[FOM] Possible worlds

[Harvey Friedman]

On 12/18/06 10:34 AM, "Timothy Y. Chow" <tchow at alum.mit.edu> 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