# Re: Fitch's paradox and OWA

Date: Thu, 17 Dec 2009 19:40:05 -0500

Message-ID: <bZOdneC2hM_7UrfWnZ2dnUVZ_uqdnZ2d_at_giganews.com>

"Reinier Post" <rp_at_raampje.lan> wrote in message
news:4b2ab63e$0$28714$703f8584_at_news.kpn.nl...

*> Nilone wrote:*

*>*

*>>Does Fitch's paradox prove an inherent contradiction in the open-world*

*>>assumption?*

*>*

*> I don't understand the paradox.*

*>*

*> http://plato.stanford.edu/entries/fitch-paradox/*

*>*

*> explains:*

*>*

*> suppose that*

*>*

*> (KP) all truths are knowable, i.e. can be known by somebody at some time*

*>*

*> and*

*>*

*> (NonO) not all truths are known now*

*>*

*> then*

*>*

*> (1) there is an unknown truth p*

*>*

*> and then*

*>*

*> (2) p is true and unknown is itself a truth*

*>*

*> and hence, by KP,*

*>*

*> (3) (p is true and unknown) can be known by somebody at some time*

*>*

*> "However, it can be shown independently that it is impossible*

*> to know this conjunction. Line 3 is false."*

*>*

Your addition of 'now' to (NonO) is the cause of your confusion. Go back and re-read what you cited.

If K is the epistemic operator meaning 'it is known by someone at some time that,' then not K would have to deny that, meaning 'it is not known by anyone at any time that,' so with that in mind....

(KP) forall p(p implies possibly Kp): all truths are knowable by somebody at some time.

(NonO) exists p(p and not Kp): there is a truth that is not known by anybody at any time.

These are contradictory. If all truths are knowable by somebody at some time then there can't be a truth that is not known by anybody at any time.

*> I'm eager to see that demonstration. Clearly, if p is unknown (1),*

*> then so is the truth than p is true and unknown (2), but KP doesn't*

*> contradict that - all it says is that p may be known, perhaps at some*

*> other time, and indeed, at that same time, the statement that p was true*

*> but unknown will also be known to be true.*

*>*

*> They seem to mess up the scoping of K and P, simplifying their language*

*> until paradoxes become inevitable; the paradox results from that,*

*> as far as I can see. In any case, the paradox depends*

*> on the exact formalization on K and P, which isn't given.*

*> Once again, I'm left with the feeling that these Stanford guys*

*> could use some field experience in database design.*

*>*

*> -- *

*> Reinier *

Received on Thu Dec 17 2009 - 18:40:05 CST