Re: Fitch's paradox and OWA

Jan Hidders says...
>
>On 31 dec 2009, 18:47, stevendaryl3..._at_yahoo.com (Daryl McCullough)
>wrote:

>> From this it follows:
>>
>> 6. K_w'(p0) & K_w'(~K_w0(p0))
>>
>> Since only true things are knowable, we have:
>>
>> 7. K_w'(p0) & ~K_w0(p0)
>>
>> That's no contradiction at all! The proposition p0 is
>> known in one world, w', but not in another world, w0.
>> It only becomes a contradiction when you erase the
>> world suffixes.
>
>True, but you have now fundamentally changed the semantics of the K
>operator in the sense that the model theory now looks very different.
>You have essentially turned K from a unary operator K(p) to a binary
>operator K(w,p).

That's not a change of the *semantics*. That's a change of the *syntax*. My claim is that in the possible worlds semantics, every predicate (and operator) that can vary from world to world implicitly is a function of the world. That complexity can usually be avoided because implicitly we assume that everything is talking the same world. But when you nest <> and K, it is no longer possible to make that assumption. Not without restrictions on what can be said. My point is that the knowability principle doesn't make any sense without explicit mention of possible worlds.

It might make sense if we restrict the principle to propositions p that don't involve the knowability operator. But if we restrict it that way, we can't carry out Fitch's proof.

--
Daryl McCullough
Ithaca, NY