>>>>>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.
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 (Cor. 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 Cor. 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.
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.
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., Cor. 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 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., Cor. 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.
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.,
Cor. 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.
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. vii.). 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.