Re: Fitch's paradox and OWA
Date: 21 Dec 2009 21:41:46 GMT
Mr. Scott wrote:
>"Reinier Post" <rp_at_raampje.lan> wrote in message
>> Nilone wrote:
>>>Does Fitch's paradox prove an inherent contradiction in the open-world
>> I don't understand the paradox.
>Your addition of 'now' to (NonO) is the cause of your confusion. Go back
>and re-read what you cited.
I just did.
>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....
Yes indeed, that's how they define K ... I should have seen that the first time around. Thank you.
>(KP) forall p(p implies possibly Kp): all truths are knowable by somebody at
>(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.
Now, the contradiction is direct: KP says that all truths are knowable while NonO says that some truth isn't. There is no paradox, just a contradiction.
But that's not how NonO is introduced:
| And suppose that collectively we are non-omniscient, that there is an unknown truth: | | (NonO) ∃p(p ∧ ¬Kp).
See: here they say 'unknown', not 'unknowable'. Hence my confusion. Once it's merely 'unknown' I believe the scoping issue arises.
-- ReinierReceived on Mon Dec 21 2009 - 22:41:46 CET