Whether God Can Know Infinite Things?
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.
Obj. 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.
Obj. 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 (A.
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 Obj. 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 (A. 7). Hence there is nothing to prevent Him from
knowing infinite things.
Reply Obj. 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 Obj. 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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