PROP. XII.  Whatsoever comes to pass in the object of the idea,
which constitutes the human mind, must be perceived by the human
mind, or there will necessarily be an idea in the human mind of
the said occurrence.  That is, if the object of the idea
constituting the human mind be a body, nothing can take place in
that body without being perceived by the mind.
    Proof.-Whatsoever comes to pass in the object of any idea,
the knowledge thereof is necessarily in God (II. ix. Coroll.), in
so far as he is considered as affected by the idea of the said
object, that is (II. xi.), in so far as he constitutes the mind
of anything.  Therefore, whatsoever takes place in the object
constituting the idea of the human mind, the knowledge thereof is
necessarily in God, in so far as he constitutes the essence of
the human mind; that is (by II. xi. Coroll.) the knowledge of
the said thing will necessarily be in the mind, in other words
the mind perceives it.
    Note.-This proposition is also evident, and is more clearly
to be understood from II. vii., which see.

PROP. XIII.  The object of the idea constituting the human mind
is the body, in other words a certain mode of extension which
actually exists, and nothing else.
    Proof.-If indeed the body were not the object of the human
mind, the ideas of the modifications of the body would not be in
God (II. ix. Coroll.) in virtue of his constituting our mind, but
in virtue of his constituting the mind of something else; that
is (II. xi. Coroll.) the ideas of the modifications of the body
would not be in our mind: now (by II. Ax. iv.) we do possess the
idea of the modifications of the body.  Therefore the object of
the idea constituting the human mind is the body, and the body as
it actually exists (II. xi.).  Further, if there were any other
object of the idea constituting the mind besides body, then, as
nothing can exist from which some effect does not follow (I.
xxxvi.) there would necessarily have to be in our mind an idea,
which would be the effect of that other object (II. xi.); but
(I. Ax. v.) there is no such idea.  Wherefore the object of our
mind is the body as it exists, and nothing else.  Q.E.D.
    Note.-We thus comprehend, not only that the human mind is
united to the body, but also the nature of the union between mind
and body.  However, no one will be able to grasp this adequately
or distinctly, unless he first has adequate knowledge of the
nature of our body.  The propositions we have advanced hitherto
have been entirely general, applying not more to men than to
other individual things, all of which, though in different
degrees, are animated.[3]  For of everything there is necessarily
an idea in God, of which God is the cause, in the same way as
there is an idea of the human body; thus  whatever we have
asserted of the idea of the human body must necessarily also be
asserted of the idea of everything else.  Still, on the other
hand, we cannot deny that ideas, like objects, differ one from
the other, one being more excellent than another and containing
more reality, just as the object of one idea is more excellent
than the object of another idea, and contains more reality.

[3] "Animata"

