Tuesday, June 17, 2014

Kinds of Infinity in Creatures


1.  Thomas continues his discussion of God’s infinity by asking whether any thing other than God can be infinite by its essence.  The main function of this article is to work out the kinds and degrees of infinity in creatures.

2.  Thomas provides three arguments to show that things other than God can be essentially infinite.  The first is from God’s power: since God himself is infinite, and a thing’s power is proportionate to what it is, God could create an infinite effect.

3.  The second objection is from the nature of the intellect.  As Aristotle says, the mind is potentially all things. Thus, since the mind can come to know what is universal and what extends to everything, it can be said to have an infinite power.  But nothing can have an infinite power unless its essence is also infinite, since a thing’s power is proportionate to its essence.  Thus every created intellectual substance is infinite in its essence.

4.  The third objection is from the nature of prime matter.  Prime matter, recall, is pure potency without any form.  Prime matter, he says, is infinite, but we have earlier established that it is distinct from God.  Therefore something other than God is infinite.

5.  His Sed Contra is taken from Aristotle, the third book of the Physics.  Since the infinite has no beginning, and everything other than God has its origin in God, nothing other than God can be said to be absolutely infinite.

6.  In the Corpus he clarifies.  Things other than God can be said to be infinite in a qualified way (secundum quid) but not absolutely (simpliciter).  He considers three cases: material things, forms received in matter, and separate forms subsisting in themselves.  In the case of material things, though they are relatively infinite by their potency to an infinite variety of forms, still actually they are limited by the forms they presently possess, and no material being is utterly unformed, since as we have discussed elsewhere, to be utterly unformed would be to cease to exist.  In the case of forms received in matter, there is no infinity at all, since the form itself is limited by its proper act, and it is further limited by being received into matter, since this particular matter receives this particular form only to the extent that it is capable, as determined both by its quality and by its quantity.  Finally, in the case of separate, subsisting forms, (of which the angels are examples, according to St. Thomas), though there is an infinity because the form is not limited by its reception in matter, still the form is limited by its determination to a particular nature, and by the fact that its existence is received from another.  Thus unlike God’s act, which has an utterly unlimited nature, and in which act and essence are one, the angels are not absolutely infinite.

7.  He answers the first objection by observing that it is contrary to the notion of a made thing for its essence to be identical with its existence, since otherwise it would not be made.  And as God cannot make something so that it is unmade (since this is absurd), it follows that he cannot make something which, being utterly unlimited in its being, has its very existence from its essence.  He can, however, make things which are relatively infinite, as discussed above.

8.  The infinity of the intellect is that of a form not received in matter: absolutely separate in the case of angels, and separate by not being the act of any bodily organ, in the case of the human intellect.  Both of these will be discussed extensively in the later questions of the Prima Pars.

9.  He answers the third objection by pointing out that prime matter is not an actually existing thing, and its infinity is both a potential infinity, and is infinite only secundum quid, because prime matter is in potency to become only finite, natural things (and could never become God).


- God, being infinitely powerful, could create an infinite being.
- The intellect is capable of receiving all forms, and is therefore infinite.
- Prime matter is infinite.

- Things other than God can be called infinite secundum quid, but not simpliciter.
- Existing material things are infinite in their potency to become an infinite variety of things, but are limited by their possession of a particular form.
- Forms received in matter are finite both on account of the matter in which they are received, and by their own essential finitude (as to their nature, existence, origin).
- Separate, subsistent forms are infinite by their separation from matter, but finite inasmuch as their existence is received and terminated by a particular, finite essence.

- To be infinite simpliciter a thing would have to supply its own act of existing.  But this is by definition impossible for a creature.
- The infinity of the intellect is that of a separate form.
- Primary matter does not exist in itself; its infinity is both potential and absolutely limited.

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