# Re: Fitch's paradox and OWA

Date: 31 Dec 2009 07:10:52 -0800

Message-ID: <hhiets0mph_at_drn.newsguy.com>

>So what I wanted to say with the above is the following. You are of

*>course right that what (C) really says is:
**>
**>(C) if |- f then |- []f
**>
**>And, assuming that for all f it holds that |- f iff ||- f, this is in
**>fact confirmed by the model theory. However, in the inference process
**>of the paradox as described on the Stanford page the rule is used as
**>if it says f |- []f or |- f->[]f, and that would have the much
**>stronger model-theoretic meaning that I described.
*

I don't see a rule saying f |- []f. Where did you see that?

I don't think that's a sensible modal logic rule. That is essentially saying that there is no difference between f and []f. (Usually, the accessibility relation on worlds is set up so that []f -> f. So if we add f -> []f, then f and []f are logically equivalent.)

>Their reasoning can be simplified to this:

*>
**>(1) p & ~Kp (assumption, for arbitrary variable p)
**>(2) <>Kp (from (1) using KP)
**>(3) []~Kp (from (1) using (C))
*

No, we don't have |- ~Kp. We only have (W,w) ||- ~Kp. So we can't conclude |- []~Kp.

-- Daryl McCullough Ithaca, NYReceived on Thu Dec 31 2009 - 16:10:52 CET