    Wherefore, in order to determine, wherein the human mind
differs from other things, and wherein it surpasses them, it is
necessary for us to know the nature of its object, that is, of
the human body.  What this nature is, I am not able here to
explain, nor is it necessary for the proof of what I advance,
that I should do so.  I will only say generally, that in
proportion as any given body is more fitted than others for doing
many actions or receiving many impressions at once, so also is
the mind, of which it is the object, more fitted than others for
forming many simultaneous perceptions; and the more the actions
of the body depend on itself alone, and the fewer other bodies
concur with it in action, the more fitted is the mind of which it
is the object for distinct comprehension.  We may thus recognize
the superiority of one mind over others, and may further see the
cause, why we have only a very confused knowledge of our body,
and also many kindred questions, which I will, in the following
propositions, deduce from what has been advanced.  Wherefore I
have thought it worth while to explain and prove more strictly my
present statements.  In order to do so, I must premise a few
propositions concerning the nature of bodies.
    AXIOM I.  All bodies are either in motion or at rest.
    AXIOM II.  Every body is moved sometimes more slowly,
sometimes more quickly.
    LEMMA I.  Bodies are distinguished from one another in
respect of motion and rest, quickness and slowness, and not in
respect of substance.
    Proof.-The first part of this proposition is, I take it,
self-evident.  That bodies are not distinguished in respect of
substance, is plain both from I. v. and I. viii.  It is brought
out still more clearly from I. xv, note.
    LEMMA II.  All bodies agree in certain respects.
    Proof.-All bodies agree in the fact, that they involve the
conception of one and the same attribute (II., Def. i.).
Further, in the fact that they may be moved less or more quickly,
and may be absolutely in motion or at rest.
    LEMMA III.  A body in motion or at rest must be determined to
motion or rest by another body, which other body has been
determined to motion or rest by a third body, and that third
again by a fourth, and so on to infinity.
    Proof.-Bodies are individual things (II., Def. i.), which
(Lemma I.) are distinguished one from the other in respect to
motion and rest; thus (I. xxviii.) each must necessarily be
determined to motion or rest by another individual thing, namely
(II. vi.), by another body, which other body is also (Ax. i.) in
motion or at rest.  And this body again can only have been set in
motion or caused to rest by being determined by a third body to
motion or rest.   This third body again by a fourth, and so on to
infinity.  Q.E.D.
    Corollary.-Hence it follows, that a body in motion keeps in
motion, until it is determined to a state of rest by some other
body; and a body at rest remains so, until it is determined to a
state of motion by some other body.  This is indeed self-evident.
For when I suppose, for instance, that a given body, A, is at
rest, and do not take into consideration other bodies in motion,
I cannot affirm anything concerning the body A, except that it is
at rest.  If it afterwards comes to pass that A is in motion,
this cannot have resulted from its having been at rest, for no
other consequence could have been involved than its remaining at
rest.  If, on the other hand, A be given in motion, we shall, so
long as we only consider A, be unable to affirm anything
concerning it, except that it is in motion.   If A is
subsequently found to be at rest, this rest cannot be the result
of A's previous motion, for such motion can only have led to
continued motion; the state of rest therefore must have resulted
from something, which was not in A, namely, from an external
cause determining A to a state of rest.
    Axiom I.-All modes, wherein one body is affected by another
body, follow simultaneously from the nature of the body affected
and the body affecting; so that one and the same body may be
moved in different modes, according to the difference in the
nature of the bodies moving it; on the other hand, different
bodies may be moved in different modes by one and the same body.
    Axiom II.-When a body in motion impinges on another body at
rest, which it is unable to move, it recoils, in order to
continue its motion, and the angle made by the line of motion in
the recoil and the plane of the body at rest, whereon the moving
body has impinged, will be equal to the angle formed by the line
of motion of incidence and the same plane.
    So far we have been speaking only of the most simple bodies,
which are only distinguished one from the other by motion and
rest, quickness and slowness.  We now pass on to compound bodies.
    Definition.-When any given bodies of the same or different
magnitude are compelled by other bodies to remain in contact, or
if they be moved at the same or different rates of speed, so that
their mutual movements should preserve among themselves a certain
fixed relation, we say that such bodies are in union, and that
together they compose one body or individual, which is
distinguished from other bodies by the fact of this union.
    Axiom III.-In proportion as the parts of an individual, or a
compound body, are in contact over a greater or less superficies,
they will with greater or less difficulty admit of being moved
from their position; consequently the individual will, with
greater or less difficulty, be brought to assume another form.
Those bodies, whose parts are in contact over large superficies,
are called hard; those, whose parts are in contact over small
superficies, are called soft; those, whose parts are in motion
among one another, are called fluid.
    LEMMA IV.  If from a body or individual, compounded of
several bodies, certain bodies be separated, and if, at the same
time, an equal number of other bodies of the same nature take
their place, the individual will preserve its nature as before,
without any change in its actuality (forma).
    Proof.-Bodies (Lemma i.) are not distinguished in respect of
substance: that which constitutes the actuality (formam) of an
individual consists (by the last Def.) in a union of bodies; but
this union, although there is a continual change of bodies, will
(by our hypothesis) be maintained; the individual, therefore,
will retain its nature as before, both in respect of substance
and in respect of mode.  Q.E.D.
    LEMMA V.  If the parts composing an individual become greater
or less, but in such proportion, that they all preserve the same
mutual relations of motion and rest, the individual will still
preserve its original nature, and its actuality will not be
changed.
    Proof.-The same as for the last Lemma.
    LEMMA VI.  If certain bodies composing an individual be
compelled to change the motion, which they have in one direction,
for motion in another direction, but in such a manner, that they
be able to continue their motions and their mutual communication
in the same relations as before, the individual will retain its
own nature without any change of its actuality.
    Proof.-This proposition is self-evident, for the individual
is supposed to retain all that, which, in its definition, we
spoke of as its actual being.
    LEMMA VII.  Furthermore, the individual thus composed
preserves its nature, whether it be, as a whole, in motion or at
rest, whether it be moved in this or that direction; so long as
each part retains its motion, and preserves its communication
with other parts as before.
    Proof.-This proposition is evident from the definition of an
individual prefixed to Lemma iv.
    Note.-We thus see, how a composite individual may be affected
in many different ways, and preserve its nature notwithstanding.
Thus far we have conceived an individual as composed of bodies
only distinguished one from the other in respect of motion and
rest, speed and slowness; that is, of bodies of the most simple
character.  If, however, we now conceive another individual
composed of several individuals of diverse natures, we shall find
that the number of ways in which it can be affected, without
losing its nature, will be greatly multiplied.  Each of its parts
would consist of several bodies, and therefore (by Lemma vi.)
each part would admit, without change to its nature, of quicker
or slower motion, and would consequently be able to transmit its
motions more quickly or more slowly to the remaining parts.  If
we further conceive a third kind of individuals composed of
individuals of this second kind, we shall find that they may be
affected in a still greater number of ways without changing their
actuality.  We may easily proceed thus to infinity, and conceive
the whole of nature as one individual, whose parts, that is, all
bodies, vary in infinite ways, without any change in the
individual as a whole.  I should feel bound to explain and
demonstrate this point at more length, if I were writing a
special treatise on body.  But I have already said that such is
not my object; I have only touched on the question, because it
enables me to prove easily that which I have in view.

