the essence of that body, except in so far as they communicate
their motions to one another in a certain fixed relation (Def.
after Lemma iii.), not in so far as they can be regarded as
individuals without relation to the human body. The parts of
the human body are highly complex individuals (Post. i.), whose
parts (Lemma iv.) can be separated from the human body without in
any way destroying the nature and distinctive quality of the
latter, and they can communicate their motions (Ax. i., after
Lemma iii.) to other bodies in another relation; therefore (II.
iii.) the idea or knowledge of each part will be in God,
inasmuch (II. ix.) as he is regarded as affected by another idea
of a particular thing, which particular thing is prior in the
order of nature to the aforesaid part (II. vii.). We may affirm
the same thing of each part of each individual composing the
human body; therefore, the knowledge of each part composing the
human body is in God, in so far as he is affected by very many
ideas of things, and not in so far as he has the idea of the
human body only, in other words, the idea which constitutes the
nature of the human mind (II. xiii.); therefore (II. xi. Cor.),
the human mind does not involve an adequate knowledge of the
human body. Q.E.D.
XXV. The idea of each modification of the human body does not
involve an adequate knowledge of the external body.
>>>>>Proof--We have shown that the idea of a modification of the
human body involves the nature of an external body, in so far as
that external body conditions the human body in a given manner.
But, in so far as the external body is an individual, which has
no reference to the human body, the knowledge or idea thereof is
in God (II. ix.), in so far as God is regarded as affected by
the idea of a further thing, which (II. vii.) is naturally prior
to the said external body. Wherefore an adequate knowledge of
the external body is not in God, in so far as he has the idea of
the modification of the human body; in other words, the idea of
the modification of the human body does not involve an adequate
knowledge of the external body. Q.E.D.
XXVI. The human mind does not perceive any external body as
actually existing, except through the ideas of the modifications
of its own body.
>>>>>Proof--If the human body is in no way affected by a given
external body, then (II. vii.) neither is the idea of the human
body, in other words, the human mind, affected in any way by the
idea of the existence of the said external body, nor does it in
any manner perceive its existence. But, in so far as the human
body is affected in any way by a given external body, thus far
(II. xvi. and Cor.) it perceives that external body. Q.E.D.
<<<<<Corollary--In so far as the human mind imagines an external
body, it has not an adequate knowledge thereof.
>>>>>Proof--When the human mind regards external bodies through
the ideas of the modifications of its own body, we say that it
imagines (see II. xvii. note); now the mind can only imagine
external bodies as actually existing. Therefore (by II. xxv.),
in so far as the mind imagines external bodies, it has not an
adequate knowledge of them. Q.E.D.
XXVII. The idea of each modification of the human body does not
involve an adequate knowledge of the human body itself.
>>>>>Proof--Every idea of a modification of the human body
involves the nature of the human body, in so far as the human
body is regarded as affected in a given manner (II. xvi.). But
inasmuch as the human body is an individual which may be affected
in many other ways, the idea of the said modification, &c.
Q.E.D.
XXVIII. The ideas of the modifications of the human body, in so
far as they have reference only to the human mind, are not clear
and distinct, but confused.
>>>>>Proof--The ideas of the modifications of the human body
involve the nature both of the human body and of external bodies
(II. xvi.); they must involve the nature not only of the human
body but also of its parts; for the modifications are modes
(Post. iii.), whereby the parts of the human body, and,
consequently, the human body as a whole are affected. But (by
II. xxiv., xxv.) the adequate knowledge of external bodies, as
also of the parts composing the human body, is not in God, in
so far as he is regarded as affected by the human mind, but in
so far as he is regarded as affected by other ideas. These ideas
of modifications, in so far as they are referred to the human
mind alone, are as consequences without premisses, in other
words, confused ideas. Q.E.D.
*****Note--The idea which constitutes the nature of the human
mind is, in the same manner, proved not to be, when considered
in itself and alone, clear and distinct; as also is the case
with the idea of the human mind, and the ideas of the ideas of
the modifications of the human body, in so far as they are
referred to the mind only, as everyone may easily see.
XXIX. The idea of the idea of each modification of the human
body does not involve an adequate knowledge of the human mind.
