Re: Fitch's paradox and OWA

From: Jan Hidders <hidders_at_gmail.com>
Date: Fri, 1 Jan 2010 01:51:12 -0800 (PST)
Message-ID: <c2eb97cc-c185-49b1-afe0-d37d90f13032_at_a21g2000yqc.googlegroups.com>


On 1 jan, 05:26, stevendaryl3..._at_yahoo.com (Daryl McCullough) wrote:
> Marshall says...
>
> >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.
>
> That's exactly the step that I was talking about.
> Steps (4), (5) and (6) and (7) constitute a proof
> of ~K(p  ∧ ~Kp). Therefore, we have
> |- ~K(p  ∧ ~Kp)
>
> By C, if you have |- f, then you have |- [] f.
> Letting f = ~K(p  ∧ ~Kp), it follows that

> |- [] ~K(p  ∧ ~Kp)
> which is step (8).
>
> >Are your comfortable with how step 8 is
> >obtained from step 7 via Rule C as described
> >on this page?
> >http://plato.stanford.edu/entries/fitch-paradox/
>
> Yes, that's exactly what they are doing. They
> didn't use the |- symbol in step 7, but it is
> clear that (7) is the conclusion of a proof.

Wow. You are right. They correctly conclude in (7) that |- ~K(p  ∧ ~Kp).

Hmm. I need to think this over. I'm beginning to believe now that the inference in the paradox is in fact correct.

  • Jan Hidders
Received on Fri Jan 01 2010 - 10:51:12 CET

Original text of this message