Re: Fitch's paradox and OWA
Date: Fri, 1 Jan 2010 12:41:51 -0800 (PST)
On 1 jan, 16:28, stevendaryl3..._at_yahoo.com (Daryl McCullough) wrote:
> Jan Hidders says...
> >On 31 dec 2009, 18:47, stevendaryl3..._at_yahoo.com (Daryl McCullough)
> >> 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.
Explicit in the formulas? So you reallly do want to change the syntax? If not, I'm a bit puzzled as to how you want to change the semantics. It would help if you could provide a model theory to explain how you want to change the semantics. Right now the model theory I gave already does allow the operator K to be different in possible worlds. So how would your semantics differ from that?
- Jan Hidders