The Ethics | Page 8

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