Re: Fitch's paradox and OWA

From: Reinier Post <rp_at_raampje.lan>
Date: 17 Dec 2009 22:52:46 GMT
Message-ID: <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."

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 - 16:52:46 CST

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