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The Ethics by Benedict de Spinoza

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The Ethics
(Ethica Ordine Geometrico Demonstrata)

by Benedict de Spinoza

Translated from the Latin by R. H. M. Elwes

PART I. CONCERNING GOD.

DEFINITIONS.

I. By that which is self-caused, I mean that of which the
essence involves existence, or that of which the nature is only
conceivable as existent.

II. A thing is called finite after its kind, when it can be
limited by another thing of the same nature ; for instance, a
body is called finite because we always conceive another greater
body. So, also, a thought is limited by another thought, but a
body is not limited by thought, nor a thought by body.

III. By substance, I mean that which is in itself, and is
conceived through itself : in other words, that of which a
conception can be formed independently of any other conception.

IV. By attribute, I mean that which the intellect perceives as
constituting the essence of substance.

V. By mode, I mean the modifications1 of substance, or that
which exists in, and is conceived through, something other than
itself.

VI. By God, I mean a being absolutely infinite-that is, a
substance consisting in infinite attributes, of which each
expresses eternal and infinite essentiality.
Explanation-I say absolutely infinite, not infinite after its
kind : for, of a thing infinite only after its kind, infinite
attributes may be denied ; but that which is absolutely infinite,
contains in its essence whatever expresses reality, and involves
no negation.

VII. That thing is called free, which exists solely by the
necessity of its own nature, and of which the action is
determined by itself alone. On the other hand, that thing is
necessary, or rather constrained, which is determined by
something external to itself to a fixed and definite method of
existence or action.

VIII. By eternity, I mean existence itself, in so far as it is
conceived necessarily to follow solely from the definition of
that which is eternal.
Explanation-Existence of this kind is conceived as an eternal
truth, like the essence of a thing, and, therefore, cannot be
explained by means of continuance or time, though continuance may
be conceived without a beginning or end.

AXIOMS.

I. Everything which exists, exists either in itself or in
something else.

II. That which cannot be conceived through anything else must be
conceived through itself.

III. From a given definite cause an effect necessarily follows ;
and, on the other hand, if no definite cause be granted, it is
impossible that an effect can follow.

IV. The knowledge of an effect depends on and involves the
knowledge of a cause.

V. Things which have nothing in common cannot be understood, the
one by means of the other ; the conception of one does not
involve the conception of the other.

VI. A true idea must correspond with its ideate or object.

VII. If a thing can be conceived as non-existing, its essence
does not involve existence.

PROPOSITIONS.

PROP. I. Substance is by nature prior to its modifications.
Proof.-This is clear from Deff. iii. and v.

PROP. II. Two substances, whose attributes are different, have
nothing in common.
Proof.-Also evident from Def. iii. For each must exist in
itself, and be conceived through itself ; in other words, the
conception of one does not imply the conception of the other.

PROP. III. Things which have nothing in common cannot be one the
cause of the other.
Proof.-If they have nothing in common, it follows that one
cannot be apprehended by means of the other (Ax. v.), and,
therefore, one cannot be the cause of the other (Ax. iv.).
Q.E.D.

PROP. IV. Two or more distinct things are distinguished one from
the other, either by the difference of the attributes of the
substances, or by the difference of their modifications.
Proof.-Everything which exists, exists either in itself or in
something else (Ax. i.),-that is (by Deff. iii. and v.), nothing
is granted in addition to the understanding, except substance and
its modifications. Nothing is, therefore, given besides the
understanding, by which several things may be distinguished one
from the other, except the substances, or, in other words (see
Ax. iv.), their attributes and modifications. Q.E.D.

PROP. V. There cannot exist in the universe two or more
substances having the same nature or attribute.
Proof.-If several distinct substances be granted, they must
be distinguished one from the other, either by the difference of
their attributes, or by the difference of their modifications
(Prop. iv.). If only by the difference of their attributes, it
will be granted that there cannot be more than one with an
identical attribute. If by the difference of their
modifications-as substance is naturally prior to its
modifications (Prop. i.),-it follows that setting the
modifications aside, and considering substance in itself, that is
truly, (Deff. iii. and vi.), there cannot be conceived one
substance different from another,-that is (by Prop. iv.), there
cannot be granted several substances, but one substance only.
Q.E.D.

PROP. VI. One substance cannot be produced by another substance.
Proof.-It is impossible that there should be in the universe
two substances with an identical attribute, i.e. which have
anything common to them both (Prop. ii.), and, therefore (Prop.
iii.), one cannot be the cause of the other, neither can one be
produced by the other. Q.E.D.
Corollary.-Hence it follows that a substance cannot be
produced by anything external to itself. For in the universe
nothing is granted, save substances and their modifications (as
appears from Ax. i. and Deff. iii. and v.). Now (by the last
Prop.) substance cannot be produced by another substance,
therefore it cannot be produced by anything external to itself.
Q.E.D. This is shown still more readily by the absurdity of the
contradictory. For, if substance be produced by an external
cause, the knowledge of it would depend on the knowledge of its
cause (Ax. iv.), and (by Def. iii.) it would itself not be
substance.

PROP. VII. Existence belongs to the nature of substances.
Proof.-Substance cannot be produced by anything external
(Corollary, Prop vi.), it must, therefore, be its own cause-that
is, its essence necessarily involves existence, or existence
belongs to its nature.

PROP. VIII. Every substance is necessarily infinite.
Proof.-There can only be one substance with an identical
attribute, and existence follows from its nature (Prop. vii.) ;
its nature, therefore, involves existence, either as finite or
infinite. It does not exist as finite, for (by Def. ii.) it
would then be limited by something else of the same kind, which
would also necessarily exist (Prop. vii.) ; and there would be
two substances with an identical attribute, which is absurd
(Prop. v.). It therefore exists as infinite. Q.E.D.
Note I.-As finite existence involves a partial negation, and
infinite existence is the absolute affirmation of the given
nature, it follows (solely from Prop. vii.) that every substance
is necessarily infinite.
Note II.-No doubt it will be difficult for those who think
about things loosely, and have not been accustomed to know them
by their primary causes, to comprehend the demonstration of Prop.
vii. : for such persons make no distinction between the
modifications of substances and the substances themselves, and
are ignorant of the manner in which things are produced ; hence
they may attribute to substances the beginning which they observe
in natural objects. Those who are ignorant of true causes, make
complete confusion-think that trees might talk just as well as
men-that men might be formed from stones as well as from seed ;
and imagine that any form might be changed into any other. So,
also, those who confuse the two natures, divine and human,
readily attribute human passions to the deity, especially so long
as they do not know how passions originate in the mind. But, if
people would consider the nature of substance, they would have no
doubt about the truth of Prop. vii. In fact, this proposition
would be a universal axiom, and accounted a truism. For, by
substance, would be understood that which is in itself, and is
conceived through itself-that is, something of which the
conception requires not the conception of anything else ; whereas
modifications exist in something external to themselves, and a
conception of them is formed by means of a conception of the
thing in which they exist. Therefore, we may have true ideas of
non-existent modifications ; for, although they may have no
actual existence apart from the conceiving intellect, yet their
essence is so involved in something external to themselves that
they may through it be conceived. Whereas the only truth
substances can have, external to the intellect, must consist in
their existence, because they are conceived through themselves.
Therefore, for a person to say that he has a clear and
distinct-that is, a true-idea of a substance, but that he is not
sure whether such substance exists, would be the same as if he
said that he had a true idea, but was not sure whether or no it
was false (a little consideration will make this plain) ; or if
anyone affirmed that substance is created, it would be the same
as saying that a false idea was true-in short, the height of
absurdity. It must, then, necessarily be admitted that the
existence of substance as its essence is an eternal truth. And
we can hence conclude by another process of reasoning-that there
is but one such substance. I think that this may profitably be
done at once ; and, in order to proceed regularly with the
demonstration, we must premise :-
1. The true definition of a thing neither involves nor
expresses anything beyond the nature of the thing defined. From
this it follows that-
2. No definition implies or expresses a certain number of
individuals, inasmuch as it expresses nothing beyond the nature
of the thing defined. For instance, the definition of a triangle
expresses nothing beyond the actual nature of a triangle : it
does not imply any fixed number of triangles.
3. There is necessarily for each individual existent thing a
cause why it should exist.
4. This cause of existence must either be contained in the
nature and definition of the thing defined, or must be postulated
apart from such definition.
It therefore follows that, if a given number of individual
things exist in nature, there must be some cause for the
existence of exactly that number, neither more nor less. For
example, if twenty men exist in the universe (for simplicity's
sake, I will suppose them existing simultaneously, and to have
had no predecessors), and we want to account for the existence of
these twenty men, it will not be enough to show the cause of
human existence in general ; we must also show why there are
exactly twenty men, neither more nor less : for a cause must be
assigned for the existence of each individual. Now this cause
cannot be contained in the actual nature of man, for the true
definition of man does not involve any consideration of the
number twenty. Consequently, the cause for the existence of
these twenty men, and, consequently, of each of them, must
necessarily be sought externally to each individual. Hence we may
lay down the absolute rule, that everything which may consist of
several individuals must have an external cause. And, as it has
been shown already that existence appertains to the nature of
substance, existence must necessarily be included in its
definition ; and from its definition alone existence must be
deducible. But from its definition (as we have shown, notes ii.,
iii.), we cannot infer the existence of several substances ;
therefore it follows that there is only one substance of the same
nature. Q.E.D.

PROP. IX. The more reality or being a thing has, the greater the
number of its attributes (Def. iv.).

PROP. X. Each particular attribute of the one substance must be
conceived through itself.
Proof.-An attribute is that which the intellect perceives of
substance, as constituting its essence (Def. iv.), and,
therefore, must be conceived through itself (Def. iii.). Q.E.D.
Note-It is thus evident that, though two attributes are, in
fact, conceived as distinct-that is, one without the help of the
other-yet we cannot, therefore, conclude that they constitute two
entities, or two different substances. For it is the nature of
substance that each of its attributes is conceived through
itself, inasmuch as all the attributes it has have always existed
simultaneously in it, and none could be produced by any other ;
but each expresses the reality or being of substance. It is,
then, far from an absurdity to ascribe several attributes to one
substance : for nothing in nature is more clear than that each
and every entity must be conceived under some attribute, and that
its reality or being is in proportion to the number of its
attributes expressing necessity or eternity and infinity.
Consequently it is abundantly clear, that an absolutely infinite
being must necessarily be defined as consisting in infinite
attributes, each of which expresses a certain eternal and
infinite essence.
If anyone now ask, by what sign shall he be able to
distinguish different substances, let him read the following
propositions, which show that there is but one substance in the
universe, and that it is absolutely infinite, wherefore such a
sign would be sought in vain.

