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Objection 1: It seems that God cannot know infinite things. For
the infinite, as such, is unknown; since the infinite is that which,
"to those who measure it, leaves always something more to be
measured," as the Philosopher says (Phys. iii). Moreover,
Augustine says (De Civ. Dei xii) that "whatever is comprehended
by knowledge, is bounded by the comprehension of the knower." Now
infinite things have no boundary. Therefore they cannot be
comprehended by the knowledge of God.
Objection 2: Further, if we say that things infinite in themselves
are finite in God's knowledge, against this it may be urged that the
essence of the infinite is that it is untraversable, and the finite
that it is traversable, as said in Phys. iii. But the infinite is
not traversable either by the finite or by the infinite, as is proved
in Phys. vi. Therefore the infinite cannot be bounded by the
finite, nor even by the infinite; and so the infinite cannot be finite
in God's knowledge, which is infinite.
Objection 3: Further, the knowledge of God is the measure of what
is known. But it is contrary to the essence of the infinite that it be
measured. Therefore infinite things cannot be known by God.
On the contrary, Augustine says (De Civ. Dei xii), "Although
we cannot number the infinite, nevertheless it can be comprehended by
Him whose knowledge has no bounds."
I answer that, Since God knows not only things actual but also
things possible to Himself or to created things, as shown above
(Article 9), and as these must be infinite, it must be held that
He knows infinite things. Although the knowledge of vision which has
relation only to things that are, or will be, or were, is not of
infinite things, as some say, for we do not say that the world is
eternal, nor that generation and movement will go on for ever, so that
individuals be infinitely multiplied; yet, if we consider more
attentively, we must hold that God knows infinite things even by the
knowledge of vision. For God knows even the thoughts and affections
of hearts, which will be multiplied to infinity as rational creatures
go on for ever.
The reason of this is to be found in the fact that the knowledge of
every knower is measured by the mode of the form which is the principle
of knowledge. For the sensible image in sense is the likeness of only
one individual thing, and can give the knowledge of only one
individual. But the intelligible species of our intellect is the
likeness of the thing as regards its specific nature, which is
participable by infinite particulars; hence our intellect by the
intelligible species of man in a certain way knows infinite men; not
however as distinguished from each other, but as communicating in the
nature of the species; and the reason is because the intelligible
species of our intellect is the likeness of man not as to the individual
principles, but as to the principles of the species. On the other
hand, the divine essence, whereby the divine intellect understands,
is a sufficing likeness of all things that are, or can be, not only as
regards the universal principles, but also as regards the principles
proper to each one, as shown above. Hence it follows that the
knowledge of God extends to infinite things, even as distinct from
each other.
Reply to Objection 1: The idea of the infinite pertains to
quantity, as the Philosopher says (Phys. i). But the idea of
quantity implies the order of parts. Therefore to know the infinite
according to the mode of the infinite is to know part after part; and
in this way the infinite cannot be known; for whatever quantity of
parts be taken, there will always remain something else outside. But
God does not know the infinite or infinite things, as if He
enumerated part after part; since He knows all things simultaneously,
and not successively, as said above (Article 7). Hence there is
nothing to prevent Him from knowing infinite things.
Reply to Objection 2: Transition imports a certain succession of
parts; and hence it is that the infinite cannot be traversed by the
finite, nor by the infinite. But equality suffices for
comprehension, because that is said to be comprehended which has
nothing outside the comprehender. Hence it is not against the idea of
the infinite to be comprehended by the infinite. And so, what is
infinite in itself can be called finite to the knowledge of God as
comprehended; but not as if it were traversable.
Reply to Objection 3: The knowledge of God is the measure of
things, not quantitatively, for the infinite is not subject to this
kind of measure; but it is the measure of the essence and truth of
things. For everything has truth of nature according to the degree in
which it imitates the knowledge of God, as the thing made by art
agrees with the art. Granted, however, an actually infinite number
of things, for instance, an infinitude of men, or an infinitude in
continuous quantity, as an infinitude of air, as some of the ancients
held; yet it is manifest that these would have a determinate and finite
being, because their being would be limited to some determinate
nature. Hence they would be measurable as regards the knowledge of
God.
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