that there are certain ideas or
notions common to all men ; for (by Lemma ii.) all bodies agree
in certain respects, which (by the foregoing Prop.) must be
adequately or clearly and distinctly perceived by all.

PROP. XXXIX. That, which is common to and a property of the
human body and such other bodies as are wont to affect the human
body, and which is present equally in each part of either, or in
the whole, will be represented by an adequate idea in the mind.
Proof.-If A be that, which is common to and a property of the
human body and external bodies, and equally present in the human
body and in the said external bodies, in each part of each
external body and in the whole, there will be an adequate idea of
A in God (II. vii. Coroll.), both in so far as he has the idea of
the human body, and in so far as he has the ideas of the given
external bodies. Let it now be granted, that the human body is
affected by an external body through that, which it has in common
therewith, namely, A ; the idea of this modification will involve
the property A (II. xvi.), and therefore (II. vii. Coroll.) the
idea of this modification, in so far as it involves the property
A, will be adequate in God, in so far as God is affected by the
idea of the human body ; that is (II. xiii.), in so far as he
constitutes the nature of the human mind ; therefore (II. xi.
Coroll.) this idea is also adequate in the human mind. Q.E.D.
Corollary.-Hence it follows that the mind is fitted to
perceive adequately more things, in proportion as its body has
more in common with other bodies.

PROP. XL. Whatsoever ideas in the mind follow from ideas which
are therein adequate, are also themselves adequate.
Proof.-This proposition is self-evident. For when we say
that an idea in the human mind follows from ideas which are
therein adequate, we say, in other words (II. xi. Coroll.), that
an idea is in the divine intellect, whereof God is the cause, not
in so far as he is infinite, nor in so far as he is affected by
the ideas of very many particular things, but only in so far as
he constitutes the essence of the human mind.
Note I.-I have thus set forth the cause of those notions,
which are common to all men, and which form the basis of our
ratiocination. But there are other causes of certain axioms or
notions, which it would be to the purpose to set forth by this
method of ours ; for it would thus appear what notions are more
useful than others, and what notions have scarcely any use at
all. Furthermore, we should see what notions are common to all
men, and what notions are only clear and distinct to those who
are unshackled by prejudice, and we should detect those which are
ill-founded. Again we should discern whence the notions called
secondary derived their origin, and consequently the axioms on
which they are founded, and other points of interest connected
with these questions. But I have decided to pass over the
subject here, partly because I have set it aside for another
treatise, partly because I am afraid of wearying the reader by
too great prolixity. Nevertheless, in order not to omit anything
necessary to be known, I will briefly set down the causes, whence
are derived the terms styled transcendental, such as Being,
Thing, Something. These terms arose from the fact, that the
human body, being limited, is only capable of distinctly forming
a certain number of images (what an image is I explained in the
II. xvii. note) within itself at the same time ; if this number
be exceeded, the images will begin to be confused ; if this
number of images, of which the body is capable of forming
distinctly within itself, be largely exceeded, all will become
entirely confused one with another. This being so, it is evident
(from II. Prop. xvii. Coroll., and xviii.) that the human mind
can distinctly imagine as many things simultaneously, as its body
can form images simultaneously. When the images become quite
confused in the body, the mind also imagines all bodies
confusedly without any distinction, and will comprehend them, as
it were, under one attribute, namely, under the attribute of
Being, Thing, &c. The same conclusion can be drawn from the fact
that images are not always equally vivid, and from other
analogous causes, which there is no need to explain here ; for
the purpose which we have in view it is sufficient for us to
consider one only. All may be reduced to this, that these terms
represent ideas in the highest degree confused. From similar
causes arise those notions, which we call general, such as man,
horse, dog, &c. They arise, to wit, from the fact that so many
images, for instance, of men, are formed simultaneously in the
human mind, that the powers of imagination break down, not indeed
utterly, but to the extent of the mind losing count of small
differences between individuals (e.g. colour, size, &c.) and
their definite number, and only distinctly imagining that, in
which all the individuals, in so far as the body is affected by
them, agree ; for that is the point, in which each of the said
individuals chiefly affected the body ; this the mind expresses
by the name man, and this it predicates of an infinite number of
particular individuals. For, as we have said, it is unable to
imagine the definite number of individuals. We must, however,
bear in mind, that these general notions are not formed by all
men in the same way, but vary in each individual according as the
point varies, whereby the body has been most often affected and
which the mind most easily imagines or remembers. For instance,
those who have most often regarded with admiration the stature of
man, will by the name of man understand an animal of erect
stature ; those who have been accustomed to regard some other
attribute, will form a different general image of man, for
instance, that man is a laughing animal, a two-footed animal
without feathers, a rational animal, and thus, in other cases,
everyone will form general images of things according to the
habit of his body.
It is thus not to be wondered at, that among philosophers,
who seek to explain things in nature merely by the images formed
of them, so many controversies should have arisen.
Note II.-From all that has been said above it is clear, that
we, in many cases, perceive and form our general notions :-(1.)
From particular things represented to our intellect
fragmentarily, confusedly, and without order through our senses
(II. xxix. Coroll.) ; I have settled to call such perceptions by
the name of knowledge from the mere suggestions of experience.4
(2.) From symbols, e.g., from the fact of having read or heard
certain words we remember things and form certain ideas
concerning them, similar to those through which we imagine things
(II. xviii. note). I shall call both these ways of regarding
things knowledge of the first kind, opinion, or imagination.
(3.) From the fact that we have notions common to all men, and
adequate ideas of the properties of things (II. xxxviii. Coroll.,
xxxix. and Coroll. and xl.) ; this I call reason and knowledge of
the second kind. Besides these two kinds of knowledge, there is,
as I will hereafter show, a third kind of knowledge, which we
will call intuition. This kind of knowledge proceeds from an
adequate idea of the absolute essence of certain attributes of
God to the adequate knowledge of the essence of things. I will
illustrate all three kinds of knowledge by a single example.
Three numbers are given for finding a fourth, which shall be to
the third as the second is to the first. Tradesmen without
hesitation multiply the second by the third, and divide the
product by the first ; either because they have not forgotten the
rule which they received from a master without any proof, or
because they have often made trial of it with simple numbers, or
by virtue of the proof of the nineteenth proposition of the
seventh book of Euclid, namely, in virtue of the general property
of proportionals.
But with very simple numbers there is no need of this. For
instance, one, two, three, being given, everyone can see that the
fourth proportional is six ; and this is much clearer, because we
infer the fourth number from an intuitive grasping of the ratio,
which the first bears to the second.

