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 ;