PROP. XI. God, or substance, consisting of infinite attributes,
of which each expresses eternal and infinite essentiality,
necessarily exists.
Proof.-If this be denied, conceive, if possible, that God
does not exist : then his essence does not involve existence.
But this (Prop. vii.) is absurd. Therefore God necessarily
exists.
Another proof.-Of everything whatsoever a cause or reason
must be assigned, either for its existence, or for its
non-existence-e.g. if a triangle exist, a reason or cause must be
granted for its existence ; if, on the contrary, it does not
exist, a cause must also be granted, which prevents it from
existing, or annuls its existence. This reason or cause must
either be contained in the nature of the thing in question, or be
external to it. For instance, the reason for the non-existence
of a square circle is indicated in its nature, namely, because it
would involve a contradiction. On the other hand, the existence
of substance follows also solely from its nature, inasmuch as its
nature involves existence. (See Prop. vii.)
But the reason for the existence of a triangle or a circle
does not follow from the nature of those figures, but from the
order of universal nature in extension. From the latter it must
follow, either that a triangle necessarily exists, or that it is
impossible that it should exist. So much is self-evident. It
follows therefrom that a thing necessarily exists, if no cause or
reason be granted which prevents its existence.
If, then, no cause or reason can be given, which prevents the
existence of God, or which destroys his existence, we must
certainly conclude that he necessarily does exist. If such a
reason or cause should be given, it must either be drawn from the
very nature of God, or be external to him-that is, drawn from
another substance of another nature. For if it were of the same
nature, God, by that very fact, would be admitted to exist. But
substance of another nature could have nothing in common with God
(by Prop. ii.), and therefore would be unable either to cause or
to destroy his existence.
As, then, a reason or cause which would annul the divine
existence cannot be drawn from anything external to the divine
nature, such cause must perforce, if God does not exist, be drawn
from God's own nature, which would involve a contradiction. To
make such an affirmation about a being absolutely infinite and
supremely perfect is absurd ; therefore, neither in the nature of
God, nor externally to his nature, can a cause or reason be
assigned which would annul his existence. Therefore, God
necessarily exists. Q.E.D.
Another proof.-The potentiality of non-existence is a
negation of power, and contrariwise the potentiality of existence
is a power, as is obvious. If, then, that which necessarily
exists is nothing but finite beings, such finite beings are more
powerful than a being absolutely infinite, which is obviously
absurd ; therefore, either nothing exists, or else a being
absolutely infinite necessarily exists also. Now we exist either
in ourselves, or in something else which necessarily exists (see
Axiom. i. and Prop. vii.). Therefore a being absolutely
infinite-in other words, God (Def. vi.)-necessarily exists.
Q.E.D.
Note.-In this last proof, I have purposely shown God's
existence ą posteriori, so that the proof might be more easily
followed, not because, from the same premises, God's existence
does not follow ą priori. For, as the potentiality of existence
is a power, it follows that, in proportion as reality increases
in the nature of a thing, so also will it increase its strength
for existence. Therefore a being absolutely infinite, such as
God, has from himself an absolutely infinite power of existence,
and hence he does absolutely exist. Perhaps there will be many
who will be unable to see the force of this proof, inasmuch as
they are accustomed only to consider those things which flow from
external causes. Of such things, they see that those which
quickly come to pass-that is, quickly come into existence-quickly
also disappear ; whereas they regard as more difficult of
accomplishment-that is, not so easily brought into
existence-those things which they conceive as more complicated.
However, to do away with this misconception, I need not here
show the measure of truth in the proverb, "What comes quickly,
goes quickly," nor discuss whether, from the point of view of
universal nature, all things are equally easy, or otherwise : I
need only remark that I am not here speaking of things, which
come to pass through causes external to themselves, but only of
substances which (by Prop. vi.) cannot be produced by any
external cause. Things which are produced by external causes,
whether they consist of many parts or few, owe whatsoever
perfection or reality they possess solely to the efficacy of
their external cause ; and therefore their existence arises
solely from the perfection of their external cause, not from
their own. Contrrariwise, whatsoever perfection is possessed by
substance is due to no external cause ; wherefore the existence
of substance must arise solely from its own nature, which is
nothing else but its essence. Thus, the perfection of a thing
does not annul its existence, but, on the contrary, asserts it.
Imperfection, on the other hand, does annul it ; therefore we
cannot be more certain of the existence of anything, than of the
existence of a being absolutely infinite or perfect-that is, of
God. For inasmuch as his essence excludes all imperfection, and
involves absolute perfection, all cause for doubt concerning his
existence is done away, and the utmost certainty on the question
is given. This, I think, will be evident to every moderately
attentive reader.

PROP. XII. No attribute of substance can be conceived from which
it would follow that substance can be divided.
Proof.-The parts into which substance as thus conceived would
be divided either will retain the nature of substance, or they
will not. If the former, then (by Prop. viii.) each part will
necessarily be infinite, and (by Prop. vi.) self-caused, and (by
Prop. v.) will perforce consist of a different attribute, so
that, in that case, several substances could be formed out of one
substance, which (by Prop. vi.) is absurd. Moreover, the parts
(by Prop. ii.) would have nothing in common with their whole, and
the whole (by Def. iv. and Prop. x.) could both exist and be
conceived without its parts, which everyone will admit to be
absurd. If we adopt the second alternative-namely, that the
parts will not retain the nature of substance-then, if the whole
substance were divided into equal parts, it would lose the nature
of substance, and would cease to exist, which (by Prop. vii.) is
absurd.

PROP. XIII. Substance absolutely infinite is indivisible.
Proof.-If it could be divided, the parts into which it was
divided would either retain the nature of absolutely infinite
substance, or they would not. If the former, we should have
several substances of the same nature, which (by Prop. v.) is
absurd. If the latter, then (by Prop. vii.) substance absolutely
infinite could cease to exist, which (by Prop. xi.) is also
absurd.
Corollary.-It follows, that no substance, and consequently no
extended substance, in so far as it is substance, is divisible.
Note.-The indivisibility of substance may be more easily
understood as follows. The nature of substance can only be
conceived as infinite, and by a part of substance, nothing else
can be understood than finite substance, which (by Prop. viii)
involves a manifest contradiction.

PROP. XIV. Besides God no substance can be granted or conceived.
Proof.-As God is a being absolutely infinite, of whom no
attribute that expresses the essence of substance can be denied
(by Def. vi.), and he necessarily exists (by Prop. xi.) ; if any
substance besides God were granted, it would have to be explained
by some attribute of God, and thus two substances with the same
attribute would exist, which (by Prop. v.) is absurd ; therefore,
besides God no substance can be granted, or, consequently, be
conceived. If it could be conceived, it would necessarily have
to be conceived as existent ; but this (by the first part of this
proof) is absurd. Therefore, besides God no substance can be
granted or conceived. Q.E.D.
Corollary I.-Clearly, therefore : 1. God is one, that is (by
Def. vi.) only one substance can be granted in the universe, and
that substance is absolutely infinite, as we have already
indicated (in the note to Prop. x.).
Corollary II.-It follows : 2. That extension and thought
are either attributes of God or (by Ax. i.) accidents
(affectiones) of the attributes of God.

