Non-Standard Escape Routes
I've been busy working on the logic book, playing with music software, meeting friends, lazing around, looking after Magdalena (who was ill again), protesting against the war, and thinking that it was a good idea to have voted for Livingstone (as I did when I lived in London). I hope to get back to philosophy soon.
Catching up with the philosophy papers blog, I noticed that Hartry Field has written yet another paper about how to avoid paradoxes by using non-standard logic. I fear that I may eventually have to reconsider my standard reaction to efforts like this, which is to say that using non-standard logic amounts to a change of topic.
For example, the naive comprehension principle says that for each predicate there is a property that is had by some thing x iff x satisfies the predicate. Field proposes to block Russell's paradox by using some non-standard logic in which "R instantiates R iff R does not instantiate R" does not imply the contradiction "R instantiates R and R does not instantiate R". But I can't help finding "R instantiates R iff R does not instantiate R" itself inconsistent. I can see that on Field's interpretation of "iff" it doesn't actually imply everything. But why isn't this reinterpretation of "iff" simply a rejection of the original comprehension principle, which he wants to defend? What Field defends is a rather different principle that superficially looks like the naive comprehension principle.
Similarly, a while ago Heinrich
Wansing was in Berlin and presented a "solution" to the knowability
paradox by showing that "(p 
possibly Kp) (p Kp)"
does not follow from innocent assumptions about knowledge in a certain
paraconsistent relevance logic, in which "" does not have its ordinary truth-functional meaning.
But did anybody doubt that the string of symbols expressing the
knowability paradox could be given a consistent interpretation? I would
have thought the paradox was what that string expressed under its standard
interpretation, not the string itself.
This reaction is probably everybody's first reaction. Hence the more I see clever people ignoring it, the more I fear something must be wrong with it.