# 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:
>
>>assumption?
>
> I don't understand the 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."
>

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