PROP. XV. Whatsoever is, is in God, and without God nothing can
be, or be conceived.
Proof.-Besides God, no substance is granted or can be
conceived (by Prop. xiv.), that is (by Def. iii.) nothing which
is in itself and is conceived through itself. But modes (by Def.
v.) can neither be, nor be conceived without substance ;
wherefore they can only be in the divine nature, and can only
through it be conceived. But substances and modes form the sum
total of existence (by Ax. i.), therefore, without God nothing
can be, or be conceived. Q.E.D.
Note.-Some assert that God, like a man, consists of body and
mind, and is susceptible of passions. How far such persons have
strayed from the truth is sufficiently evident from what has been
said. But these I pass over. For all who have in anywise
reflected on the divine nature deny that God has a body. Of this
they find excellent proof in the fact that we understand by body
a definite quantity, so long, so broad, so deep, bounded by a
certain shape, and it is the height of absurdity to predicate
such a thing of God, a being absolutely infinite. But meanwhile
by other reasons with which they try to prove their point, they
show that they think corporeal or extended substance wholly apart
from the divine nature, and say it was created by God. Wherefrom
the divine nature can have been created, they are wholly ignorant
; thus they clearly show, that they do not know the meaning of
their own words. I myself have proved sufficiently clearly, at
any rate in my own judgment (Coroll. Prop. vi, and note 2, Prop.
viii.), that no substance can be produced or created by anything
other than itself. Further, I showed (in Prop. xiv.), that
besides God no substance can be granted or conceived. Hence we
drew the conclusion that extended substance is one of the
infinite attributes of God. However, in order to explain more
fully, I will refute the arguments of my adversaries, which all
start from the following points :-
Extended substance, in so far as it is substance, consists,
as they think, in parts, wherefore they deny that it can be
infinite, or consequently, that it can appertain to God. This
they illustrate with many examples, of which I will take one or
two. If extended substance, they say, is infinite, let it be
conceived to be divided into two parts ; each part will then be
either finite or infinite. If the former, then infinite
substance is composed of two finite parts, which is absurd. If
the latter, then one infinite will be twice as large as another
infinite, which is also absurd.
Further, if an infinite line be measured out in foot lengths,
it will consist of an infinite number of such parts ; it would
equally consist of an infinite number of parts, if each part
measured only an inch : therefore, one infinity would be twelve
times as great as the other.
Lastly, if from a single point there be conceived to be drawn
two diverging lines which at first are at a definite distance
apart, but are produced to infinity, it is certain that the
distance between the two lines will be continually increased,
until at length it changes from definite to indefinable. As
these absurdities follow, it is said, from considering quantity
as infinite, the conclusion is drawn, that extended substance
must necessarily be finite, and, consequently, cannot appertain
to the nature of God.
The second argument is also drawn from God's supreme
perfection. God, it is said, inasmuch as he is a supremely
perfect being, cannot be passive ; but extended substance,
insofar as it is divisible, is passive. It follows, therefore,
that extended substance does not appertain to the essence of God.
Such are the arguments I find on the subject in writers, who
by them try to prove that extended substance is unworthy of the
divine nature, and cannot possibly appertain thereto. However, I
think an attentive reader will see that I have already answered
their propositions ; for all their arguments are founded on the
hypothesis that extended substance is composed of parts, and such
a hypothesis I have shown (Prop. xii., and Coroll. Prop. xiii.)
to be absurd. Moreover, anyone who reflects will see that all
these absurdities (if absurdities they be, which I am not now
discussing), from which it is sought to extract the conclusion
that extended substance is finite, do not at all follow from the
notion of an infinite quantity, but merely from the notion that
an infinite quantity is measurable, and composed of finite parts
: therefore, the only fair conclusion to be drawn is that
infinite quantity is not measurable, and cannot be composed of
finite parts. This is exactly what we have already proved (in
Prop. xii.). Wherefore the weapon which they aimed at us has in
reality recoiled upon themselves. If, from this absurdity of
theirs, they persist in drawing the conclusion that extended
substance must be finite, they will in good sooth be acting like
a man who asserts that circles have the properties of squares,
and, finding himself thereby landed in absurdities, proceeds to
deny that circles have any center, from which all lines drawn to
the circumference are equal. For, taking extended substance,
which can only be conceived as infinite, one, and indivisible
(Props. viii., v., xii.) they assert, in order to prove that it
is finite, that it is composed of finite parts, and that it can
be multiplied and divided.
So, also, others, after asserting that a line is composed of
points, can produce many arguments to prove that a line cannot be
infinitely divided. Assuredly it is not less absurd to assert
that extended substance is made up of bodies or parts, than it
would be to assert that a solid is made up of surfaces, a surface
of lines, and a line of points. This must be admitted by all who
know clear reason to be infallible, and most of all by those who
deny the possibility of a vacuum. For if extended substance
could be so divided that its parts were really separate, why
should not one part admit of being destroyed, the others
remaining joined together as before? And why should all be so
fitted into one another as to leave no vacuum? Surely in the
case of things, which are really distinct one from the other, one
can exist without the other, and can remain in its original
condition. As, then, there does not exist a vacuum in nature
(of which anon), but all parts are bound to come together to
prevent it, it follows from this that the parts cannot really be
distinguished, and that extended substance in so far as it is
substance cannot be divided.
If anyone asks me the further question, Why are we naturally
so prone to divide quantity? I answer, that quantity is
conceived by us in two ways ; in the abstract and superficially,
as we imagine it ; or as substance, as we conceive it solely by
the intellect. If, then, we regard quantity as it is represented
in our imagination, which we often and more easily do, we shall
find that it is finite, divisible, and compounded of parts ; but
if we regard it as it is represented in our intellect, and
conceive it as substance, which it is very difficult to do, we
shall then, as I have sufficiently proved, find that it is
infinite, one, and indivisible. This will be plain enough to all
who make a distinction between the intellect and the imagination,
especially if it be remembered, that matter is everywhere the
same, that its parts are not distinguishable, except in so far as
we conceive matter as diversely modified, whence its parts are
distinguished, not really, but modally. For instance, water, in
so far as it is water, we conceive to be divided, and its parts
to be separated one from the other ; but not in so far as it is
extended substance ; from this point of view it is neither
separated nor divisible. Further, water, in so far as it is
water, is produced and corrupted ; but, in so far as it is
substance, it is neither produced nor corrupted.
I think I have now answered the second argument ; it is, in
fact, founded on the same assumption as the first-namely, that
matter, in so far as it is substance, is divisible, and composed
of parts. Even if it were so, I do not know why it should be
considered unworthy of the divine nature, inasmuch as besides God
(by Prop. xiv.) no substance can be granted, wherefrom it could
receive its modifications. All things, I repeat, are in God, and
all things which come to pass, come to pass solely through the
laws of the infinite nature of God, and follow (as I will shortly
show) from the necessity of his essence. Wherefore it can in
nowise be said, that God is passive in respect to anything other
than himself, or that extended substance is unworthy of the
Divine nature, even if it be supposed divisible, so long as it is
granted to be infinite and eternal. But enough of this for the
present.

PROP. XVI. From the necessity of the divine nature must follow
an infinite number of things in infinite ways-that is, all things
which can fall within the sphere of infinite intellect.
Proof.-This proposition will be clear to everyone, who
remembers that from the given definition of any thing the
intellect infers several properties, which really necessarily
follow therefrom (that is, from the actual essence of the thing
defined) ; and it infers more properties in proportion as the
definition of the thing expresses more reality, that is, in
proportion as the essence of the thing defined involves more
reality. Now, as the divine nature has absolutely infinite
attributes (by Def. vi.), of which each expresses infinite
essence after its kind, it follows that from the necessity of its
nature an infinite number of things (that is, everything which
can fall within the sphere of an infinite intellect) must
necessarily follow. Q.E.D.
Corollary I.-Hence it follows, that God is the efficient
cause of all that can fall within the sphere of an infinite
intellect.
Corollary II.-It also follows that God is a cause in himself,
and not through an accident of his nature.
Corollary III.-It follows, thirdly, that God is the
absolutely first cause.

PROP. XVII. God acts solely by the laws of his own nature, and
is not constrained by anyone.
Proof.-We have just shown (in Prop. xvi.), that solely from
the necessity of the divine nature, or, what is the same thing,
solely from the laws of his nature, an infinite number of things
absolutely follow in an infinite number of ways ; and we proved
(in Prop. xv.), that without God nothing can be nor be conceived
; but that all things are in God. Wherefore nothing can exist
outside himself, whereby he can be conditioned or constrained to
act. Wherefore God acts solely by the laws of his own nature,
and is not constrained by anyone. Q.E.D.
Corollary I.-It follows : 1. That there can be no cause
which, either extrinsically or intrinsically, besides the
perfection of his own nature, moves God to act.
Corollary II.-It follows : 2. That God is the sole free
cause. For God alone exists by the sole necessity of his nature
(by Prop. xi. and Prop. xiv., Coroll. i.), and acts by the sole
necessity of his own nature, wherefore God is (by Def. vii.) the
sole free cause. Q.E.D.
Note.-Others think that God is a free cause, because he can,
as they think, bring it about, that those things which we have
said follow from his nature-that is, which are in his power,
should not come to pass, or should not be produced by him. But
this is the same as if they said, that God could bring it about,
that it should follow from the nature of a triangle that its
three interior angles should not be equal to two right angles ;
or that from a given cause no effect should follow, which is
absurd.
Moreover, I will show below, without the aid of this
proposition, that neither intellect nor will appertain to God's
nature. I know that there are many who think that they can show,
that supreme intellect and free will do appertain to God's nature
; for they say they know of nothing more perfect, which they can
attribute to God, than that which is the highest perfection in
ourselves. Further, although they conceive God as actually
supremely intelligent, they yet do not believe that he can bring
into existence everything which he actually understands, for they
think that they would thus destroy God's power. If, they
contend, God had created everything which is in his intellect, he
would not be able to create anything more, and this, they think,
would clash with God's omnipotence ; therefore, they prefer to
asset that God is indifferent to all things, and that he creates
nothing except that which he has decided, by some absolute
exercise of will, to create. However, I think I have shown
sufficiently clearly (by Prop. xvi.), that from God's supreme
power, or infinite nature, an infinite number of things-that is,
all things have necessarily flowed forth in an infinite number of
ways, or always flow from the same necessity ; in the same way as
from the nature of a triangle it follows from eternity and for
eternity, that its three interior angles are equal to two right
angles. Wherefore the omnipotence of God has been displayed from
all eternity, and will for all eternity remain in the same state
of activity. This manner of treating the question attributes to
God an omnipotence, in my opinion, far more perfect. For,
otherwise, we are compelled to confess that God understands an
infinite number of creatable things, which he will never be able
to create, for, if he created all that he understands, he would,
according to this showing, exhaust his omnipotence, and render
himself imperfect. Wherefore, in order to establish that God is
perfect, we should be reduced to establishing at the same time,
that he cannot bring to pass everything over which his power
extends ; this seems to be a hypothesis most absurd, and most
repugnant to God's omnipotence.
Further (to say a word here concerning the intellect and the
will which we attribute to God), if intellect and will appertain
to the eternal essence of God, we must take these words in some
significance quite different from those they usually bear. For
intellect and will, which should constitute the essence of God,
would perforce be as far apart as the poles from the human
intellect and will, in fact, would have nothing in common with
them but the name ; there would be about as much correspondence
between the two as there is between the Dog, the heavenly
constellation, and a dog, an animal that barks. This I will
prove as follows. If intellect belongs to the divine nature, it
cannot be in nature, as ours is generally thought to be,
posterior to, or simultaneous with the things understood,
inasmuch as God is prior to all things by reason of his causality
(Prop. xvi., Coroll. i.). On the contrary, the truth and formal
essence of things is as it is, because it exists by
representation as such in the intellect of God. Wherefore the
intellect of God, in so far as it is conceived to constitute
God's essence, is, in reality, the cause of things, both of their
essence and of their existence. This seems to have been
recognized by those who have asserted, that God's intellect,
God's will, and God's power, are one and the same. As,
therefore, God's intellect is the sole cause of things, namely,
both of their essence and existence, it must necessarily differ
from them in respect to its essence, and in respect to its
existence. For a cause differs from a thing it causes, precisely
in the quality which the latter gains from the former.
For example, a man is the cause of another man's existence,
but not of his essence (for the latter is an eternal truth), and,
therefore, the two men may be entirely similar in essence, but
must be different in existence ; and hence if the existence of
one of them cease, the existence of the other will not
necessarily cease also ; but if the essence of one could be
destroyed, and be made false, the essence of the other would be
destroyed also. Wherefore, a thing which is the cause both of
the essence and of the existence of a given effect, must differ
from such effect both in respect to its essence, and also in
respect to its existence. Now the intellect of God is the cause
both of the essence and the existence of our intellect ;
therefore, the intellect of God in so far as it is conceived to
constitute the divine essence, differs from our intellect both in
respect to essence and in respect to existence, nor can it in
anywise agree therewith save in name, as we said before. The
reasoning would be identical in the case of the will, as anyone
can easily see.

