Re: Fitch's paradox and OWA
From: Daryl McCullough <stevendaryl3016_at_yahoo.com>
Date: 31 Dec 2009 11:22:33 -0800
Message-ID: <hhitlp01lsc_at_drn.newsguy.com>
Date: 31 Dec 2009 11:22:33 -0800
Message-ID: <hhitlp01lsc_at_drn.newsguy.com>
Marshall says...
>
>On Dec 31, 7:10=A0am, stevendaryl3..._at_yahoo.com (Daryl McCullough)
>wrote:
>> 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
No, I don't think they did that. What they did was to assume K(p & ~K(p)), and show that that leads to a contradiction. That's a proof of ~K(p & ~K(p)). So we have |- ~K(p & ~K(p)). Then we can apply the rule "If |- f, then |- [] f" to conclude []~K(p & ~K(p))
-- Daryl McCullough Ithaca, NYReceived on Thu Dec 31 2009 - 20:22:33 CET