The Principle of Contingent Causation: The Impossibility of Infinite Regress.

[Belacqua]

Aquinas does not object in principle to an infinite regress. He argues that the existence of the world, however, cannot be attributed to such a series.

[...] Aquinas’ objection comes from the wholly derivative nature of essentially ordered series, not from a general antipathy to infinite series. Indeed, in his commentary on Aristotle’s Metaphysics Aquinas, following Aristotle, explicitly states that whether the intermediate causes are finite or infinite in number makes no difference to whether there must be a first cause: “Nor again does it make any difference whether there are a finite or infinite number of intermediates, because so long as they have the nature of an intermediate they cannot be the first cause of motion.”35 Aquinas does not reject infinite essentially ordered causal series because he rejects series that go on to infinity.36 Indeed, Aquinas allows for several types of infinite series, including certain sorts of infinite causal series.

Similarly, Aquinas does not reject these series because they would lack a temporal beginning, as is clear from his position that reason cannot demonstrate that the world has a temporal beginning.37 Now these infinite series would all be actually infinite, since all their members would exist at once, and Aquinas does give a general argument against the possibility of any simultaneously actual infinite multitude later in the ST.38 However, even if Aquinas would deny that there can be a simultaneously actual infinite multitude, that denial is not the grounds for his rejection of infinite essentially ordered causal series. As I just noted, he is happy to wave his objection to the actual infinite in order to make clear the fundamental reason for rejecting infinite essentially ordered causal series. Moreover, in later texts Aquinas seems to allow for the possibility of an actually infinite multitude of spiritual entities.39 This suggests that Aquinas would concede that an actually infinite multitude of necessary beings having their necessity from another, such as angels, is possible. Indeed, later in the Summa Aquinas also allows that certain causal series that are not wholly derivative can be infinite while in the Quaestiones de quolibet he suggests that the existence of an actual infinite would not be contrary to God’s power.40

https://philarchive.org/archive/COHTMB