Whether Anything but God Can Be Essentially Infinite?
Objection 1: It seems that something else besides God can be
essentially infinite. For the power of anything is proportioned to its
essence. Now if the essence of God is infinite, His power must also be
infinite. Therefore He can produce an infinite effect, since the
extent of a power is known by its effect.
Obj. 2: Further, whatever has infinite power, has an infinite
essence. Now the created intellect has an infinite power; for it
apprehends the universal, which can extend itself to an infinitude of
singular things. Therefore every created intellectual substance is
infinite.
Obj. 3: Further, primary matter is something other than God, as
was shown above (Q. 3, A. 8). But primary matter is infinite.
Therefore something besides God can be infinite.
_On the contrary,_ The infinite cannot have a beginning, as said in
Phys. iii. But everything outside God is from God as from its first
principle. Therefore besides God nothing can be infinite.
_I answer that,_ Things other than God can be relatively infinite, but
not absolutely infinite. For with regard to infinite as applied to
matter, it is manifest that everything actually existing possesses a
form; and thus its matter is determined by form. But because matter,
considered as existing under some substantial form, remains in
potentiality to many accidental forms, which is absolutely finite can
be relatively infinite; as, for example, wood is finite according to
its own form, but still it is relatively infinite, inasmuch as it is
in potentiality to an infinite number of shapes. But if we speak of
the infinite in reference to form, it is manifest that those things,
the forms of which are in matter, are absolutely finite, and in no way
infinite. If, however, any created forms are not received into matter,
but are self-subsisting, as some think is the case with angels, these
will be relatively infinite, inasmuch as such kinds of forms are not
terminated, nor contracted by any matter. But because a created form
thus subsisting has being, and yet is not its own being, it follows
that its being is received and contracted to a determinate nature.
Hence it cannot be absolutely infinite.
Reply Obj. 1: It is against the nature of a made thing for its
essence to be its existence; because subsisting being is not a created
being; hence it is against the nature of a made thing to be absolutely
infinite. Therefore, as God, although He has infinite power, cannot
make a thing to be not made (for this would imply that two
contradictories are true at the same time), so likewise He cannot make
anything to be absolutely infinite.
Reply Obj. 2: The fact that the power of the intellect extends
itself in a way to infinite things, is because the intellect is a form
not in matter, but either wholly separated from matter, as is the
angelic substance, or at least an intellectual power, which is not the
act of any organ, in the intellectual soul joined to a body.
Reply Obj. 3: Primary matter does not exist by itself in
nature, since it is not actually being, but potentially only; hence it
is something concreated rather than created. Nevertheless, primary
matter even as a potentiality is not absolutely infinite, but
relatively, because its potentiality extends only to natural forms.
_______________________