Saturday, October 06, 2012
Slater on Fitch
In the most recent edition of The Reasoner, October 2012, the always contentious but always interesting Hartley Slater has discussion of the Fitch paradox of knowability. In it he rightly notes that the paradox disappears if one recognizes that epistemic modalities can be relativized. I once argued something like this in graduate school, but my argument was, like much of what I have ever done in modal logic, clunky and clumsy and went about things a rather roundabout way. [If one doesn't relativize, it seems to me that the relevant logic would have to be paraconsistent, given that K would have to cover different epistemic situations: it's not much of a paradox to say that something is unknown and that it is known that it is unknown if John doesn't know it and Jane knows he doesn't. This is not really something I've looked at.] As Slater notes, there are worries about illegitimate self-reference with the relativization approach, but these are not really insuperable. In any case, I thought it was interesting; it will also be interesting to see if there are any responses to it.