POSTULATES
    I.  The human body is composed of a number of individual
parts, of diverse nature, each one of which is in itself
extremely complex.
    II.  Of the individual parts composing the human body some
are fluid, some soft, some hard.
    III.  The individual parts composing the human body, and
consequently the human body itself, are affected in a variety of
ways by external bodies.
    IV.  The human body stands in need for its preservation of a
number of other bodies, by which it is continually, so to speak,
regenerated.
    V.  When the fluid part of the human body is determined by an
external body to impinge often on another soft part, it changes
the surface of the latter, and, as it were, leaves the impression
thereupon of the external body which impels it.
    VI.  The human body can move external bodies, and arrange
them in a variety of ways.

PROP. XIV.  The human mind is capable of perceiving a great
number of things, and is so in proportion as its body is capable
of receiving a great number of impressions.
    Proof.-The human body (by Post. iii. and vi.) is affected in
very many ways by external bodies, and is capable in very many
ways of affecting external bodies.  But (II. xii.)  the human
mind must perceive all that takes place in the human body; the
human mind is, therefore, capable of perceiving a great number of
things, and is so in proportion, &c.  Q.E.D.

PROP. XV.  The idea, which constitutes the actual being of the
human mind, is not simple, but compounded of a great number of
ideas.
    Proof.-The idea constituting the actual being of the human
mind is the idea of the body (II. xiii.), which (Post. i.) is
composed of a great number of complex individual parts.  But
there is necessarily in God the idea of each individual part
whereof the body is composed (II. viii. Coroll.); therefore
(II. vii.), the idea of the human body is composed of these
numerous ideas of its component parts.  Q.E.D.

