Re: Fitch's paradox and OWA

From: Jan Hidders <hidders_at_gmail.com>
Date: Fri, 1 Jan 2010 15:43:23 -0800 (PST)
Message-ID: <f02cf193-a806-4429-96f5-65228b3fbead_at_a15g2000yqm.googlegroups.com>


On 1 jan, 19:15, "Jesse F. Hughes" <je..._at_phiwumbda.org> wrote:
> stevendaryl3..._at_yahoo.com (Daryl McCullough) writes:
> > That's not a change of the *semantics*. That's a change of the
> > *syntax*. My claim is that in the possible worlds semantics,
> > every predicate (and operator) that can vary from world to world
> > implicitly is a function of the world. That complexity can usually
> > be avoided because implicitly we assume that everything is talking
> > the same world. But when you nest <> and K, it is no longer possible
> > to make that assumption. Not without restrictions on what can be
> > said. My point is that the knowability principle doesn't make
> > any sense without explicit mention of possible worlds.
>
> > It might make sense if we restrict the principle to propositions
> > p that don't involve the knowability operator. But if we restrict
> > it that way, we can't carry out Fitch's proof.
>
> I haven't worked through the semantic details (at least not recently),
> but the proof clearly "works" and the intuition behind the proof seems
> plausible enough.
>
> Suppose that p is true, but I don't know it.  Then p & ~Kp is true.
> But surely, I could not know p & ~Kp.  That is, I couldn't know "p is
> true, but I don't know that p is true."
>
> After all, if I know that conjunction, then I know that p is true, so
> how could I know that I don't know that p is true?
>
> The argument seems perfectly clear to me, both formally and
> informally.

Yes, it does. Thanks. Very nicely formulated.

It did strike me that you formulated K as "I know that P". For some reason it made me realize that it was formulated on the Stanford page as "Somebody at some time knows that P". Under the latter interpretation it seems now indeed a bit strange to me to require that all facts, and specifically those of the form ~Kp, are possibly known. I can imagine there are facts p for which we can never establish definitively that they will not be known to somebody at some time, except after waiting until we run out of time or persons, and by then there will be nobody left to know this. So ~Kp might very well be both true and unknowable.

  • Jan Hidders
Received on Sat Jan 02 2010 - 00:43:23 CET

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