[FOM] Possible worlds

Alexey Romanov alexey.v.romanov at gmail.com
Fri Dec 22 08:31:02 EST 2006

Mirco Mannucci wrote:
> The PFTMs are precisely constructive partial possible worlds, representing
> the de facto mathematical knowledge of a concrete individual or a machine.
> It is perfectly conceivable that, for a specific notion of feasibility,
> in some of the PFTMs associated to PA FLT is false (in  these worlds
> there are no attainable proofs of FLT, and thus the mathematicians living
> inside of them will conclude that it is not true).

I'd think FLT would be indecidable in these worlds, and not false. In 
particular, they could hardly exhibit a counterexample to it. (Unless I 
misunderstand what you mean by PFTMs.)

> I wish to point out that PFTMs are in a sense a "possible world semantics" for
> FOL theories, but freed from "infinitistic" assumptions that still
> underly Kripke's models.
> Best to all
> Mirco A. Mannucci

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