Hegel's Lectures on the History of Philosophy: Volume 3 (of 3)
Georg Hegel · en
“The inequalities of the space between A B and C D exceed every number;
and yet the space which lies between is not so very great.” That is to
say, if I wish to determine them all, I must enter upon an infinite
series. This “beyond” always, however, remains defective, is always
affected with negation; and yet this false infinite is there to hand,
circumscribed, affirmative, actual and present in that plane as a
complete space between the two circles. Or a finite line consists of
an infinite number of points; and yet the line is present here and
determined; the “beyond” of the infinite number of points, which are not
complete, is in it complete and called back into unity. The infinite
should be represented as actually present, and this comes to pass in the
Notion of the cause of itself, which is therefore the true infinity. As
soon as the cause has something else opposed to it—the effect—finitude
is present; but here this something else is at the same time abrogated
and it becomes once more the cause itself. The affirmative is thus
negation of negation, since, according to the well-known grammatical
rule, _duplex negatio affirmat_. In the same way Spinoza’s earlier
definitions have also the infinite already implied in them, for instance
in the case of the just mentioned cause of itself, inasmuch as he defines
it as that whose essence involves existence (_supra_, p. 258). Notion
and existence are each the Beyond of the other; but cause of itself, as
thus including them, is really the carrying back of this “beyond” into
unity. Or (_supra_, p. 259) “Substance is that which is in itself and is
conceived from itself;” that is the same unity of Notion and existence.
The infinite is in the same way in itself and has also its Notion in
itself; its Notion is its Being, and its Being its Notion; true infinity
is therefore to be found in Spinoza. But he has no consciousness of this;
he has not recognized this Notion as absolute Notion, and therefore has
not expressed it as a moment of true existence; for with him the Notion
falls outside of existence, into the thought of existence.
g. Finally Spinoza says in the seventh place: “God is a Being absolutely
infinite, _i.e._ a substance consisting of infinite attributes, each of
which expresses an eternal and infinite essence.” Does substance, one
might here ask, possess an infinite number of attributes? But as with
Spinoza there are only two attributes, thought and extension, with which
he invests God, “infinite” is not to be taken here in the sense of the
indeterminate many, but positively, as a circle is perfect infinity in
itself.