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; 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.
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.
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.
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