>>>>>Proof--The idea of a modification of the human body (II.
xxvii.) does not involve an adequate knowledge of the said body,
in other words, does not adequately express its nature; that is
(II. xiii.) it does not agree with the nature of the mind
adequately; therefore (I. Ax. vi.) the idea of this idea does
not adequately express the nature of the human mind, or does not
involve an adequate knowledge thereof.
<<<<<Corollary--Hence it follows that the human mind, when it
perceives things after the common order of nature, has not an
adequate but only a confused and fragmentary knowledge of
itself, of its own body, and of external bodies. For the mind
does not know itself, except in so far as it perceives the ideas
of the modifications of body (II. xxiii.). It only perceives
its own body (II. xix.) through the ideas of the modifications of
body (II. xxiii.). It only perceives its own body (II. xix.)
through the ideas of the modifications, and only perceives
external bodies through the same means; thus, in so far as it has
such ideas of modification, it has not an adequate knowledge of
itself (II. xxix.), nor of its own body (II. xxvii.), nor of
external bodies (II. xxv.), but only a fragmentary and confused
knowledge thereof (II. xxviii. and note). Q.E.D.
*****Note--I say expressly, that the mind has not an adequate but
only a confused knowledge of itself, its own body, and of
external bodies, whenever it perceives things after the common
order of nature; that is, whenever it is determined from without,
namely, by the fortuitous play of circumstance, to regard this
or that; not at such times as it is determined from within, that
is, by the fact of regarding several things at once, to
understand their points of agreement, difference, and contrast.
Whenever it is determined in anywise from within, it regards
things clearly and distinctly, as I will show below.
XXX. We can only have a very inadequate knowledge of the duration
of our body.
>>>>>Proof--The duration of our body does not depend on its
essence (II. Ax. i.), nor on the absolute nature of God (I.
xxi.). But (I. xxviii.) it is conditioned to exist and operate
by causes, which in their turn are conditioned to exist and
operate in a fixed and definite relation by other causes, these
last again being conditioned by others, and so on to infinity.
The duration of our body therefore depends on the common order of
nature, or the constitution of things. Now, however a thing may
be constituted, the adequate knowledge of that thing is in God,
in so far as he has the ideas of all things, and not in so far as
he has the idea of the human body only (II. ix. Cor.).
Wherefore the knowledge of the duration of our body is in God
very inadequate, in so far as he is only regarded as constituting
the nature of the human mind; that is (II. xi. Cor.), this
knowledge is very inadequate to our mind. Q.E.D.
XXXI. We can only have a very inadequate knowledge of the
duration of particular things external to ourselves.
>>>>>Proof--Every particular thing, like the human body, must be
conditioned by another particular thing to exist and operate in
a fixed and definite relation; this other particular thing must
likewise be conditioned by a third, and so on to infinity (I.
xxviii.). As we have shown in the foregoing proposition, from
this common property of particular things, we have only a very
inadequate knowledge of the duration of our body; we must draw a
similar conclusion with regard to the duration of particular
things, namely, that we can only have a very inadequate
knowledge of the duration thereof. Q.E.D.
<<<<<Corollary--Hence it follows that all particular things are
contingent and perishable. For we can have no adequate idea of
their duration (by the last Prop.), and this is what we must
understand by the contingency and perishableness of things (I.
xxxiii., Note i.). For (I. xxix.), except in this sense,
nothing is contingent.
XXXII. All ideas, in so far as they are referred to God, are
true.
>>>>>Proof--All ideas which are in God agree in every respect
with their objects (II. ii. Cor.), therefore (I. Ax. vi.) they
are all true. Q.E.D.
XXXII. 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.
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. Cor.), 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.
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.
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. Cor.)
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.
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.
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. Cor.), 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. Cor.) 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.
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. Cor.), 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. Cor.) 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.
Cor.) 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.
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. Cor.), 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
ratiocinations. 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. Cor., 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. Cor.); I have settled to call such perceptions by the
name of knowledge from the mere suggestions of experience. (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. Cor., xxxix. and Cor., 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.
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.
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.
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. Cor.). 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. Cor.), 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.