FOM: Intuitionism

[richman]

>== Original Message From Jesper Carlstrom <jesper at matematik.su.se>==

>On Fri, 17 May 2002, wiman lucas raymond wrote:
>
>> would an intuitionist accept the statment
>> "either p is provable, not-p is provable, or neither is provable"?
>
>The principle
>
>   If a proposition cannot be known to be true,
>   then it can be known to be false
>
>is defended from an intuitionistic point of view in Martin-Löf ...

I'm not sure what that principle means, nor do I see what it has to do with 
the question. Surely no intuitionist would accept the statement under 
consideration. For one thing, intuitionists don't normally distinguish between 
provable and true. However, if "provable" here means provable in some 
particular formal system, then the statement would be rejected, in general, as 
requiring the law of excluded middle.

Is the principle supposed to apply to the statement? What is it that can't be 
known to be true, and what could we conclude from the fact that it can be 
known to be false?

--Fred