I had a great time talking about Fitch this afternoon with some members of the NAMICONA group. I got some very interesting comments and I want to make a note of some of them before I forget - though this post follows a couple of post-talk drinks so apologies if it falls below even my usual standards of clarity ...
One intriguing suggestion, made by Lars Gundersen: maybe saying that p is knowable-if-true is not a matter of asserting 'p --> possibly-Kp', but rather a matter of attributing some sort of dispositional property to p, which might be finkish. To take the conditional to capture this property would be to commit (something close to) the conditional fallacy. (NB: the rest of this post consists in reflections on things Lars and others said in the session - they take no blame for any nonsense in what follows.)
Compare: killer yellow is visible, even though if one were to look at it one would not see it but would in fact perish. It would be a mistake to assume that the dispositional property of visibility is captured by any counterfactual of the form 'if you were to look at it then you would see it'.
To get closer to the Fitch case, consider super-killer-yellow, which is visible, even though necessarily all who look upon it instantly perish. To get even closer again, consider super-suicidal-yellow, which necessarily disappears when someone looks at it. The visibility of super-suicidal-yellow (one might think) is a finkish dispositional property.
But note that we are still some distance from the conditional that generates the Fitch argument, since that conditional is material and so far we're still talking about counterfactuals. But if being knowable-if-true is indeed a dispositional property, perhaps the first step in rejecting its analysis as (p --> possibly-Kp) will be to argue that if any conditional captures it at all it won't be a material one. (The next step will presumably be to argue that if any strightforward counterfactual captures it then what goes on the left hand side of that counterfactual is not 'p' but some description of the stimulus - investigation presumably - which typically triggers the response of becoming known-if-true. And what goes on the right hand side is a description of this response.)
And note that we are getting close to what we want insofar as we've established that the visibility of super-suicidal-yellow is not threatened by the falsity of 'super-suicidal-yellow is possibly seen'. Maybe we can argue by analogy that the knowability-if-true of (p and not-Kp) is not threatened by the falsity of '(p and not-Kp) is possibly true and known'.
Assuming something like a Lewisian analysis of dispositions (for the sake of argument), we might try something like the following:
A proposition p is knowable-if-true at time t (i.e. disposed at time t to give response r - becoming known-if-true - to stimulus s - being sufficiently investigated) if and only if, for some property B that p has at t, for some time t’ after t, if p were to undergo stimulus s at time t and retain property B until t’, s and p’s having of B would jointly cause p’s giving response r.
('Sufficient investigation' = investigation sufficient to produce knowledge of p if p is true and knowledge of not-p if p is false.)
One thing about treating Fitch cases (and any others where the appearance of s necessarily prevents the retention of B) this way, though, at least if we also assume a Lewisian analysis of counterfactuals, is that the counterfactual involved in the analysis will be trivially true in the interesting cases, since it is impossible for any true proposition of the form (p and not-Kp) to retain it's truth-value (which I would imagine must be part of B) while being sufficiently investigated. So I guess we would need to plug in some other analysis of the counterfactual, or else demand that the counterfactual be assertible as well as trivially true, or something of that kind.
There might, of course, also be more promising non-Lewisian analyses of the relevant dispositional properties that don't involve counterfactuals at all.
[Aside: It could be that on some ways of developing this thought, it might end up quite close to some of the things I think about Fitch. Ascribing the relevant dispositional property might depend on (what I would descibe as) the thought that the state of affairs (if any) which makes p true is recognizable. The base property might be a matter of p's relation to that state of affairs (if any). Another extrinsically-based disposition, perhaps!]