PROP. XLI. Knowledge of the first kind is the only source of
falsity, knowledge of the second and third kinds is necessarily
true.
Proof.-To knowledge of the first kind we have (in the
foregoing note) assigned all those ideas, which are inadequate
and confused ; therefore this kind of knowledge is the only
source of falsity (II. xxxv.). Furthermore, we assigned to the
second and third kinds of knowledge those ideas which are
adequate ; therefore these kinds are necessarily true (II.
xxxiv.). Q.E.D.

PROP. XLII. Knowledge of the second and third kinds, not
knowledge of the first kind, teaches us to distinguish the true
from the false.
Proof.-This proposition is self-evident. He, who knows how
to distinguish between true and false, must have an adequate idea
of true and false. That is (II. xl., note ii.), he must know the
true and the false by the second or third kind of knowledge.

PROP. XLIII. He, who has a true idea, simultaneously knows that
he has a true idea, and cannot doubt of the truth of the thing
perceived.
Proof.-A true idea in us is an idea which is adequate in God,
in so far as he is displayed through the nature of the human mind
(II. xi. Coroll.). Let us suppose that there is in God, in so
far as he is displayed through the human mind, an adequate idea,
A. The idea of this idea must also necessarily be in God, and be
referred to him in the same way as the idea A (by II. xx.,
whereof the proof is of universal application). But the idea A
is supposed to be referred to God, in so far as he is displayed
through the human mind ; therefore, the idea of the idea A must
be referred to God in the same manner ; that is (by II. xi.
Coroll.), the adequate idea of the idea A will be in the mind,
which has the adequate idea A ; therefore he, who has an adequate
idea or knows a thing truly (II. xxxiv.), must at the same time
have an adequate idea or true knowledge of his knowledge ; that
is, obviously, he must be assured. Q.E.D.
Note.-I explained in the note to II. xxi. what is meant by
the idea of an idea ; but we may remark that the foregoing
proposition is in itself sufficiently plain. No one, who has a
true idea, is ignorant that a true idea involves the highest
certainty. For to have a true idea is only another expression
for knowing a thing perfectly, or as well as possible. No one,
indeed, can doubt of this, unless he thinks that an idea is
something lifeless, like a picture on a panel, and not a mode of
thinking-namely, the very act of understanding. And who, I ask,
can know that he understands anything, unless he do first
understand it? In other words, who can know that he is sure of a
thing, unless he be first sure of that thing? Further, what can
there be more clear, and more certain, than a true idea as a
standard of truth? Even as light displays both itself and
darkness, so is truth a standard both of itself and of falsity.
I think I have thus sufficiently answered these
questions-namely, if a true idea is distinguished from a false
idea, only in so far as it is said to agree with its object, a
true idea has no more reality or perfection than a false idea
(since the two are only distinguished by an extrinsic mark) ;
consequently, neither will a man who has a true idea have any
advantage over him who has only false ideas. Further, how comes
it that men have false ideas? Lastly, how can anyone be sure,
that he has ideas which agree with their objects? These
questions, I repeat, I have, in my opinion, sufficiently
answered. The difference between a true idea and a false idea is
plain : from what was said in II. xxxv., the former is related to
the latter as being is to not-being. The causes of falsity I
have set forth very clearly in II. xix. and II. xxxv. with the
note. From what is there stated, the difference between a man
who has true ideas, and a man who has only false ideas, is made
apparent. As for the last question-as to how a man can be sure
that he has ideas that agree with their objects, I have just
pointed out, with abundant clearness, that his knowledge arises