PROP. XVI.  The idea of every mode, in which the human body is
affected by external bodies, must involve the nature of the human
body, and also the nature of the external body.
    Proof.-All the modes, in which any given body is affected,
follow from the nature of the body affected, and also from the
nature of the affecting body (by Ax. i., after the Coroll. of
Lemma iii.), wherefore their idea also necessarily (by I. Ax.
iv.) involves the nature of both bodies; therefore, the idea of
every mode, in which the human body is affected by external
bodies, involves the nature of the human body and of the external
body.  Q.E.D.
    Corollary I.-Hence it follows, first, that the human mind
perceives the nature of a variety of bodies, together with the
nature of its own.
    Corollary II.-It follows, secondly, that the ideas, which we
have of external bodies, indicate rather the constitution of our
own body than the nature of external bodies.  I have amply
illustrated this in the Appendix to Part I.

PROP. XVII.  If the human body is affected in a manner which
involves the nature of any external body, the human mind will
regard the said external body as actually existing, or as present
to itself, until the human body be affected in such a way, as to
exclude the existence or the presence of the said external body.
    Proof.-This proposition is self-evident, for so long as the
human body continues to be thus affected, so long will the human
mind (II. xii.) regard this modification of the body-that is (by
the last Prop.), it will have the idea of the mode as actually
existing, and this idea involves the nature of the external body.
In other words, it will have the idea which does not exclude, but
postulates the existence or presence of the nature of the
external body; therefore the mind (by II. xvi., Coroll. i.) will
regard the external body as actually existing, until it is
affected, &c.  Q.E.D.
    Corollary.-The mind is able to regard as present external
bodies, by which the human body has once been affected, even
though they be no longer in existence or present.
    Proof.-When external bodies determine the fluid parts of the
human body, so that they often impinge on the softer parts, they
change the surface of the last named (Post. v.); hence (Ax. ii.,
after the Coroll. of Lemma iii.) they are refracted therefrom in
a different manner from that which they followed before such
change; and, further, when afterwards they impinge on the new
surfaces by their own spontaneous movement, they will be
refracted in the same manner, as though they had been impelled
towards those surfaces by external bodies; consequently, they
will, while they continue to be thus refracted, affect the human
body in the same manner, whereof the mind (II. xii.) will again
take cognizance-that is (II. xvii.), the mind will again regard
the external body as present, and will do so, as often as the
fluid parts of the human body impinge on the aforesaid surfaces
by their own spontaneous motion.  Wherefore, although the
external bodies, by which the human body has once been affected,
be no longer in existence, the mind will nevertheless regard them
as present, as often as this action of the body is repeated.
Q.E.D.
    Note.-We thus see how it comes about, as is often the case,
that we regard as present many things which are not.  It is
possible that the same result may be brought about by other
causes; but I think it suffices for me here to have indicated
one possible explanation, just as well as if I had pointed out
the true cause.  Indeed, I do not think I am very far from the
truth, for all my assumptions are based on postulates, which
rest, almost without exception, on experience, that cannot be
controverted by those who have shown, as we have, that the human
body, as we feel it, exists (Coroll. after II. xiii.).
Furthermore (II. vii.  Coroll., II. xvi. Coroll. ii.), we clearly
understand what is the difference between the idea, say, of
Peter, which constitutes the essence of Peter's mind, and the
idea of the said Peter, which is in another man, say, Paul.  The
former directly answers to the essence of Peter's own body, and
only  implies existence so long as Peter exists; the latter
indicates rather the disposition of Paul's body than the nature
of Peter, and, therefore, while this disposition of Paul's body
lasts, Paul's mind will regard Peter as present to itself, even
though he no longer exists.  Further, to retain the usual
phraseology,  the modifications of the human body, of which the
ideas represent external bodies as present to us, we will call
the images of things, though they do not recall the figure of
things.  When the mind regards bodies in this fashion, we say
that it imagines.  I will here draw attention to the fact, in
order to indicate where error lies, that the imaginations of the
mind, looked at in themselves, do not contain error.  The mind
does not err in the mere act of imagining, but only in so far as
it is regarded as being without the idea, which excludes the
existence of such things as it imagines to be present to it.  If
the mind, while imagining non-existent things as present to it,
is at the same time conscious that they do not really exist, this
power of imagination must be set down to the efficacy of its
nature, and not to a fault, especially if this faculty of
imagination depend solely on its own nature-that is (I. Def.
vii.), if this faculty of imagination be free.

