[FOM] Classical logic and the mathematical practice

[Michael Kremer]

At 09:45 AM 5/12/2005 -0400, Timothy Y. Chow wrote:


>It generally
>takes considerable philosophical education before someone seriously
>entertains the notion that if there is no way to decide whether X happened
>or not, then maybe X neither happened nor didn't happen.


One needs to be careful here.  The intuitionist shouldn't "entertain the 
notion that maybe X neither happened nor didn't happen" (maybe ~(X v ~X)) 
-- which notion is refutable even in intuitionist logic (one can prove ~~(X 
v ~X)).  (Unless the intuitionist doesn't mind contradicting herself, that 
is.)  The intuitionist merely refrains from committing  herself to "either 
X happened or X didn't happen" -- always open to discovering that, in fact, 
one or the other did happen. To think that what the intuitionist entertains 
is "the notion that maybe X neither happened nor didn't happen" is to think 
like a classical logician.

--Michael Kremer