from the simple fact, that he has an idea which corresponds with
its object-in other words, that truth is its own standard. We
may add that our mind, in so far as it perceives things truly, is
part of the infinite intellect of God (II. xi. Coroll.) ;
therefore, the clear and distinct ideas of the mind are as
necessarily true as the ideas of God.

PROP. XLIV. It is not in the nature of reason to regard things
as contingent, but as necessary.
Proof.-It is in the nature of reason to perceive things truly
(II. xli.), namely (I. Ax. vi.), as they are in themselves-that
is (I. xxix.), not as contingent, but as necessary. Q.E.D.
Corollary I.-Hence it follows, that it is only through our
imagination that we consider things, whether in respect to the
future or the past, as contingent.
Note.-How this way of looking at things arises, I will
briefly explain. We have shown above (II. xvii. and Coroll.)
that the mind always regards things as present to itself, even
though they be not in existence, until some causes arise which
exclude their existence and presence. Further (II. xviii.), we
showed that, if the human body has once been affected by two
external bodies simultaneously, the mind, when it afterwards
imagines one of the said external bodies, will straightway
remember the other-that is, it will regard both as present to
itself, unless there arise causes which exclude their existence
and presence. Further, no one doubts that we imagine time, from
the fact that we imagine bodies to be moved some more slowly than
others, some more quickly, some at equal speed. Thus, let us
suppose that a child yesterday saw Peter for the first time in
the morning, Paul at noon, and Simon in the evening ; then, that
today he again sees Peter in the morning. It is evident, from
II. Prop. xviii., that, as soon as he sees the morning light, he
will imagine that the sun will traverse the same parts of the
sky, as it did when he saw it on the preceding day ; in other
words, he will imagine a complete day, and, together with his
imagination of the morning, he will imagine Peter ; with noon, he
will imagine Paul ; and with evening, he will imagine Simon-that
is, he will imagine the existence of Paul and Simon in relation
to a future time ; on the other hand, if he sees Simon in the
evening, he will refer Peter and Paul to a past time, by
imagining them simultaneously with the imagination of a past
time. If it should at any time happen, that on some other
evening the child should see James instead of Simon, he will, on
the following morning, associate with his imagination of evening
sometimes Simon, sometimes James, not both together : for the
child is supposed to have seen, at evening, one or other of them,
not both together. His imagination will therefore waver ; and,
with the imagination of future evenings, he will associate first
one, then the other-that is, he will imagine them in the future,
neither of them as certain, but both as contingent. This
wavering of the imagination will be the same, if the imagination
be concerned with things which we thus contemplate, standing in
relation to time past or time present : consequently, we may
imagine things as contingent, whether they be referred to time
present, past, or future.
Corollary II.-It is in the nature of reason to perceive
things under a certain form of eternity (sub quâdam æternitatis
specie).
Proof.-It is in the nature of reason to regard things, not as
contingent, but as necessary (II. xliv.). Reason perceives this
necessity of things (II. xli.) truly-that is (I. Ax. vi.), as it
is in itself. But (I. xvi.) this necessity of things is the very
necessity of the eternal nature of God ; therefore, it is in the
nature of reason to regard things under this form of eternity.
We may add that the bases of reason are the notions (II.
xxxviii.), which answer to things common to all, and which (II.
xxxvii.) do not answer to the essence of any particular thing :
which must therefore be conceived without any relation to time,
under a certain form of eternity.

