Re: Fitch's paradox and OWA

From: Reinier Post <rp_at_raampje.lan>
Date: 21 Dec 2009 21:41:46 GMT
Message-ID: <4b2feb9a$0$19371$>

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.
>> explains:


>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
>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.

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.

Received on Mon Dec 21 2009 - 22:41:46 CET

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