PROP. XVIII. God is the indwelling and not the transient cause
of all things.
Proof.-All things which are, are in God, and must be
conceived through God (by Prop. xv.), therefore (by Prop. xvi.,
Coroll. i.) God is the cause of those things which are in him.
This is our first point. Further, besides God there can be no
substance (by Prop. xiv.), that is nothing in itself external to
God. This is our second point. God, therefore, is the
indwelling and not the transient cause of all things. Q.E.D.

PROP. XIX. God, and all the attributes of God, are eternal.
Proof.-God (by Def. vi.) is substance, which (by Prop. xi.)
necessarily exists, that is (by Prop. vii.) existence appertains
to its nature, or (what is the same thing) follows from its
definition ; therefore, God is eternal (by Def. viii.). Further,
by the attributes of God we must understand that which (by Def.
iv.) expresses the essence of the divine substance-in other
words, that which appertains to substance : that, I say, should
be involved in the attributes of substance. Now eternity
appertains to the nature of substance (as I have already shown in
Prop. vii.) ; therefore, eternity must appertain to each of the
attributes, and thus all are eternal. Q.E.D.
Note.-This proposition is also evident from the manner in
which (in Prop. xi.) I demonstrated the existence of God ; it is
evident, I repeat, from that proof, that the existence of God,
like his essence, is an eternal truth. Further (in Prop. xix. of
my "Principles of the Cartesian Philosophy"), I have proved the
eternity of God, in another manner, which I need not here repeat.

PROP. XX. The existence of God and his essence are one and the
same.
Proof.-God (by the last Prop.) and all his attributes are
eternal, that is (by Def. viii.) each of his attributes expresses
existence. Therefore the same
attributes of God which explain his eternal essence, explain at
the same time his eternal existence-in other words, that which
constitutes God's essence constitutes at the same time his
existence. Wherefore God's existence and God's essence are one
and the same. Q.E.D.
Coroll. I.-Hence it follows that God's existence, like his
essence, is an eternal truth.
Coroll. II-Secondly, it follows that God, and all the
attributes of God, are unchangeable. For if they could be
changed in respect to existence, they must also be able to be
changed in respect to essence-that is, obviously, be changed from
true to false, which is absurd.

PROP. XXI. All things which follow from the absolute nature of
any attribute of God must always exist and be infinite, or, in
other words, are eternal and infinite through the said attribute.
Proof.-Conceive, if it be possible (supposing the proposition
to be denied), that something in some attribute of God can follow
from the absolute nature of the said attribute, and that at the
same time it is finite, and has a conditioned existence or
duration ; for instance, the idea of God expressed in the
attribute thought. Now thought, in so far as it is supposed to
be an attribute of God, is necessarily (by Prop. xi.) in its
nature infinite. But, in so far as it possesses the idea of God,
it is supposed finite. It cannot, however, be conceived as
finite, unless it be limited by thought (by Def. ii.) ; but it is
not limited by thought itself, in so far as it has constituted
the idea of God (for so far it is supposed to be finite) ;
therefore, it is limited by thought, in so far as it has not
constituted the idea of God, which nevertheless (by Prop. xi.)
must necessarily exist.
We have now granted, therefore, thought not constituting the
idea of God, and, accordingly, the idea of God does not naturally
follow from its nature in so far as it is absolute thought (for
it is conceived as constituting, and also as not constituting,
the idea of God), which is against our hypothesis. Wherefore, if
the idea of God expressed in the attribute thought, or, indeed,
anything else in any attribute of God (for we may take any
example, as the proof is of universal application) follows from
the necessity of the absolute nature of the said attribute, the
said thing must necessarily be infinite, which was our first
point.
Furthermore, a thing which thus follows from the necessity of
the nature of any attribute cannot have a limited duration. For
if it can, suppose a thing, which follows from the necessity of
the nature of some attribute, to exist in some attribute of God,
for instance, the idea of God expressed in the attribute thought,
and let it be supposed at some time not to have existed, or to be
about not to exist.
Now thought being an attribute of God, must necessarily exist
unchanged (by Prop. xi., and Prop. xx., Coroll. ii.) ; and beyond
the limits of the duration of the idea of God (supposing the
latter at some time not to have existed, or not to be going to
exist) thought would perforce have existed without the idea of
God, which is contrary to our hypothesis, for we supposed that,
thought being given, the idea of God necessarily flowed
therefrom. Therefore the idea of God expressed in thought, or
anything which necessarily follows from the absolute nature of
some attribute of God, cannot have a limited duration, but
through the said attribute is eternal, which is our second point.
Bear in mind that the same proposition may be affirmed of
anything, which in any attribute necessarily follows from God's
absolute nature.

PROP. XXII. Whatsoever follows from any attribute of God, in so
far as it is modified by a modification, which exists necessarily
and as infinite, through the said attribute, must also exist
necessarily and as infinite.
Proof.-The proof of this proposition is similar to that of
the preceding one.

PROP. XXIII. Every mode, which exists both necessarily and as
infinite, must necessarily follow either from the absolute nature
of some attribute of God, or from an attribute modified by a
modification which exists necessarily, and as infinite.
Proof.-A mode exists in something else, through which it must
be conceived (Def. v.), that is (Prop. xv.), it exists solely in
God, and solely through God can be conceived. If therefore a mode
is conceived as necessarily existing and infinite, it must
necessarily be inferred or perceived through some attribute of
God, in so far as such attribute is conceived as expressing the
infinity and necessity of existence, in other words (Def. viii.)
eternity ; that is, in so far as it is considered absolutely. A
mode, therefore, which necessarily exists as infinite, must
follow from the absolute nature of some attribute of God, either
immediately (Prop. xxi.) or through the means of some
modification, which follows from the absolute nature of the said
attribute ; that is (by Prop. xxii.), which exists necessarily
and as infinite.

PROP. XXIV. The essence of things produced by God does not
involve existence.
Proof.-This proposition is evident from Def. i. For that of
which the nature (considered in itself) involves existence is
self-caused, and exists by the sole necessity of its own nature.
Corollary.-Hence it follows that God is not only the cause of
things coming into existence, but also of their continuing in
existence, that is, in scholastic phraseology, God is cause of
the being of things (essendi rerum). For whether things exist,
or do not exist, whenever we contemplate their essence, we see
that it involves neither existence nor duration ; consequently,
it cannot be the cause of either the one or the other. God must
be the sole cause, inasmuch as to him alone does existence
appertain. (Prop. xiv. Coroll. i.) Q.E.D.

PROP. XXV. God is the efficient cause not only of the existence
of things, but also of their essence.
Proof.-If this be denied, then God is not the cause of the
essence of things ; and therefore the essence of things can (by
Ax. iv.) be conceived without God. This (by Prop. xv.) is
absurd. Therefore, God is the cause of the essence of things.
Q.E.D.
Note.-This proposition follows more clearly from Prop. xvi.
For it is evident thereby that, given the divine nature, the
essence of things must be inferred from it, no less than their
existence-in a word, God must be called the cause of all things,
in the same sense as he is called the cause of himself. This
will be made still clearer by the following corollary.
Corollary.-Individual things are nothing but modifications of
the attributes of God, or modes by which the attributes of God
are expressed in a fixed and definite manner. The proof appears
from Prop. xv. and Def. v.

PROP. XXVI. A thing which is conditioned to act in a particular
manner, has necessarily been thus conditioned by God ; and that
which has not been conditioned by God cannot condition itself to
act.
Proof.-That by which things are said to be conditioned to act
in a particular manner is necessarily something positive (this is
obvious) ; therefore both of its essence and of its existence God
by the necessity of his nature is the efficient cause (Props.
xxv. and xvi.) ; this is our first point. Our second point is
plainly to be inferred therefrom. For if a thing, which has not
been conditioned by God, could condition itself, the first part
of our proof would be false, and this, as we have shown is
absurd.

PROP. XXVII. A thing, which has been conditioned by God to act
in a particular way, cannot render itself unconditioned.
Proof.-This proposition is evident from the third axiom.

PROP. XXVIII. Every individual thing, or everything which is
finite and has a conditioned existence, cannot exist or be
conditioned to act, unless it be conditioned for existence and
action by a cause other than itself, which also is finite, and
has a conditioned existence ; and likewise this cause cannot in
its turn exist, or be conditioned to act, unless it be
conditioned for existence and action by another cause, which also
is finite, and has a conditioned existence, and so on to
infinity.
Proof.-Whatsoever is conditioned to exist and act, has been
thus conditioned by God (by Prop. xxvi. and Prop. xxiv.,
Coroll.).
But that which is finite, and has a conditioned existence,
cannot be produced by the absolute nature of any attribute of God
; for whatsoever follows from the absolute nature of any
attribute of God is infinite and eternal (by Prop. xxi.). It
must, therefore, follow from some attribute of God, in so far as
the said attribute is considered as in some way modified ; for
substance and modes make up the sum total of existence (by Ax. i.
and Def. iii., v.), while modes are merely modifications of the
attributes of God. But from God, or from any of his attributes,
in so far as the latter is modified by a modification infinite
and eternal, a conditioned thing cannot follow. Wherefore it
must follow from, or be conditioned for, existence and action by
God or one of his attributes, in so far as the latter are
modified by some modification which is finite, and has a
conditioned existence. This is our first point. Again, this
cause or this modification (for the reason by which we
established the first part of this proof) must in its turn be
conditioned by another cause, which also is finite, and has a
conditioned existence, and, again, this last by another (for the
same reason) ; and so on (for the same reason) to infinity.
Q.E.D.
Note.-As certain things must be produced immediately by God,
namely those things which necessarily follow from his absolute
nature, through the means of these primary attributes, which,
nevertheless, can neither exist nor be conceived without God, it
follows :-1. That God is absolutely the proximate cause of those
things immediately produced by him. I say absolutely, not after
his kind, as is usually stated. For the effects of God cannot
either exist or be conceived without a cause (Prop. xv. and Prop.
xxiv. Coroll.). 2. That God cannot properly be styled the remote
cause of individual things, except for the sake of distinguishing
these from what he immediately produces, or rather from what
follows from his absolute nature. For, by a remote cause, we
understand a cause which is in no way conjoined to the effect.
But all things which are, are in God, and so depend on God, that
without him they can neither be nor be conceived.