PROP. XLV. Every idea of every body, or of every particular
thing actually existing, necessarily involves the eternal and
infinite essence of God.
Proof.-The idea of a particular thing actually existing
necessarily involves both the existence and the essence of the
said thing (II. viii.). Now particular things cannot be
conceived without God (I. xv.) ; but, inasmuch as (II. vi.) they
have God for their cause, in so far as he is regarded under the
attribute of which the things in question are modes, their ideas
must necessarily involve (I. Ax. iv.) the conception of the
attributes of those ideas-that is (I. vi.), the eternal and
infinite essence of God. Q.E.D.
Note.-By existence I do not here mean duration-that is,
existence in so far as it is conceived abstractedly, and as a
certain form of quantity. I am speaking of the very nature of
existence, which is assigned to particular things, because they
follow in infinite numbers and in infinite ways from the eternal
necessity of God's nature (I. xvi.). I am speaking, I repeat, of
the very existence of particular things, in so far as they are in
God. For although each particular thing be conditioned by
another particular thing to exist in a given way, yet the force
whereby each particular thing perseveres in existing follows from
the eternal necessity of God's nature (cf. I. xxiv. Coroll.).

PROP. XLVI. The knowledge of the eternal and infinite essence of
God which every idea involves is adequate and perfect.
Proof.-The proof of the last proposition is universal ; and
whether a thing be considered as a part or a whole, the idea
thereof, whether of the whole or of a part (by the last Prop.),
will involve God's eternal and infinite essence. Wherefore,
that, which gives knowledge of the eternal and infinite essence
of God, is common to all, and is equally in the part and in the
whole ; therefore (II. xxxviii.) this knowledge will be adequate.
Q.E.D.

PROP. XLVII. The human mind has an adequate knowledge of the
eternal and infinite essence of God.
Proof.-The human mind has ideas (II. xxii.), from which (II.
xxiii.) it perceives itself and its own body (II. xix.) and
external bodies (II. xvi. Coroll. i. and II. xvii.) as actually
existing ; therefore (II. xlv. and xlvi.) it has an adequate
knowledge of the eternal and infinite essence of God. Q.E.D.
Note.-Hence we see, that the infinite essence and the
eternity of God are known to all. Now as all things are in God,
and are conceived through God, we can from this knowledge infer
many things, which we may adequately know, and we may form that
third kind of knowledge of which we spoke in the note to II. xl.,
and of the excellence and use of which we shall have occasion to
speak in Part V. Men have not so clear a knowledge of God as
they have of general notions, because they are unable to imagine
God as they do bodies, and also because they have associated the
name God with images of things that they are in the habit of
seeing, as indeed they can hardly avoid doing, being, as they
are, men, and continually affected by external bodies. Many
errors, in truth, can be traced to this head, namely, that we do
not apply names to things rightly. For instance, when a man says
that the lines drawn from the centre of a circle to its
circumference are not equal, he then, at all events, assuredly
attaches a meaning to the word circle different from that
assigned by mathematicians. So again, when men make mistakes in
calculation, they have one set of figures in their mind, and
another on the paper. If we could see into their minds, they do
not make a mistake ; they seem to do so, because we think, that
they have the same numbers in their mind as they have on the
paper. If this were not so, we should not believe them to be in
error, any more than I thought that a man was in error, whom I
lately heard exclaiming that his entrance hall had flown into a
neighbour's hen, for his meaning seemed to me sufficiently clear.
Very many controversies have arisen from the fact, that men do
not rightly explain their meaning, or do not rightly interpret
the meaning of others. For, as a matter of fact, as they flatly
contradict themselves, they assume now one side, now another, of
the argument, so as to oppose the opinions, which they consider
mistaken and absurd in their opponents.

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