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> Date: Mon, 18 Dec 2006 12:42:24 -0500
> From: Harvey Friedman
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> On 12/18/06 10:34 AM, "Timothy Y. Chow"
> <tchow-FrUbXkNCsVf2fBVCVOL8/A@xxxxxxxxxxxxxxxx> wrote:
>
> > A popular way of dealing with the notions of possibility and necessity is
> > to appeal to the concept of possible worlds.
>
> It doesn't apply to the case you are talking about from mathematics.
> >
> > In 1990, if you had said, "Fermat's Last Theorem might be false," then
> > most people would have agreed with you. Today, most people will not. The
> > sense of possibility involved here does not seem to me to be easily
> > handled in the standard framework of possible worlds.
>
> The notion of possibility being used in your example is an epistemic one,
> not an ontological or metaphysical one.
>
> What is needed is a general theory of knowledge, where what is known changes
> monotonically over time.
>
> I think that the computer science literature, rather than the philosophy
> literature, is what is most relevant. In the computer science literature,
> the non monotonic case is also treated, where things that were "known" are
> retracted. This makes especially good sense in database theory.
>
> In any case, there are quite a number of people on the FOM who could comment
> on this diverse and extensive literature from computer science far far
> better than I can.
>
> Harvey Friedman
I think possible world formalisms are likely to be useful for some
purposes. Indeed I used them in an article "Two puzzles concerning
knowledge."
I think partial possible worlds are useful, although I didn't formally
use them in the puzzles article. I am perfectly willing to use
partial possible worlds in which FLT is false, and it is unlikely to
get me into contradiction, since the proof of FLT is far beyond my
ability to follow.
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