PROP. XVIII.  If the human body has once been affected by two or
more bodies at the same time, when the mind afterwards imagines
any of them, it will straightway remember the others also.
    Proof.-The mind (II. xvii. Coroll.) imagines any given body,
because the human body is affected and disposed by the
impressions from an external body, in the same manner as it is
affected when certain of its parts are acted on by the said
external body; but (by our hypothesis) the body was then so
disposed, that the mind imagined two bodies at once; therefore,
it will also in the second case imagine two bodies at once, and
the mind, when it imagines one, will straightway remember the
other.  Q.E.D.
    Note.-We now clearly see what Memory is.  It is simply a
certain association of ideas involving the nature of things
outside the human body, which association arises in the mind
according to the order and association of the modifications
(affectiones) of the human body.  I say, first, it is an
association of those ideas only, which involve the nature of
things outside the human body: not of ideas which answer to the
nature of the said things: ideas of the modifications of the
human body are, strictly speaking (II. xvi.), those which involve
the nature both of the human body and of external bodies.  I say,
secondly, that this association arises according to the order and
association of the modifications of the human body, in order to
distinguish it from that association of ideas, which arises from
the order of the intellect, whereby the mind perceives things
through their primary causes, and which is in all men the same.
And hence we can further clearly understand, why the mind from
the thought of one thing, should straightway arrive at the
thought of another thing, which has no similarity with the first;
for instance, from the thought of the word pomum (an apple), a
Roman would straightway arrive at the thought of the fruit apple,
which has no similitude with the articulate sound in question,
nor anything in common with it, except that the body of the man
has often been affected by these two things; that is, that the
man has often heard the word pomum, while he was looking at the
fruit; similarly every man will go on from one thought to
another, according as his habit has ordered the images of things
in his body.  For a soldier, for instance, when he sees the
tracks of a horse in sand, will at once pass from the thought of
a horse to the thought of a horseman, and thence to the thought
of war, &c.; while a countryman will proceed from the thought of
a horse to the thought of a plough, a field, &c.  Thus every man
will follow this or that train of thought, according as he has
been in the habit of conjoining and associating the mental images
of things in this or that manner.

PROP. XIX.  The human mind has no knowledge of the body, and does
not know it to exist, save through the ideas of the modifications
whereby the body is affected.
    Proof.-The human mind is the very idea or knowledge of the
human body (II. xiii.), which (II. ix.) is in God, in so far as
he is regarded as affected by another idea of a particular thing
actually existing: or, inasmuch as (Post. iv.) the human body
stands in need of very many bodies whereby it is, as it were,
continually regenerated; and the order and connection of ideas
is the same as the order and connection of causes (II. vii.);
this idea will therefore be in God, in so far as he is regarded
as affected by the ideas of very many particular things.  Thus
God has the idea of the human body, or knows the human body, in
so far as he is affected by very many other ideas, and not in so
far as he constitutes the nature of the human mind; that is (by
II. xi. Coroll.), the human mind does not know the human body.
But the ideas of the modifications of body are in God, in so far
as  he constitutes the nature of the human mind, or the human
mind perceives those modifications (II. xii.), and consequently
(II. xvi.) the human body itself, and as actually existing;
therefore the mind perceives thus far only the human body.
Q.E.D.

PROP. XX.  The idea or knowledge of the human mind is also in
God, following in God in the same manner, and being referred to
God in the same manner, as the idea or knowledge of the human
body.
    Proof.-Thought is an attribute of God (II. i.); therefore
(II. iii.) there must necessarily be in God the idea both of
thought itself and of all its modifications, consequently also of
the human mind (II. xi.).  Further, this idea or knowledge of the
mind does not follow from God, in so far as he is infinite, but
in so far as he is affected by another idea of an individual
thing (II. ix.).  But (II. vii.) the order and connection of
ideas is the same as the order and connection of causes;
therefore this idea or knowledge of the mind is in God and is
referred to God, in the same manner as the idea or knowledge of
the body.  Q.E.D.

