FOM: Intuitionism (Tait)

[charles silver]

> Charlie Volkstorf wrote:
>
> >Must the proof of P be the same as the proof that this proof proves P?
>
> What is a proof? What is a proof which demonstrates that something is a
> proof?

    Frequently it is thought that the proof that neither Godel's sentence G
("I am not provable") is provable nor is Not-G provable is *itself* a
"proof" of G (namely that G is not provable).   The argument is that G
*says* it's not provable, which is true.   (Not-G says it's provable, which
is false).   However, this is not a "proof," where "proof" is defined as a
certain sequence of patterns inside a well-defined formal system.
(Incidentally, this insight {that the undecidability of G constitutes a
"proof of G outside the system"}has led a number of philosophers to draw
various conclusions about the relationship between humans and formal
systems.)

Charlie Silver