PROP. XXIX. Nothing in the universe is contingent, but all
things are conditioned to exist and operate in a particular
manner by the necessity of the divine nature.
Proof.-Whatsoever is, is in God (Prop. xv.). But God cannot
be called a thing contingent. For (by Prop. xi.) he exists
necessarily, and not contingently. Further, the modes of the
divine nature follow therefrom necessarily, and not contingently
(Prop. xvi.) ; and they thus follow, whether we consider the
divine nature absolutely, or whether we consider it as in any way
conditioned to act (Prop. xxvii.). Further, God is not only the
cause of these modes, in so far as they simply exist (by Prop.
xxiv, Coroll.), but also in so far as they are considered as
conditioned for operating in a particular manner (Prop. xxvi.).
If they be not conditioned by God (Prop. xxvi.), it is
impossible, and not contingent, that they should condition
themselves ; contrariwise, if they be conditioned by God, it is
impossible, and not contingent, that they should render
themselves unconditioned. Wherefore all things are conditioned by
the necessity of the divine nature, not only to exist, but also
to exist and operate in a particular manner, and there is nothing
that is contingent. Q.E.D.
Note.-Before going any further, I wish here to explain, what
we should understand by nature viewed as active (natura
naturans), and nature viewed as passive (natura naturata). I say
to explain, or rather call attention to it, for I think that,
from what has been said, it is sufficiently clear, that by nature
viewed as active we should understand that which is in itself,
and is conceived through itself, or those attributes of
substance, which express eternal and infinite essence, in other
words (Prop. xiv., Coroll. i., and Prop. xvii., Coroll. ii) God,
in so far as he is considered as a free cause.
By nature viewed as passive I understand all that which
follows from the necessity of the nature of God, or of any of the
attributes of God, that is, all the modes of the attributes of
God, in so far as they are considered as things which are in God,
and which without God cannot exist or be conceived.

PROP. XXX. Intellect, in function (actu) finite, or in function
infinite, must comprehend the attributes of God and the
modifications of God, and nothing else.
Proof.-A true idea must agree with its object (Ax. vi.) ; in
other words (obviously), that which is contained in the intellect
in representation must necessarily be granted in nature. But in
nature (by Prop. xiv., Coroll. i.) there is no substance save
God, nor any modifications save those (Prop. xv.) which are in
God, and cannot without God either be or be conceived. Therefore
the intellect, in function finite, or in function infinite, must
comprehend the attributes of God and the modifications of God,
and nothing else. Q.E.D.

PROP. XXXI. The intellect in function, whether finite or
infinite, as will, desire, love, &c., should be referred to
passive nature and not to active nature.
Proof.-By the intellect we do not (obviously) mean absolute
thought, but only a certain mode of thinking, differing from
other modes, such as love, desire, &c., and therefore (Def. v.)
requiring to be conceived through absolute thought. It must (by
Prop. xv. and Def. vi.), through some attribute of God which
expresses the eternal and infinite essence of thought, be so
conceived, that without such attribute it could neither be nor be
conceived. It must therefore be referred to nature passive
rather than to nature active, as must also the other modes of
thinking. Q.E.D.
Note.-I do not here, by speaking of intellect in function,
admit that there is such a thing as intellect in potentiality :
but, wishing to avoid all confusion, I desire to speak only of
what is most clearly perceived by us, namely, of the very act of
understanding, than which nothing is more clearly perceived. For
we cannot perceive anything without adding to our knowledge of
the act of understanding.

PROP. XXXII. Will cannot be called a free cause, but only a
necessary cause.
Proof.-Will is only a particular mode of thinking, like
intellect ; therefore (by Prop. xxviii.) no volition can exist,
nor be conditioned to act, unless it be conditioned by some cause
other than itself, which cause is conditioned by a third cause,
and so on to infinity. But if will be supposed infinite, it must
also be conditioned to exist and act by God, not by virtue of his
being substance absolutely infinite, but by virtue of his
possessing an attribute which expresses the infinite and eternal
essence of thought (by Prop. xxiii.). Thus, however it be
conceived, whether as finite or infinite, it requires a cause by
which it should be conditioned to exist and act. Thus (Def.
vii.) it cannot be called a free cause, but only a necessary or
constrained cause. Q.E.D.
Coroll. I.-Hence it follows, first, that God does not act
according to freedom of the will.
Coroll. II.-It follows, secondly, that will and intellect
stand in the same relation to the nature of God as do motion, and
rest, and absolutely all natural phenomena, which must be
conditioned by God (Prop. xxix.) to exist and act in a particular
manner. For will, like the rest, stands in need of a cause, by
which it is conditioned to exist and act in a particular manner.
And although, when will or intellect be granted, an infinite
number of results may follow, yet God cannot on that account be
said to act from freedom of the will, any more than the infinite
number of results from motion and rest would justify us in saying
that motion and rest act by free will. Wherefore will no more
appertains to God than does anything else in nature, but stands
in the same relation to him as motion, rest, and the like, which
we have shown to follow from the necessity of the divine nature,
and to be conditioned by it to exist and act in a particular
manner.

PROP. XXXIII. Things could not have been brought into being by
God in any manner or in any order different from that which has
in fact obtained.
Proof-All things necessarily follow from the nature of God
(Prop. xvi.), and by the nature of God are conditioned to exist
and act in a particular way (Prop. xxix.). If things, therefore,
could have been of a different nature, or have been conditioned
to act in a different way, so that the order of nature would have
been different, God's nature would also have been able to be
different from what it now is ; and therefore (by Prop. xi.) that
different nature also would have perforce existed, and
consequently there would have been able to be two or more Gods.
This (by Prop. xiv., Coroll. i.) is absurd. Therefore things
could not have been brought into being by God in any other
manner, &c. Q.E.D.
Note I.-As I have thus shown, more clearly than the sun at
noonday, that there is nothing to justify us in calling things
contingent, I wish to explain briefly what meaning we shall
attach to the word contingent ; but I will first explain the
words necessary and impossible.
A thing is called necessary either in respect to its essence
or in respect to its cause ; for the existence of a thing
necessarily follows, either from its essence and definition, or
from a given efficient cause. For similar reasons a thing is
said to be impossible ; namely, inasmuch as its essence or
definition involves a contradiction, or because no external cause
is granted, which is conditioned to produce such an effect ; but
a thing can in no respect be called contingent, save in relation
to the imperfection of our knowledge.
A thing of which we do not know whether the essence does or
does not involve a contradiction, or of which, knowing that it
does not involve a contradiction, we are still in doubt
concerning the existence, because the order of causes escapes
us,-such a thing, I say, cannot appear to us either necessary or
impossible. Wherefore we call it contingent or possible.
Note II.-It clearly follows from what we have said, that
things have been brought into being by God in the highest
perfection, inasmuch as they have necessarily followed from a
most perfect nature. Nor does this prove any imperfection in
God, for it has compelled us to affirm his perfection. From its
contrary proposition, we should clearly gather (as I have just
shown), that God is not supremely perfect, for if things had been
brought into being in any other way, we should have to assign to
God a nature different from that, which we are bound to attribute
to him from the consideration of an absolutely perfect being.
I do not doubt, that many will scout this idea as absurd, and
will refuse to give their minds up to contemplating it, simply
because they are accustomed to assign to God a freedom very
different from that which we (Def. vii.) have deduced. They
assign to him, in short, absolute free will. However, I am also
convinced that if such persons reflect on the matter, and duly
weigh in their minds our series of propositions, they will reject
such freedom as they now attribute to God, not only as nugatory,
but also as a great impediment to organized knowledge. There is
no need for me to repeat what I have said in the note to Prop.
xvii. But, for the sake of my opponents, I will show further,
that although it be granted that will pertains to the essence of
God, it nevertheless follows from his perfection, that things
could not have been by him created other than they are, or in a
different order ; this is easily proved, if we reflect on what
our opponents themselves concede, namely, that it depends solely
on the decree and will of God, that each thing is what it is. If
it were otherwise, God would not be the cause of all things.
Further, that all the decrees of God have been ratified from all
eternity by God himself. If it were otherwise, God would be
convicted of imperfection or change. But in eternity there is no
such thing as when, before, or after ; hence it follows solely
from the perfection of God, that God never can decree, or never
could have decreed anything but what is ; that God did not exist
before his decrees, and would not exist without them. But, it is
said, supposing that God had made a different universe, or had
ordained other decrees from all eternity concerning nature and
her order, we could not therefore conclude any imperfection in
God. But persons who say this must admit that God can change his
decrees. For if God had ordained any decrees concerning nature
and her order, different from those which he has ordained-in
other words, if he had willed and conceived something different
concerning nature-he would perforce have had a different
intellect from that which he has, and also a different will. But
if it were allowable to assign to God a different intellect and a
different will, without any change in his essence or his
perfection, what would there be to prevent him changing the
decrees which he has made concerning created things, and
nevertheless remaining perfect? For his intellect and will
concerning things created and their order are the same, in
respect to his essence and perfection, however they be conceived.
Further, all the philosophers whom I have read admit that
God's intellect is entirely actual, and not at all potential ; as
they also admit that God's intellect, and God's will, and God's
essence are identical, it follows that, if God had had a
different actual intellect and a different will, his essence
would also have been different ; and thus, as I concluded at
first, if things had been brought into being by God in a
different way from that which has obtained, God's intellect and
will, that is (as is admitted) his essence would perforce have
been different, which is absurd.
As these things could not have been brought into being by God
in any but the actual way and order which has obtained ; and as
the truth of this proposition follows from the supreme perfection
of God ; we can have no sound reason for persuading ourselves to
believe that God did not wish to create all the things which were
in his intellect, and to create them in the same perfection as he
had understood them.
But, it will be said, there is in things no perfection nor
imperfection ; that which is in them, and which causes them to be
called perfect or imperfect, good or bad, depends solely on the
will of God. If God had so willed, he might have brought it
about that what is now perfection should be extreme imperfection,
and vice versā. What is such an assertion, but an open
declaration that God, who necessarily understands that which he
wishes, might bring it about by his will, that he should
understand things differently from the way in which he does
understand them? This (as we have just shown) is the height of
absurdity. Wherefore, I may turn the argument against its
employers, as follows :-All things depend on the power of God.
In order that things should be different from what they are,
God's will would necessarily have to be different. But God's
will cannot be different (as we have just most clearly
demonstrated) from God's perfection. Therefore neither can
things be different. I confess, that the theory which subjects
all things to the will of an indifferent deity, and asserts that
they are all dependent on his fiat, is less far from the truth
than the theory of those, who maintain that God acts in all
things with a view of promoting what is good. For these latter
persons seem to set up something beyond God, which does not
depend on God, but which God in acting looks to as an exemplar,
or which he aims at as a definite goal. This is only another
name for subjecting God to the dominion of destiny, an utter
absurdity in respect to God, whom we have shown to be the first
and only free cause of the essence of all things and also of
their existence. I need, therefore, spend no time in refuting
such wild theories.

