the boundaries of language

I'd really like to write a paper on the matters I'm going to discuss in this post. Since I have no idea where to begin writing said (non-existent) paper, or whether the ideas it would contain are even worth pursuing, I thought I'd air them here. To set the scene, I'll post here something I wrote as a comment over at Duncan's Epistemic Value:

A question I got interested in a while ago is whether there is worrying analogue of Prichard's dilemma in epistemology. Scanlon presents the original version as a dilemma facing any account of what makes an action wrong. We want to know why the fact (assuming for now that it is one) that an act is wrong gives us reason not to do it. The worry is that we'll either end up giving an uninformative answer like 'Because it's wrong!', or we'll end up citing some feature of the act which supposedly substantively explains why we have reason not to perform it which intuitively has no connection to its wrongness (that performing the act would lead to social ostracism, for example); as Scanlon notes, it is not such features of the act which we'd expect 'a moral person first and foremost to be moved by'.

In his critical study of Scanlon, David Sosa suggests that there's no worrying theoretical analogue of Prichard's dilemma - that when we ask 'why does the fact that p is false give us reason not to believe that p?', we can be satisfied with the answer 'Because p is false!' - and that this should make us suspect that trivial answers should be satisfactory in the ethical case too. I'm inclined to think Prichard's dilemma bites in both cases.

David writes of the 'Because p is false!' response:

'Is this not the kind of answer that is wanted? Ultimately (if not sooner), it is truth in which at least one sort of theoretical rationality is grounded. Any intermediate theoretical purpose that might be served by not believing the proposition could function as a reason only derivatively through its own relation to the truth. And to whatever extent that relation is not necessary, then we will feel that the alternative lacks the right sort of modal force.' ('A Big Good Thing': 374)

I want to suggest that in certain cases, we can do quite a bit better here that David is suggesting we can. Take mathematical statements for example. If one asks why some set-theoretical statement s being false gives one reason not to believe that s, can we do better than to simply point out that s is false? Surely we can; usually we will be able to prove that ~s follows from some mutually shared set of axioms. This may not always be the case, given that these axioms will fail to settle some statements about the set-theoretic universe which we may nonetheless take ourselves to have good reason not to believe (CH and its relatives, for example). In general though, we take provability to be precisely the kind of thing counting in favor of a particular mathematical statement that a rational agent considering which mathematical statements to believe would be 'first and foremost' moved by. And it's more informative than simply saying that the statement is true or false, since it appeals to the implications of some mutually accepted set of statements, often thought to have some privileged epistemic status.

So it seems clear that proof has the right kind of close connection to truth. Is it the case, as David suggests, that that fact that a statement's negation is provable is only a reason to believe it derivatively because of that close connection to truth? That's an enormous question, but I don't see any immediate grounds for a positive answer. In fact, I see lots of room to explore in defense of a negative answer.

Let's imagine there's something to all this, i.e. that we can't be satisfied with trivial answers to the theoretical analogue of Prichard's dilemma, and that a satisfactory epistemology of mathematics vindicates my suggestion that provability is just the right kind of notion to invoke in a satisfactory non-trivial response to Prichard's dilemma targeted at mathematical statements. What follows?

Well, nothing probably. But the seductive thought is the following. Firstly, that realist (bivalent, potentially verification-transcendent) truth doesn't connect up in the right way to provability to allow the above response to Prichard's dilemma to be given; the relationship of truth to proof on that picture 'lacks the right sort of modal force' to borrow David's expression from the quote above. In contrast, the anti-realist's conceptions of truth and proof gel in just way we want (of course, some anti-realists identify truth with proof. I'll bracket such potential complications here, since I'm already quite muddled enough). More generally, that an anti-realist will have some notion that connects up in the right way to truth to allow him to offer a satisfying substantive general response to the theoretical version of Prichard's dilemma; I'm imagining this to be some notion which, like Crispin Wright's notion of superassertability, is built out of the notion of warranted assertability but which mimics the notion of proof in crucial respects (see 'Can a Davidsonian Theory of Meaning.....' in Crispin's Realism, Meaning, & Truth). The contention, of course, would be that the realist has put any such notion well beyond her reach.

This is obviously ludicrously sketchy and overambitious, holding out hostages in the epistemology of mathematics, both the theoretical and the practical domains of normative theory, plus it inherits general worries about the possibility of the formulation of an anti-realistic notion that applies to non-mathematical statements but which possesses the requisite proof-like qualities, plus an argument is wanting that realist truth creates special difficulties here. But anyway, you'll all see why I don't know how to write this paper. Maybe that's for the best - I'll remain agnostic for now.

Labels: Anti-Realism, Epistemology