[FOM] Possible worlds
Timothy Y. Chow
tchow at alum.mit.edu
Wed Dec 20 18:48:38 EST 2006
On Wed, 20 Dec 2006, joeshipman at aol.com wrote:
> The problem with this is that, although Wiles's proof is extremely
> complicated, there are many other theorems which were open questions for
> a long time, where the eventual proof was short (though very hard to
> find, for the same reasons NP seems to be bigger than P), and for these
> theorems introducing a notion of feasibility doesn't help.
I don't see this as a fatal objection. The relevant notion of
"feasibility" doesn't have to be a cleanly defined mathematical notion
that applies uniformly to all utterances; it can vary from statement to
statement, encompassing whatever limited set of deductions are relevant
for analyzing the meaning of the statement of current interest. For
example, the set of deductions could be just the deductions that a
particular person finds "obvious" at a given time.
Tim
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