PROP. XXI.  This idea of the mind is united to the mind in the
same way as the mind is united to the body.
    Proof.-That the mind is united to the body we have shown from
the fact, that the body is the object of the mind (II. xii. and
xiii.); and so for the same reason the idea of the mind must be
united with its object, that is, with the mind in the same manner
as the mind is united to the body.  Q.E.D.
    Note.-This proposition is comprehended much more clearly from
what we have said in the note to II. vii.  We there showed that
the idea of body and body, that is, mind and body (II. xiii.),
are one and the same individual conceived now under the attribute
of thought, now under the attribute of extension; wherefore the
idea of the mind and the mind itself are one and the same thing,
which is conceived under one and the same attribute, namely,
thought.  The idea of the mind, I repeat, and the mind itself are
in God by the same necessity and follow from him from the same
power of thinking.  Strictly speaking, the idea of the mind, that
is, the idea of an idea, is nothing but the distinctive quality
(forma) of the idea in so far as it is conceived as a mode of
thought without reference to the object; if a man knows
anything, he, by that very fact, knows that he knows it, and at
the same time knows that he knows that he knows it, and so on to
infinity.  But I will treat of this hereafter.

PROP. XXII.  The human mind perceives not only the modifications
of the body, but also the ideas of such modifications.
    Proof.-The ideas of the ideas of modifications follow in God
in the same manner, and are referred to God in the same manner,
as the ideas of the said modifications.  This is proved in the
same way as II. xx.  But the ideas of the modifications of the
body are in the human mind (II. xii.), that is, in God, in so far
as he constitutes the essence of the human mind; therefore the
ideas of these ideas will be in God, in so far as he has the
knowledge or idea of the human mind, that is (II. xxi.), they
will be in the human mind itself, which therefore perceives not
only the modifications of the body, but also the ideas of such
modifications.  Q.E.D.

PROP. XXIII.  The mind does not know itself, except in so far as
it perceives the ideas of the modifications of the body.
    Proof.-The idea or knowledge of the mind (II. xx.) follows in
God in the same manner, and is referred to God in the same
manner, as the idea or knowledge of the body.  But since (II.
xix.) the human mind does not know the human body itself, that is
(II. xi. Coroll.), since the knowledge of the human body is not
referred to God, in so far as he constitutes the nature of the
human mind; therefore, neither is the knowledge of the mind
referred to God, in so far as he constitutes the essence of the
human mind; therefore (by the same Coroll. II. xi.), the human
mind thus far has no knowledge of itself.  Further the ideas of
the modifications, whereby the body is affected, involve the
nature of the human body itself (II. xvi.), that is (II. xiii.),
they agree with the nature of the mind; wherefore the knowledge
of these ideas necessarily involves knowledge of the mind; but
(by the last Prop.) the knowledge of these ideas is in the human
mind itself; wherefore the human mind thus far only has
knowledge of itself.  Q.E.D.

PROP. XXIV.  The human mind does not involve an adequate
knowledge of the parts composing the human body.
    Proof.-The parts composing the human body do not belong to
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.
Coroll.), the human mind does not involve an adequate knowledge
of the human body.  Q.E.D.

PROP. 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.

PROP. 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 Coroll.) 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.

PROP. 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.

PROP. 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 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.

PROP. 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, 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.

PROP. 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. Coroll.)
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. Coroll.), this
knowledge is very inadequate to our mind.  Q.E.D.

PROP. 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.

PROP. 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. vii. Coroll.), therefore (I. Ax. vi.) they are
all true.  Q.E.D.

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]

[4] A Baconian phrase.  Nov. Org. Aph. 100.  [Pollock, p. 126, n.]

(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.