Does St. Thomas Aquinas' cosmological argument from contingency assume that an infinite regress of contingent things is impossible?

Question

The Third Way: Argument from Possibility and Necessity (Reductio argument)

1. We find in nature things that are possible to be and not to be, that come into being and go out of being i.e., contingent beings.

2. Assume that every being is a contingent being.

3. For each contingent being, there is a time it does not exist.

4. Therefore it is impossible for these always to exist.

5. Therefore there could have been a time when no things existed.

6. Therefore at that time there would have been nothing to bring the currently existing contingent beings into existence.

7. Therefore, nothing would be in existence now.

8. We have reached an absurd result from assuming that every being is a contingent being.

9. Therefore not every being is a contingent being.

C. Therefore some being exists of its own necessity, and does not receive its existence from another being, but rather causes them. This all men speak of as God.

Premise 3 states, 'For each contingent being, there is a time it does not exist.' This doesn't negate the possibility of an infinite regress, as each contingent thing would, at one point, not have existed in an infinite chain of causation.

The argument doesn't seem prove a time in which nothing existed, he states in premise 5, 'Therefore there could have been a time when no things existed.' Notice Aquinas uses the word 'could', implying the possibility of this not occurring.

Answer 1

From the original argument, Summa Theologica Part I, Question 2, Article 3:

"We find in nature things that are possible to be and not to be, since they are found to be generated, and to corrupt, and consequently, they are possible to be and not to be. But it is impossible for these always to exist, for that which is possible not to be at some time is not. Therefore, if everything is possible not to be, then at one time there could have been nothing in existence"

Aquinas seems to argue about the totality of everything "contingent", not about "contingent" things one by one. One may object to such compositional treatment of "contingency" (the totality of "contingencies" is itself "contingent"), but it is more understandable given the Aristotelian "contingency" he worked with. Note that it is very different from the modern term in modal logic, see What do necessity and possibility mean in Aquinas' Third Way argument for the existence of God? Thomist "possibility" comes from Aristotle's potentiality in actual time, not from detached possible worlds unto themselves.

Not that it matters here, but Aquinas would deny an infinite chain of contingent beings causing each other as well. Aristotle's thesis on this was coined into a Latin maxim, infinitum actu non datur, there is no actual infinity. Aristotle himself uses this as a prohibition on infinite regress in multiple places, particularly in his argument for the unmoved mover, a protoype of the cosmological argument. It does come into play in the later part of Aquinas's argument as well, but concerning necessary things:

"Therefore, not all beings are merely possible, but there must exist something the existence of which is necessary. But every necessary thing either has its necessity caused by another, or not. Now it is impossible to go on to infinity in necessary things which have their necessity caused by another, as has been already proved in regard to efficient causes. Therefore we cannot but postulate the existence of some being having of itself its own necessity, and not receiving it from another, but rather causing in others their necessity. This all men speak of as God."

As Struik writes in Concise History of Mathematics:

"The scholastic writers of the Middle Ages, especially St. Thomas Aquinas, accepted Aristotle's infinitum actu non datur, but considered every continuum as potentially divisible ad infinitum."

See an interesting discussion As to Aristotel's "Infinitum Actu Non Datur" Thesis on Historia Matematica.