This underscores the proof-of-concept problem for infinitism:
Grant that it’s possible that every element of an infinite series could be comprehensible to us. But what evidence is there that there actually are such series? And what evidence is there that, for at least most of the things that we justifiably believe (or most of the things we know, or most of the acceptable reasoning we engage in), there is a properly structured infinite series available to us?
Or consider the defining proposition of infinitism: "There are infinite series of justifying reasons for beliefs." Is the belief in this proposition supported by a given infinite series of its own? But (exclusionary) infinitism is presented either (A) as inferred from the regress problem itself, as in:
- Foundationalism, coherentism, or infinitism is true. (More sophisticated: foundationalism, coherentism, infinitism, foundherentism, infinitary coherentism, infinitary foundationalism, or all three together, are true.)
- Foundationalism and coherentism (or...) are not true.
- Therefore, infinitism is true.
... which is just about as compact an inference as can be (perhaps the infinitist can claim that there's an infinite amount of reasoning packed into justifying (2)); or (B) the infinitist doesn't infer their position's truth as a contrast with the falsity of its "competitors," but non-inferentially justifies belief in infinite sequences of inferences by erotetic reflection. I.e. they have non-inferential, intuitive awareness of infinite sequences of questions a priori, and in this awareness can see the possibility of infinite sequences of answers, answers joined together in an infinite array of logical relations. Kant says in the Transcendental Dialectic:
This point—though a mere idea (focus imaginarius), that is, not a point from which the conceptions of the understanding do really proceed, for it lies beyond the sphere of possible experience—serves, notwithstanding, to give to these conceptions the greatest possible unity combined with the greatest possible extension. Hence arises the natural illusion which induces us to believe that these lines proceed from an object which lies out of the sphere of empirical cognition, just as objects reflected in a mirror appear to be behind it. But this illusion—which we may hinder from imposing upon us—is necessary and unavoidable, if we desire to see, not only those objects which lie before us, but those which are at a great distance behind us; that is to say, when, in the present case, we direct the aims of the understanding, beyond every given experience, towards an extension as great as can possibly be attained.
And that is the essence of transcendental illusion in cosmology: to conflate the existence of an infinite sequence of questions-in-themselves with the existence of an infinite sequence of requisite answers in experience. But the rationality, such as it is, of the questions, is not constitutive of a rational expectation on infinitely complete answers; the apriority of the generic sequence of questions apparently turns out empty of possible physical content quickly enough, so although we can see that we can ask, "Why is 1 + 1 = 2?" or, "Why do things exist?" we can also see that the very presuppositions of being able to ask such questions correspond to self-answering questions at this stage in the regress.
To be sure, then, in philosophy they have found ways to question whether 1 + 1 = 2, or if I remember correctly Bertrand Russell had a whole chapter's worth of analysis of the word "the" somewhere; and there are other fine points of uncertainty besides, throughout the literature. But so suppose you had, "Why are there why-questions at all?" in play: if the question somehow answers itself, then in questioning the answer to the question, one will not move backwards down the line of a regress, but just hover above the terminal erotetic node, here.
To illustrate:
- Why are there why-questions at all?
- "Why are there why-questions at all?" is why there are why-questions at all.
- "Why (2)?" = (1).
So (1) is an axiomatic question which, if its own answer, halts the regress of questions (not the regress of assertions) in that the act of questioning the answer to the self-answering question cycles to (1); this is a self-singleton structure, as it were. At any rate, we don't need to fall to skepticism for seeing that foundationalism, coherentism, and infinitism are, individually, insufficient to solve the regress problem altogether; all of them together can solve any regress problem. Here, it is the self-cycling of (1) that brings in a coherentistic moment, but then the ability to infer assertions from questions (via transcendental argument) grounds a foundationalistic moment, too; and all this is bracketed by the potential infinity of the rest of the erotetic series in itself, which is an infinitistic moment.
