[FOM] on bill tait's answers to GS's questions

[A.P. Hazen]

Gabriel Stolzenberg wrote:

GS: Among classical mathematicians, constructive math is the study of
what can be proved without omniscience."

WT: I doubt that you are right about what classical mathematicians would
say.

GS: Trust me.  These were my people.  And in a sense they still are.
Did you really never hear things like, "I want to do God's mathematics"?

(where I have inserted the initials identifying Stolzenberg's and 
Tait's lines in the  dialogue).

To cite  one instance in print: Rudy Rucker in his book "Infinity and 
the Mind" quotes Gaisi Takeuti as responding to a "What is set theory 
about" question with "Set theory is about the thoughts of an infinite 
mind." (I've lent my copy to a student, so that's from memory.)
---
    On the general question of omniscience in mathematics...  I 
remember as a student (in the 1970s) being very puzzled by 
expositions of intuitionism (I think the one in Beth's "Foundations 
of Mathematics" was one) that justified the rejection of LEM in terms 
of our LACK of omniscience: "What does it matter," I wanted to shout, 
"that we don't know whether or not it is the case that P?  That's not 
what LEM says: it just says that it either IS or IS NOT the case that 
P, whether we know it or not!"  Dummett's account of the 
philosophical stance appropriate to intuitionism is not above 
criticism, but his was the first exposition I read that made it sound 
like an understandable and non-silly one. (Stolzenberg has since 
written a good, thoroughly un-Dummettian, account.)

--

Allen Hazen
Philosophy Department