Re: Fitch's paradox and OWA

On 2 jan, 00:14, stevendaryl3..._at_yahoo.com (Daryl McCullough) wrote:
> Jan Hidders says...
>
> >Explicit in the formulas? So you really do want to change the syntax?
>
> I'm not advocating a change in the syntax, I'm just saying that the
> syntax of modal logic is inadequate to capture the intuition behind
> the knowability principle.

Doesn't that imply that you want to reformulate it in a different 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?
>
> I would just use first-order logic semantics, and allow explicit
> quantification over possible worlds. The point about modal logic
> is that it is a simpler fragment of full first-order logic, but
> I think that it is not expressive enough to talk about complex
> issues of necessity and knowability. Fitch's paradox shows its
> limitations.

But is that not what the given model theory already does? It uses set theory rather then FOL, but since you want to talk about possible worlds and statements about statements, that seems more appropriate to me anyway. The given model theory still seems to contain the paradox, so you will want to change it. Can you show how?

• Jan Hidders