Re: Fitch's paradox and OWA

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.

>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.

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Daryl McCullough
Ithaca, NY