Re: Fitch's paradox and OWA

Jan Hidders says...

>The purpose of (3) was only to illustrate the translation of formulas
>in the original logic to your logic. You are right that by itself it
>does not show the paradox. But if this translation exists then all
>formulas used in the proof of the paradox will have their equivalents
>in your logic.

Yes, but my point is that in the more expressive logic, the knowability principle can be expressed as

forall p:P, exists w:W, k(w,p)

The original knowability principle, when translated into this new logic, would look something like this:

forall f:W -> P, forall w:W, f(w) -> exists w':W, f(w') & k(w',f(w'))

The "propositions" of modal logic are actually functions on worlds.

>If your logic is complete it will also have the
>equivalents of all the used axioms and principles,

Yes, but I'm *rejecting* the knowability principle in favor of a more sensible (non-contradictory) principle. I'm suggesting a *different* principle, one that *doesn't* lead to a contradiction.

--
Daryl McCullough
Ithaca, NY