PROP. XXXIV. God's power is identical with his essence.
Proof.-From the sole necessity of the essence of God it
follows that God is the cause of himself (Prop. xi.) and of all
things (Prop. xvi. and Coroll.). Wherefore the power of God, by
which he and all things are and act, is identical with his
essence. Q.E.D.

PROP. XXXV. Whatsoever we conceive to be in the power of God,
necessarily exists.
Proof.-Whatsoever is in God's power, must (by the last Prop.)
be comprehended in his essence in such a manner, that it
necessarily follows therefrom, and therefore necessarily exists.
Q.E.D.

PROP. XXXVI. There is no cause from whose nature some effect
does not follow.
Proof.-Whatsoever exists expresses God's nature or essence in
a given conditioned manner (by Prop. xxv., Coroll.) ; that is,
(by Prop. xxxiv.), whatsoever exists, expresses in a given
conditioned manner God's power, which is the cause of all things,
therefore an effect must (by Prop. xvi.) necessarily follow.
Q.E.D.

APPENDIX :
In the foregoing I have explained the nature and properties
of God. I have shown that he necessarily exists, that he is one
: that he is, and acts solely by the necessity of his own nature
; that he is the free cause of all things, and how he is so ;
that all things are in God, and so depend on him, that without
him they could neither exist nor be conceived ; lastly, that all
things are predetermined by God, not through his free will or
absolute fiat, but from the very nature of God or infinite power.
I have further, where occasion afforded, taken care to remove the
prejudices, which might impede the comprehension of my
demonstrations. Yet there still remain misconceptions not a few,
which might and may prove very grave hindrances to the
understanding of the concatenation of things, as I have explained
it above. I have therefore thought it worth while to bring these
misconceptions before the bar of reason.
All such opinions spring from the notion commonly
entertained, that all things in nature act as men themselves act,
namely, with an end in view. It is accepted as certain, that God
himself directs all things to a definite goal (for it is said
that God made all things for man, and man that he might worship
him). I will, therefore, consider this opinion, asking first,
why it obtains general credence, and why all men are naturally so
prone to adopt it? secondly, I will point out its falsity ; and,
lastly, I will show how it has given rise to prejudices about
good and bad, right and wrong, praise and blame, order and
confusion, beauty and ugliness, and the like. However, this is
not the place to deduce these misconceptions from the nature of
the human mind : it will be sufficient here, if I assume as a
starting point, what ought to be universally admitted, namely,
that all men are born ignorant of the causes of things, that all
have the desire to seek for what is useful to them, and that they
are conscious of such desire. Herefrom it follows, first, that
men think themselves free inasmuch as they are conscious of their
volitions and desires, and never even dream, in their ignorance,
of the causes which have disposed them so to wish and desire.
Secondly, that men do all things for an end, namely, for that
which is useful to them, and which they seek. Thus it comes to
pass that they only look for a knowledge of the final causes of
events, and when these are learned, they are content, as having
no cause for further doubt. If they cannot learn such causes
from external sources, they are compelled to turn to considering
themselves, and reflecting what end would have induced them
personally to bring about the given event, and thus they
necessarily judge other natures by their own. Further, as they
find in themselves and outside themselves many means which assist
them not a little in the search for what is useful, for instance,
eyes for seeing, teeth for chewing, herbs and animals for
yielding food, the sun for giving light, the sea for breeding
fish, &c., they come to look on the whole of nature as a means
for obtaining such conveniences. Now as they are aware, that
they found these conveniences and did not make them, they think
they have cause for believing, that some other being has made
them for their use. As they look upon things as means, they
cannot believe them to be self-created ; but, judging from the
means which they are accustomed to prepare for themselves, they
are bound to believe in some ruler or rulers of the universe
endowed with human freedom, who have arranged and adapted
everything for human use. They are bound to estimate the nature
of such rulers (having no information on the subject) in
accordance with their own nature, and therefore they assert that
the gods ordained everything for the use of man, in order to bind
man to themselves and obtain from him the highest honor. Hence
also it follows, that everyone thought out for himself, according
to his abilities, a different way of worshipping God, so that God
might love him more than his fellows, and direct the whole course
of nature for the satisfaction of his blind cupidity and
insatiable avarice. Thus the prejudice developed into
superstition, and took deep root in the human mind ; and for this
reason everyone strove most zealously to understand and explain
the final causes of things ; but in their endeavor to show that
nature does nothing in vain, i.e. nothing which is useless to
man, they only seem to have demonstrated that nature, the gods,
and men are all mad together. Consider, I pray you, the result :
among the many helps of nature they were bound to find some
hindrances, such as storms, earthquakes, diseases, &c. : so they
declared that such things happen, because the gods are angry at
some wrong done to them by men, or at some fault committed in
their worship. Experience day by day protested and showed by
infinite examples, that good and evil fortunes fall to the lot of
pious and impious alike ; still they would not abandon their
inveterate prejudice, for it was more easy for them to class such
contradictions among other unknown things of whose use they were
ignorant, and thus to retain their actual and innate condition of
ignorance, than to destroy the whole fabric of their reasoning
and start afresh. They therefore laid down as an axiom, that
God's judgments far transcend human understanding. Such a
doctrine might well have sufficed to conceal the truth from the
human race for all eternity, if mathematics had not furnished
another standard of verity in considering solely the essence and
properties of figures without regard to their final causes.
There are other reasons (which I need not mention here) besides
mathematics, which might have caused men's minds to be directed
to these general prejudices, and have led them to the knowledge
of the truth.
I have now sufficiently explained my first point. There is
no need to show at length, that nature has no particular goal in
view, and that final causes are mere human figments. This, I
think, is already evident enough, both from the causes and
foundations on which I have shown such prejudice to be based, and
also from Prop. xvi., and the Corollary of Prop. xxxii., and, in
fact, all those propositions in which I have shown, that
everything in nature proceeds from a sort of necessity, and with
the utmost perfection. However, I will add a few remarks, in
order to overthrow this doctrine of a final cause utterly. That
which is really a cause it considers as an effect, and vice versā
: it makes that which is by nature first to be last, and that
which is highest and most perfect to be most imperfect. Passing
over the questions of cause and priority as self-evident, it is
plain from Props. xxi., xxii., xxiii. that the effect is most
perfect which is produced immediately by God ; the effect which
requires for its production several intermediate causes is, in
that respect, more imperfect. But if those things which were
made immediately by God were made to enable him to attain his
end, then the things which come after, for the sake of which the
first were made, are necessarily the most excellent of all.
Further, this doctrine does away with the perfection of God :
for, if God acts for an object, he necessarily desires something
which he lacks. Certainly, theologians and metaphysicians draw a
distinction between the object of want and the object of
assimilation ; still they confess that God made all things for
the sake of himself, not for the sake of creation. They are
unable to point to anything prior to creation, except God
himself, as an object for which God should act, and are therefore
driven to admit (as they clearly must), that God lacked those
things for whose attainment he created means, and further that he
desired them.
We must not omit to notice that the followers of this
doctrine, anxious to display their talent in assigning final
causes, have imported a new method of argument in proof of their
theory-namely, a reduction, not to the impossible, but to
ignorance ; thus showing that they have no other method of
exhibiting their doctrine. For example, if a stone falls from a
roof on to someone's head, and kills him, they will demonstrate
by their new method, that the stone fell in order to kill the man
; for, if it had not by God's will fallen with that object, how
could so many circumstances (and there are often many concurrent
circumstances) have all happened together by chance? Perhaps you
will answer that the event is due to the facts that the wind was
blowing, and the man was walking that way. "But why," they will
insist, "was the wind blowing, and why was the man at that very
time walking that way?" If you again answer, that the wind had
then sprung up because the sea had begun to be agitated the day
before, the weather being previously calm, and that the man had
been invited by a friend, they will again insist : "But why was
the sea agitated, and why was the man invited at that time?"
So they will pursue their questions from cause to cause, till at
last you take refuge in the will of God-in other words, the
sanctuary of ignorance. So, again, when they survey the frame of
the human body, they are amazed ; and being ignorant of the
causes of so great a work of art, conclude that it has been
fashioned, not mechanically, but by divine and supernatural
skill, and has been so put together that one part shall not hurt
another.
Hence anyone who seeks for the true causes of miracles, and
strives to understand natural phenomena as an intelligent being,
and not to gaze at them like a fool, is set down and denounced as
an impious heretic by those, whom the masses adore as the
interpreters of nature and the gods. Such persons know that,
with the removal of ignorance, the wonder which forms their only
available means for proving and preserving their authority would
vanish also. But I now quit this subject, and pass on to my
third point.
After men persuaded themselves, that everything which is
created is created for their sake, they were bound to consider as
the chief quality in everything that which is most useful to
themselves, and to account those things the best of all which
have the most beneficial effect on mankind. Further, they were
bound to form abstract notions for the explanation of the nature
of things, such as goodness, badness, order, confusion, warmth,
cold, beauty, deformity, and so on ; and from the belief that
they are free agents arose the further notions of praise and
blame, sin and merit.
I will speak of these latter hereafter, when I treat of human
nature ; the former I will briefly explain here.
Everything which conduces to health and the worship of God
they have called good, everything which hinders these objects
they have styled bad ; and inasmuch as those who do not
understand the nature of things do not verify phenomena in any
way, but merely imagine them after a fashion, and mistake their
imagination for understanding, such persons firmly believe that
there is an order in things, being really ignorant both of things
and their own nature. When phenomena are of such a kind, that
the impression they make on our senses requires little effort of
imagination, and can consequently be easily remembered, we say
that they are well-ordered ; if the contrary, that they are
ill-ordered or confused. Further, as things which are easily
imagined are more pleasing to us, men prefer order to
confusion-as though there were any order in nature, except in
relation to our imagination-and say that God has created all
things in order ; thus, without knowing it, attributing
imagination to God, unless, indeed, they would have it that God
foresaw human imagination, and arranged everything, so that it
should be most easily imagined. If this be their theory, they
would not, perhaps, be daunted by the fact that we find an
infinite number of phenomena, far surpassing our imagination, and
very many others which confound its weakness. But enough has
been said on this subject. The other abstract notions are
nothing but modes of imagining, in which the imagination is
differently affected : though they are considered by the ignorant
as the chief attributes of things, inasmuch as they believe that
everything was created for the sake of themselves ; and,
according as they are affected by it, style it good or bad,
healthy or rotten and corrupt. For instance, if the motion which
objects we see communicate to our nerves be conducive to health,
the objects causing it are styled beautiful ; if a contrary
motion be excited, they are styled ugly.
Things which are perceived through our sense of smell are
styled fragrant or fetid ; if through our taste, sweet or bitter,
full-flavored or insipid ; if through our touch, hard or soft,
rough or smooth, &c.
Whatsoever affects our ears is said to give rise to noise,
sound, or harmony. In this last case, there are men lunatic
enough to believe, that even God himself takes pleasure in
harmony ; and philosophers are not lacking who have persuaded
themselves, that the motion of the heavenly bodies gives rise to
harmony-all of which instances sufficiently show that everyone
judges of things according to the state of his brain, or rather
mistakes for things the forms of his imagination. We need no
longer wonder that there have arisen all the controversies we
have witnessed, and finally skepticism : for, although human
bodies in many respects agree, yet in very many others they
differ ; so that what seems good to one seems bad to another ;
what seems well ordered to one seems confused to another ; what
is pleasing to one displeases another, and so on. I need not
further enumerate, because this is not the place to treat the
subject at length, and also because the fact is sufficiently well
known. It is commonly said : "So many men, so many minds ;
everyone is wise in his own way ; brains differ as completely as
palates." All of which proverbs show, that men judge of things
according to their mental disposition, and rather imagine than
understand : for, if they understood phenomena, they would, as
mathematicians attest, be convinced, if not attracted, by what I
have urged.
We have now perceived, that all the explanations commonly
given of nature are mere modes of imagining, and do not indicate
the true nature of anything, but only the constitution of the
imagination ; and, although they have names, as though they were
entities, existing externally to the imagination, I call them
entities imaginary rather than real ; and, therefore, all
arguments against us drawn from such abstractions are easily
rebutted.
Many argue in this way. If all things follow from a
necessity of the absolutely perfect nature of God, why are there
so many imperfections in nature? such, for instance, as things
corrupt to the point of putridity, loathsome deformity,
confusion, evil, sin, &c. But these reasoners are, as I have
said, easily confuted, for the perfection of things is to be
reckoned only from their own nature and power ; things are not
more or less perfect, according as they delight or offend human
senses, or according as they are serviceable or repugnant to
mankind. To those who ask why God did not so create all men,
that they should be governed only by reason, I give no answer but
this : because matter was not lacking to him for the creation of
every degree of perfection from highest to lowest ; or, more
strictly, because the laws of his nature are so vast, as to
suffice for the production of everything conceivable by an
infinite intelligence, as I have shown in Prop. xvi.
Such are the misconceptions I have undertaken to note ; if
there are any more of the same sort, everyone may easily
dissipate them for himself with the aid of a little reflection.

