Re: Fitch's paradox and OWA

From: Mr. Scott <do_not_reply_at_noone.com>
Date: Thu, 24 Dec 2009 05:58:52 -0500
Message-ID: <n8udnfc_BfLw1K7WnZ2dnUVZ_tGdnZ2d_at_giganews.com>


"Reinier Post" <rp_at_raampje.lan> wrote in message news:4b2feb9a$0$19371$703f8584_at_news.kpn.nl...
> Mr. Scott wrote:
>
>>
>>"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:
>
> [...]
>
>>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) ^fp(p ^ ¬Kp).
>
> See: here they say 'unknown', not 'unknowable'. Hence my confusion.
> Once it's merely 'unknown' I believe the scoping issue arises.
>

Now I'm getting confused. I agree that there is something that doesn't sit right: it doesn't make sense for something being knowable to imply that it is known, or for something being unknown to imply that it is unknowable. But supposing that (NonO) is true throws a wrench into the works. If one supposes that there is a truth that is not known by anybody at any time, then it is necessary that there is a truth that is not known by anybody at any time, and that if it is necessary that there is a truth that is not known by anybody at any time, then it is not possible for that truth to be known by somebody at some time. On the page you cited, these are instances of lines (C) and (D), respectively. When something is actually true, it is necessary that it is possible, but when something is supposed to be true, it is necessary that it is not just possible but true. Received on Thu Dec 24 2009 - 11:58:52 CET

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