Book: The Ethics [Part II]

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---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.

<<<<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.

PROPOSITIONS 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.

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. Cor.); therefore (II.
vii.), the idea of the human body is composed of each of these
numerous ideas of its component parts. Q.E.D.

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 Cor. of Lemma
iii.), wherefore their idea is 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.

<<<<perceives the nature of a variety of bodies, together with the
nature of its own.

<<<<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.

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; therefore the mind (by II. xvi., Cor. i.) will
regard the external body as actually existing, until it is
affected, &c. Q.E.D.

<<<<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 Cor. 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 (Cor. after II. xiii.). Furthermore
(II. vii. Cor., II. xvi. Cor. 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.

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. Cor.) 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.

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. Cor.), 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.

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.

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.

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.

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. Cor.), 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 Cor. 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.

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. Cor.),
the human mind does not involve an adequate knowledge of the
human body. Q.E.D.

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