Re: Fitch's paradox and OWA

From: Jesse F. Hughes <>
Date: Fri, 01 Jan 2010 13:15:23 -0500
Message-ID: <> (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.

Jesse F. Hughes
"To all Leaders of the World, buy or rent the movie 'The Day
After'[...] I assure you will have a new perspective on WMDs."
                   -- practical advice from online petitions
Received on Fri Jan 01 2010 - 19:15:23 CET

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