Re: Fitch's paradox and OWA

From: Marshall <>
Date: Thu, 31 Dec 2009 10:08:10 -0800 (PST)
Message-ID: <>

On Dec 31, 7:10 am, (Daryl McCullough) wrote:
> Jan Hidders says...
> >So what I wanted to say with the above is the following. You are of
> >course right that what (C) really says is:
> >(C) if |- f then |- []f
> >And, assuming that for all f it holds that |- f iff ||- f, this is in
> >fact confirmed by the model theory. However, in the inference process
> >of the paradox as described on the Stanford page the rule is used as
> >if it says f |- []f or |- f->[]f, and that would have the much
> >stronger model-theoretic meaning that I described.
> I don't see a rule saying f |- []f. Where did you see that?

He didn't say that there was an explicitly stated rule of that form. He said that in step 8 of the derivation, they use a rule that was explicitly stated as

    If |- f then |- []f
but they use it *as if* the rule was

    f |- []f

Reading that page, it looks like what he is saying accurately describes the step taken, but I know very little about modal logic.

> I don't think that's a sensible modal logic rule.

That's his point, as I understand it.

Marshall Received on Thu Dec 31 2009 - 19:08:10 CET

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