We pragmatists do not assert (T), nor are we committed to saying there is any justification to do so. Our claim is that (T) is a regulative assumption of inquiry. This is to say that one must assume (T) in order to inquire rationally into the truth of any hypothesis. If one did not assume that properly conducted inquiry would lead one to the truth*, there would be no point inquiring.
There is a caveat to this, as indicated by 'truth*'. We have to bear in mind that the Peircean thinks of truth (esp. qua aim of inquiry) in a unique way, a way which Peirce discusses in The Fixation of Belief. Peirce maintains that what we aim for when we inquire is stable belief (n.b. this is a descriptive, not a normative claim). Crucially, this does not mean we are dogmatic, that we wish to cling to any old belief come hell or high water (the so-called 'method of tenacity'). Rather, Peirce is saying that in seeking truth we seek a belief that will remain stable even in the face of the very best future inquiries, even in the face of all future evidence. (Several commentators have likened this to the notion of superassertibility found in Crispin Wright's Truth & Objectivity, which is ironic, given that Wright is highly critical of (what he takes to be) the Peircean conception of truth in that book).
So the claim involved in the ARA is that if one does not assume that properly conducted inquiry will yield truth*, that is, yield a stable or superassertible belief, there would be no point inquiring.
Now this seems to me a very risky move for the pragmatist to make. The ARA involves invoking a new technical notion (the 'regulative assumption') which requires a good deal of unpacking and explanation, as well as some intuitive or at least theoretical precedents. (We find the latter in Kant's first critique, but the relevant (rather obscure) passages provide scant reason to endorse or deploy the notion without the confines of Kant's architectonic). The ARA also relies on the controversial claim that truth* is our only possible aim in inquiry, when most people nowadays have abandoned this idea. (see e.g. in philosophy of science, where in the face of arguments like the pessimistic meta-induction, many consider empirical adequacy or warranted assertibility the most we can sensibly aim for).
We should also perhaps acknowledge that fans of the problem of lost facts might find this unsatisfying on a more basic level. The problem seems to show that even merely assuming T is true leads to a contradiction (in cases of lost facts). Why isn't this a good enough reason to abandon (T)? Shouldn't we eschew assuming things that lead to contradictions, even if that means revising our cognitive goals (or lowering our logical expectations)?
Thus, the direction I'm leaning at the moment is that the pragmatist's best defence is to provide two things:
- A demonstration that either (T) does not lead to contradictions concerning lost facts, or (T) does generate such contradictions, but this is non-problematic.
- An explanation and defence of the notion of a 'regulative assumption' which establishes (what Wright calls) an entitlement to expect that suitably diligent inquiry will yield the truth*, that is, an entitlement to assume T.