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
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