Adding translation of "potential" to "ad infinitum"

Question

The phrase "ad infinitum" is often used in texts that are otherwise non-Latin. I would like to use a variation of this phrase in an English text. In philosophy of mathematics there is a distinction, going back to Aristotle, between potential infinity and actual infinity. I would like to make it clear that I'm referring to the former kind. Can I write "ad infinitum potentialis" or something like that (sorry if my guess is completely of the mark - I know next to nothing about Latin).

The full sentence would be as follows: "The claim is that the free creation of sequences - an arbitrary choice of an element, followed by another arbitrary choice of an element, ad infinitum potentialis - can result in sequences that cannot be defined."

Answer 1

I would suggest ad infinitum in potentia. The phrase infinitum in potentia seems to be quite established in philosophy and natural sciences, as you can see from the hits in that link. For instance, this text discusses the modes of being infinity (Chapter VI is titled quonam modo sit infinitum). One paragraph mentions infinitum in potentia and infinitum actu. So this distinguished between the potential and the actual infinity. A similar distinction between potentia and actu is found in Aquinas, (e.g. in the phrase In Deo nihil est in potentia quod non sit in actu, here).

Actually, according to the book "Guide to Latin in International Law", in potentia seems to be a Latin phrase. That article (in the full access version) states its meaning as:

In potentiality ... Contrast with In actu.

Meanwhile, In actu entry defines this expression as "In practice; in action". Both entries have this example, showing the contrast:

As regards the pactum de compromittendo, international law has made certain progress in developing the formulas regulating passage from arbitration in potentia to arbitration in actu, particularly in respect of the appointment of arbitrators by the act of a third party.

In potentia also has the benefit of being an English phrase meaning potentially.