Re: Fitch's paradox and OWA
Date: Thu, 31 Dec 2009 13:53:19 -0800 (PST)
On Dec 31, 11:22 am, stevendaryl3..._at_yahoo.com (Daryl McCullough) wrote:
> Marshall says...
> >On Dec 31, 7:10=A0am, stevendaryl3..._at_yahoo.com (Daryl McCullough)
> >> 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))
Certainly steps 4 - 9 constitute an RAA proof with the assumption being K(p & ~K(p)).
However what I was referring to was specifically how they get from step 7 to step 8 within that RAA proof. Your response does not seem to address that particular issue.
Are your comfortable with how step 8 is
obtained from step 7 via Rule C as described on this page?
It's entirely possible that I misunderstand Jan Hidder's point, or rule C, or something else entirely, however I would like to at least feel that we were discussing the same step in the proof.
Marshall Received on Thu Dec 31 2009 - 15:53:19 CST