Whether Our Intellect Can Know the Infinite?
Objection 1: It would seem that our intellect can know the infinite.
For God excels all infinite things. But our intellect can know God,
as we have said above (Q. 12, A. 1). Much more, therefore, can our
intellect know all other infinite things.
Obj. 2: Further, our intellect can naturally know genera and
species. But there is an infinity of species in some genera, as in
number, proportion, and figure. Therefore our intellect can know
the infinite.
Obj. 3: Further, if one body can coexist with another in the same
place, there is nothing to prevent an infinite number of bodies being
in one place. But one intelligible species can exist with another in
the same intellect, for many things can be habitually known at the
same time. Therefore our intellect can have an habitual knowledge of
an infinite number of things.
Obj. 4: Further, as the intellect is not a corporeal faculty, as we
have said (Q. 76, A. 1), it appears to be an infinite power. But an
infinite power has a capacity for an infinite object. Therefore our
intellect can know the infinite.
_On the contrary,_ It is said (Phys. i, 4) that "the infinite,
considered as such, is unknown."
_I answer that,_ Since a faculty and its object are proportional to
each other, the intellect must be related to the infinite, as is its
object, which is the quiddity of a material thing. Now in material
things the infinite does not exist actually, but only potentially, in
the sense of one succeeding another, as is said Phys. iii, 6.
Therefore infinity is potentially in our mind through its considering
successively one thing after another: because never does our
intellect understand so many things, that it cannot understand more.
On the other hand, our intellect cannot understand the infinite
either actually or habitually. Not actually, for our intellect cannot
know actually at the same time, except what it knows through one
species. But the infinite is not represented by one species, for if
it were it would be something whole and complete. Consequently it
cannot be understood except by a successive consideration of one part
after another, as is clear from its definition (Phys. iii, 6): for
the infinite is that "from which, however much we may take, there
always remains something to be taken." Thus the infinite could not be
known actually, unless all its parts were counted: which is
impossible.
For the same reason we cannot have habitual knowledge of the infinite:
because in us habitual knowledge results from actual consideration:
since by understanding we acquire knowledge, as is said _Ethic._ ii, 1.
Wherefore it would not be possible for us to have a habit of an
infinity of things distinctly known, unless we had already considered
the entire infinity thereof, counting them according to the succession
of our knowledge: which is impossible. And therefore neither actually
nor habitually can our intellect know the infinite, but only
potentially as explained above.
Reply Obj. 1: As we have said above (Q. 7, A. 1), God is called
infinite, because He is a form unlimited by matter; whereas in
material things, the term "infinite" is applied to that which is
deprived of any formal term. And form being known in itself, whereas
matter cannot be known without form, it follows that the material
infinite is in itself unknowable. But the formal infinite, God, is
of Himself known; but He is unknown to us by reason of our feeble
intellect, which in its present state has a natural aptitude for
material objects only. Therefore we cannot know God in our present
life except through material effects. In the future life this defect
of intellect will be removed by the state of glory, when we shall be
able to see the Essence of God Himself, but without being able to
comprehend Him.
Reply Obj. 2: The nature of our mind is to know species abstracted
from phantasms; therefore it cannot know actually or habitually
species of numbers or figures that are not in the imagination, except
in a general way and in their universal principles; and this is to
know them potentially and confusedly.
Reply Obj. 3: If two or more bodies were in the same place, there
would be no need for them to occupy the place successively, in order
for the things placed to be counted according to this succession of
occupation. On the other hand, the intelligible species enter into
our intellect successively; since many things cannot be actually
understood at the same time: and therefore there must be a definite
and not an infinite number of species in our intellect.
Reply Obj. 4: As our intellect is infinite in power, so does it know
the infinite. For its power is indeed infinite inasmuch as it is not
terminated by corporeal matter. Moreover it can know the universal,
which is abstracted from individual matter, and which consequently is
not limited to one individual, but, considered in itself, extends to
an infinite number of individuals.
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