Part II.
ON THE NATURE AND ORIGIN OF THE MIND

PREFACE

I now pass on to explaining the results, which must
necessarily follow from the essence of God, or of the eternal and
infinite being ; not, indeed, all of them (for we proved in Part
i., Prop. xvi., that an infinite number must follow in an
infinite number of ways), but only those which are able to lead
us, as it were by the hand, to the knowledge of the human mind
and its highest blessedness.

DEFINITIONS

DEFINITION I. By body I mean a mode which expresses in a certain
determinate manner the essence of God, in so far as he is
considered as an extended thing. (See Pt. i., Prop. xxv.,
Coroll.)

DEFINITION II. I consider as belonging to the essence of a thing
that, which being given, the thing is necessarily given also,
and, which being removed, the thing is necessarily removed also ;
in other words, that without which the thing, and which itself
without the thing, can neither be nor be conceived.

DEFINITION III. By idea, I mean the mental conception which is
formed by the mind as a thinking thing.
Explanation.-I say conception rather than perception, because
the word perception seems to imply that the mind is passive in
respect to the object ; whereas conception seems to express an
activity of the mind.

DEFINITION IV. By an adequate idea, I mean an idea which, in so
far as it is considered in itself, without relation to the
object, has all the properties or intrinsic marks of a true idea.
Explanation.-I say intrinsic, in order to exclude that mark
which is extrinsic, namely, the agreement between the idea and
its object (ideatum).

DEFINITION V. Duration is the indefinite continuance of
existing.
Explanation.-I say indefinite, because it cannot be
determined through the existence itself of the existing thing, or
by its efficient cause, which necessarily gives the existence of
the thing, but does not take it away.

DEFINITION VI. Reality and perfection I use as synonymous terms.

DEFINITION VII. By particular things, I mean things which are
finite and have a conditioned existence ; but if several
individual things concur in one action, so as to be all
simultaneously the effect of one cause, I consider them all, so
far, as one particular thing.

AXIOMS

I. The essence of man does not involve necessary existence, that
is, it may, in the order of nature, come to pass that this or
that man does or does not exist.

II. Man thinks.

III. Modes of thinking, such as love, desire, or any other of
the passions, do not take place, unless there be in the same
individual an idea of the thing loved, desired, &c. But the idea
can exist without the presence of any other mode of thinking.

IV. We perceive that a certain body is affected in many ways.

V. We feel and perceive no particular things, save bodies and
modes of thought.

N.B. The Postulates are given after the conclusion of Prop.
xiii.

PROPOSITIONS

PROP. I. Thought is an attribute of God, or God is a thinking
thing.
Proof.-Particular thoughts, or this and that thought, are
modes which, in a certain conditioned manner, express the nature
of God (Pt. i., Prop. xxv., Coroll.). God therefore possesses
the attribute (Pt. i., Def. v.) of which the concept is involved
in all particular thoughts, which latter are conceived thereby.
Thought, therefore, is one of the infinite attributes of God,
which express God's eternal and infinite essence (Pt. i., Def.
vi.). In other words, God is a thinking thing. Q.E.D.
Note.-This proposition is also evident from the fact, that we
are able to conceive an infinite thinking being. For, in
proportion as a thinking being is conceived as thinking more
thoughts, so is it conceived as containing more reality or
perfection. Therefore a being, which can think an infinite
number of things in an infinite number of ways, is, necessarily,
in respect of thinking, infinite. As, therefore, from the
consideration of thought alone, we conceive an infinite being,
thought is necessarily (Pt. i., Deff. iv. and vi.) one of the
infinite attributes of God, as we were desirous of showing.

PROP. II. Extension is an attribute of God, or God is an
extended thing.
Proof.-The proof of this proposition is similar to that of
the last.

PROP. III. In God there is necessarily the idea not only of his
essence, but also of all things which necessarily follow from his
essence.
Proof.-God (by the first Prop. of this Part) can think an
infinite number of things in infinite ways, or (what is the same
thing, by Prop. xvi., Part i.) can form the idea of his essence,
and of all things which necessarily follow therefrom. Now all
that is in the power of God necessarily is (Pt. i., Prop. xxxv.).
Therefore, such an idea as we are considering necessarily is, and
in God alone. Q.E.D. (Part i., Prop. xv.)
Note.-The multitude understand by the power of God the free
will of God, and the right over all things that exist, which
latter are accordingly generally considered as contingent. For
it is said that God has the power to destroy all things, and to
reduce them to nothing. Further, the power of God is very often
likened to the power of kings. But this doctrine we have refuted
(Pt. i., Prop. xxxii., Corolls. i. and ii.), and we have shown
(Part i., Prop. xvi.) that God acts by the same necessity, as
that by which he understands himself ; in other words, as it
follows from the necessity of the divine nature (as all admit),
that God understands himself, so also does it follow by the same
necessity, that God performs infinite acts in infinite ways. We
further showed (Part i., Prop. xxxiv.), that God's power is
identical with God's essence in action ; therefore it is as
impossible for us to conceive God as not acting, as to conceive
him as non-existent. If we might pursue the subject further, I
could point out, that the power which is commonly attributed to
God is not only human (as showing that God is conceived by the
multitude as a man, or in the likeness of a man), but involves a
negation of power. However, I am unwilling to go over the same
ground so often. I would only beg the reader again and again, to
turn over frequently in his mind what I have said in Part I from
Prop. xvi. to the end. No one will be able to follow my meaning,
unless he is scrupulously careful not to confound the power of
God with the human power and right of kings.

PROP. IV. The idea of God, from which an infinite number of
things follow in infinite ways, can only be one.
Proof.-Infinite intellect comprehends nothing save the
attributes of God and his modifications (Part i., Prop. xxx.).
Now God is one (Part i., Prop. xiv., Coroll.). Therefore the
idea of God, wherefrom an infinite number of things follow in
infinite ways, can only be one. Q.E.D.

PROP. V. The actual being of ideas owns God as its cause, only
in so far as he is considered as a thinking thing, not in so far
as he is unfolded in any other attribute ; that is, the ideas
both of the attributes of God and of particular things do not own
as their efficient cause their objects (ideata) or the things
perceived, but God himself in so far as he is a thinking thing.
Proof.-This proposition is evident from Prop. iii. of this
Part. We there drew the conclusion, that God can form the idea
of his essence, and of all things which follow necessarily
therefrom, solely because he is a thinking thing, and not because
he is the object of his own idea. Wherefore the actual being of
ideas owns for cause God, in so far as he is a thinking thing.
It may be differently proved as follows : the actual being of
ideas is (obviously) a mode of thought, that is (Part i., Prop.
xxv., Coroll.) a mode which expresses in a certain manner the
nature of God, in so far as he is a thinking thing, and therefore
(Part i., Prop. x.) involves the conception of no other attribute
of God, and consequently (by Part i., Ax. iv.) is not the effect
of any attribute save thought. Therefore the actual being of
ideas owns God as its cause, in so far as he is considered as a
thinking thing, &c. Q.E.D.

