Re: Fitch's paradox and OWA

Jan Hidders says...

>If we reformulate the meaning of (C) in the model theory we get:
>
>(mC) If (W,w) |- f then (W,w) |- []f.
>
>Given the semantics of []f this is equivalent with:
>
>(mC') If (W,w) |- f then (W,w') |- f for all w' in W.

I don't think that that is correct. Rule (C) says that if p is a *theorem* (that is, p is provable) then it is necessarily true (and so is true in all worlds).

In Kripke semantics, we distinguish between what is true in one world and what is provable. So you should be writing

(W,w) ||- f

to mean f is true in world w (where W is the set of all possible worlds) instead of

(W,w) |- f

I'm not sure what the latter would mean.

--
Daryl McCullough
Ithaca, NY