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Objection 1: It seems that God is not infinite. For everything
infinite is imperfect, as the Philosopher says; because it has parts
and matter, as is said in Phys. iii. But God is most perfect;
therefore He is not infinite.
Objection 2: Further, according to the Philosopher (Phys. i),
finite and infinite belong to quantity. But there is no quantity in
God, for He is not a body, as was shown above (Question 3,
Article 1). Therefore it does not belong to Him to be infinite.
Objection 3: Further, what is here in such a way as not to be
elsewhere, is finite according to place. Therefore that which is a
thing in such a way as not to be another thing, is finite according to
substance. But God is this, and not another; for He is not a stone
or wood. Therefore God is not infinite in substance.
On the contrary, Damascene says (De Fide Orth. i, 4) that
"God is infinite and eternal, and boundless."
I answer that, All the ancient philosophers attribute infinitude to
the first principle, as is said (Phys. iii), and with reason; for
they considered that things flow forth infinitely from the first
principle. But because some erred concerning the nature of the first
principle, as a consequence they erred also concerning its infinity;
forasmuch as they asserted that matter was the first principle;
consequently they attributed to the first principle a material infinity
to the effect that some infinite body was the first principle of
things.
We must consider therefore that a thing is called infinite because it
is not finite. Now matter is in a way made finite by form, and the
form by matter. Matter indeed is made finite by form, inasmuch as
matter, before it receives its form, is in potentiality to many
forms; but on receiving a form, it is terminated by that one.
Again, form is made finite by matter, inasmuch as form, considered
in itself, is common to many; but when received in matter, the form
is determined to this one particular thing. Now matter is perfected by
the form by which it is made finite; therefore infinite as attributed
to matter, has the nature of something imperfect; for it is as it were
formless matter. On the other hand, form is not made perfect by
matter, but rather is contracted by matter; and hence the infinite,
regarded on the part of the form not determined by matter, has the
nature of something perfect. Now being is the most formal of all
things, as appears from what is shown above (Question 4, Article
1, Objection 3). Since therefore the divine being is not a being
received in anything, but He is His own subsistent being as was shown
above (Question 3, Article 4), it is clear that God Himself is
infinite and perfect.
From this appears the Reply to the First Objection.
Reply to Objection 2: Quantity is terminated by its form, which
can be seen in the fact that a figure which consists in quantity
terminated, is a kind of quantitative form. Hence the infinite of
quantity is the infinite of matter; such a kind of infinite cannot be
attributed to God; as was said above, in this article.
Reply to Objection 3: The fact that the being of God is
self-subsisting, not received in any other, and is thus called
infinite, shows Him to be distinguished from all other beings, and
all others to be apart from Him. Even so, were there such a thing as
a self-subsisting whiteness, the very fact that it did not exist in
anything else, would make it distinct from every other whiteness
existing in a subject.
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