PROP. VI. The modes of any given attribute are caused by God, in
so far as he is considered through the attribute of which they
are modes, and not in so far as he is considered through any
other attribute.
Proof.-Each attribute is conceived through itself, without
any other (Part i., Prop. x.) ; wherefore the modes of each
attribute involve the conception of that attribute, but not of
any other. Thus (Part i., Ax. iv.) they are caused by God, only
in so far as he is considered through the attribute whose modes
they are, and not in so far as he is considered through any
other. Q.E.D.
Corollary.-Hence the actual being of things, which are not
modes of thought, does not follow from the divine nature, because
that nature has prior knowledge of the things. Things
represented in ideas follow, and are derived from their
particular attribute, in the same manner, and with the same
necessity as ideas follow (according to what we have shown) from
the attribute of thought.

PROP. VII. The order and connection of ideas is the same as the
order and connection of things.
Proof.-This proposition is evident from Part i., Ax. iv. For
the idea of everything that is caused depends on a knowledge of
the cause, whereof it is an effect.
Corollary.-Hence God's power of thinking is equal to his
realized power of action-that is, whatsoever follows from the
infinite nature of God in the world of extension (formaliter),
follows without exception in the same order and connection from
the idea of God in the world of thought (objective).
Note.-Before going any further, I wish to recall to mind what
has been pointed out above-namely, that whatsoever can be
perceived by the infinite intellect as constituting the essence
of substance, belongs altogether only to one substance :
consequently, substance thinking and substance extended are one
and the same substance, comprehended now through one attribute,
now through the other. So, also, a mode of extension and the
idea of that mode are one and the same thing, though expressed in
two ways. This truth seems to have been dimly recognized by
those Jews who maintained that God, God's intellect, and the
things understood by God are identical. For instance, a circle
existing in nature, and the idea of a circle existing, which is
also in God, are one and the same thing displayed through
different attributes. Thus, whether we conceive nature under the
attribute of extension, or under the attribute of thought, or
under any other attribute, we shall find the same order, or one
and the same chain of causes-that is, the same things following
in either case.
I said that God is the cause of an idea-for instance, of the
idea of a circle,-in so far as he is a thinking thing ; and of a
circle, in so far as he is an extended thing, simply because the
actual being of the idea of a circle can only be perceived as a
proximate cause through another mode of thinking, and that again
through another, and so on to infinity ; so that, so long as we
consider things as modes of thinking, we must explain the order
of the whole of nature, or the whole chain of causes, through the
attribute of thought only. And, in so far as we consider things
as modes of extension, we must explain the order of the whole of
nature through the attributes of extension only ; and so on, in
the case of the other attributes. Wherefore of things as they
are in themselves God is really the cause, inasmuch as he
consists of infinite attributes. I cannot for the present
explain my meaning more clearly.

PROP. VIII. The ideas of particular things, or of modes, that do
not exist, must be comprehended in the infinite idea of God, in
the same way as the formal essences of particular things or modes
are contained in the attributes of God.
Proof.-This proposition is evident from the last ; it is
understood more clearly from the preceding note.
Corollary.-Hence, so long as particular things do not exist,
except in so far as they are comprehended in the attributes of
God, their representations in thought or ideas do not exist,
except in so far as the infinite idea of God exists ; and when
particular things are said to exist, not only in so far as they
are involved in the attributes of God, but also in so far as they
are said to continue, their ideas will also involve existence,
through which they are said to continue.
Note.-If anyone desires an example to throw more light on
this question, I shall, I fear, not be able to give him any,
which adequately explains the thing of which I here speak,
inasmuch as it is unique ; however, I will endeavour to
illustrate it as far as possible. The nature of a circle is such
that if any number of straight lines intersect within it, the
rectangles formed by their segments will be equal to one another
; thus, infinite equal rectangles are contained in a circle. Yet
none of these rectangles can be said to exist, except in so far
as the circle exists ; nor can the idea of any of these
rectangles be said to exist, except in so far as they are
comprehended in the idea of the circle. Let us grant that, from
this infinite number of rectangles, two only exist. The ideas of
these two not only exist, in so far as they are contained in the
idea of the circle, but also as they involve the existence of
those rectangles ; wherefore they are distinguished from the
remaining ideas of the remaining rectangles.

PROP. IX. The idea of an individual thing actually existing is
caused by God, not in so far as he is infinite, but in so far as
he is considered as affected by another idea of a thing actually
existing, of which he is the cause, in so far as he is affected
by a third idea, and so on to infinity.
Proof.-The idea of an individual thing actually existing is
an individual mode of thinking, and is distinct from other modes
(by the Corollary and note to Prop. viii. of this part) ; thus
(by Prop. vi. of this part) it is caused by God, in so far only
as he is a thinking thing. But not (by Prop. xxviii. of Part i.)
in so far as he is a thing thinking absolutely, only in so far as
he is considered as affected by another mode of thinking ; and he
is the cause of this latter, as being affected by a third, and so
on to infinity. Now, the order and connection of ideas is (by
Prop. vii. of this book) the same as the order and connection of
causes. Therefore of a given individual idea another individual
idea, or God, in so far as he is considered as modified by that
idea, is the cause ; and of this second idea God is the cause, in
so far as he is affected by another idea, and so on to infinity.
Q.E.D.
Corollary.-Whatsoever takes place in the individual object of
any idea, the knowledge thereof is in God, in so far only as he
has the idea of the object.
Proof.-Whatsoever takes place in the object of any idea, its
idea is in God (by Prop. iii. of this part), not in so far as he
is infinite, but in so far as he is considered as affected by
another idea of an individual thing (by the last Prop.) ; but (by
Prop. vii. of this part) the order and connection of ideas is the
same as the order and connection of things. The knowledge,
therefore, of that which takes place in any individual object
will be in God, in so far only as he has the idea of that object.
Q.E.D.

PROP. X. The being of substance does not appertain to the
essence of man-in other words, substance does not constitute the
actual being2 of man.
Proof.-The being of substance involves necessary existence
(Part i., Prop. vii.). If, therefore, the being of substance
appertains to the essence of man, substance being granted, man
would necessarily be granted also (II.Def.ii.), and,
consequently, man would necessarily exist, which is absurd
(II.Ax.i.). Therefore, &c. Q.E.D.
Note.-This proposition may also be proved from I.v., in which
it is shown that there cannot be two substances of the same
nature ; for as there may be many men, the being of substance is
not that which constitutes the actual being of man. Again, the
proposition is evident from the other properties of
substance-namely, that substance is in its nature infinite,
immutable, indivisible, &c., as anyone may see for himself.
Corollary.-Hence it follows, that the essence of man is
constituted by certain modifications of the attributes of God.
For (by the last Prop.) the being of substance does not belong to
the essence of man. That essence therefore (by i. 15) is
something which is in God, and which without God can neither be
nor be conceived, whether it be a modification (i. 25. Coroll.),
or a mode which expresses God's nature in a certain conditioned
manner.
Note.-Everyone must surely admit, that nothing can be or be
conceived without God. All men agree that God is the one and
only cause of all things, both of their essence and of their
existence ; that is, God is not only the cause of things in
respect to their being made (secundum fieri), but also in respect
to their being (secundum esse).
At the same time many assert, that that, without which a
thing cannot be nor be conceived, belongs to the essence of that
thing ; wherefore they believe that either the nature of God
appertains to the essence of created things, or else that created
things can be or be conceived without God ; or else, as is more
probably the case, they hold inconsistent doctrines. I think the
cause for such confusion is mainly, that they do not keep to the
proper order of philosophic thinking. The nature of God, which
should be reflected on first, inasmuch as it is prior both in the
order of knowledge and the order of nature, they have taken to be
last in the order of knowledge, and have put into the first place
what they call the objects of sensation ; hence, while they are
considering natural phenomena, they give no attention at all to
the divine nature, and, when afterwards they apply their mind to
the study of the divine nature, they are quite unable to bear in
mind the first hypotheses, with which they have overlaid the
knowledge of natural phenomena, inasmuch as such hypotheses are
no help towards understanding the divine nature. So that it is
hardly to be wondered at, that these persons contradict
themselves freely.
However, I pass over this point. My intention her was only
to give a reason for not saying, that that, without which a thing
cannot be or be conceived, belongs to the essence of that thing :
individual things cannot be or be conceived without God, yet God
does not appertain to their essence. I said that "I considered
as belonging to the essence of a thing that, which being given,
the thing is necessarily given also, and which being removed, the
thing is necessarily removed also ; or that without which the
thing, and which itself without the thing can neither be nor be
conceived." (II. Def. ii.)

PROP. XI. The first element, which constitutes the actual being
of the human mind, is the idea of some particular thing actually
existing.
Proof.-The essence of man (by the Coroll. of the last Prop.)
is constituted by certain modes of the attributes of God, namely
(by II. Ax. ii.), by the modes of thinking, of all which (by II.
Ax. iii.) the idea is prior in nature, and, when the idea is
given, the other modes (namely, those of which the idea is prior
in nature) must be in the same individual (by the same Axiom).
Therefore an idea is the first element constituting the human
mind. But not the idea of a non-existent thing, for then (II.
viii. Coroll.) the idea itself cannot be said to exist ; it must
therefore be the idea of something actually existing. But not of
an infinite thing. For an infinite thing (I.xxi., xxii.), must
always necessarily exist ; this would (by II. Ax. i.) involve an
absurdity. Therefore the first element, which constitutes the
actual being of the human mind, is the idea of something actually
existing. Q.E.D.
Corollary.-Hence it follows, that the human mind is part of
the infinite intellect of God ; thus when we say, that the human
mind perceives this or that, we make the assertion, that God has
this or that idea, not in so far as he is infinite, but in so far
as he is displayed through the nature of the human mind, or in so
far as he constitutes the essence of the human mind ; and when we
say that God has this or that idea, not only in so far as he
constitutes the essence of the human mind, but also in so far as
he, simultaneously with the human mind, has the further idea of
another thing, we assert that the human mind perceives a thing in
part or inadequately.
Note.-Here, I doubt not, readers will come to a stand, and
will call to mind many things which will cause them to hesitate ;
I therefore beg them to accompany me slowly, step by step, and
not to pronounce on my statements, till they have read to the
end.

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.
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.

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