Are transcendental and indispensability arguments reciprocally structured?

Question

This question occurred to me in the course of addressing a recent question about what counts as evidence in philosophy. There, I offered that transcendental arguments are structurally akin to indispensability ones, as if the argument schematics are inverses or reciprocals of each other. This, I claimed, turns on the reciprocity of apriority vs. aposteriority. But is my claim accurate? I also claimed that indispensability arguments rely on the theory of ontological commitment, but the phrase "ontological commitment" shows up nowhere in the SEP article on transcendental arguments, and it does show up seven times in the SEP article on the indispensability argument in the philosophy of mathematics. And yet here is what the IEP article on transcendental arguments says:

A modest transcendental argument establishing the indispensability of a conceptual framework has the effect of reducing the skeptic either to inconsistency or to raising doubts in the abstract. Since the alternative is inconceivable, the skeptic cannot consistently commit to the possibility of the alternative. [emphasis added]

Apparently Enoch[11] at one points reads:

My indispensability argument for Robust Realism may be thought of as a kind of a transcendental argument.

I can't get the full text of Stokes[07] but the Google outside snippet keyed to the relevant phrases has it that the article at one point reads:

Vahid[11] seems to have a certain class of transcendental arguments as indispensability arguments:

Accordingly, while objective transcendental arguments seek to reveal truths about the world, the subjective variety is intended to show why certain beliefs are indispensable for having thoughts, experiences and so on. I call these first-order and second-order transcendental arguments respectively (reflecting the type of content their conclusions express). With this distinction in mind, I shall now proceed to show that, their surface structure notwithstanding, transcendental arguments are actually species of inference to the best explanation. [bold-face emphasis added]

Are transcendental arguments the apriority-theoretic reciprocals, structurally-speaking, of more empirically-minded indispensability arguments? Or are we really just using multiple names for the same epistemic phenomenon?

@JoWehler that's alright, if you post an answer quoting from it, you would have good evidence for your answer (whatever it would be). Go for the gold! — Kristian Berry, Dec 04 '23 at 18:28
I wrote a post long time ago about the evolution of transcendental arguments from Kant to the current "naturalized" abductive versions, see What are transcendental arguments logically? Indispensability arguments can be seen as a case of such naturalized transcendental arguments, a presuppositional version of inference to the best explanation. — Conifold, Dec 04 '23 at 20:31

score 1 · Accepted Answer · answered Dec 04 '23 at 22:29

I can understand where the idea came from that the two argument forms are opposites in some sense, because they are similar and usually presented in opposite ways:

indispensability positive: Our best theories imply P.

transcendental negative: You can't deny that P. You can say the words, but there will be something that renders your denial self defeating.

however, you can reverse the above descriptions:

indispensability negative: You can deny that P, but then there are all of these things you don't have an explanation for.

transcendental positive: All of the logically possible, rationally affirmable theories imply P.

When you compare negative to negative and positive to positive, it becomes clear how the arguments differ.

This resonates a lot with my intuition, here. I had been thinking of a back-and-forth OC → T vs. T → OC (for OC = ontological commitments and T = theories) but your representation is much clearer. — Kristian Berry, Dec 05 '23 at 03:06

Are transcendental and indispensability arguments reciprocally structured?

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