[FOM] Allen Hazen validated my perception

Gabriel Stolzenberg gstolzen at math.bu.edu
Sat Mar 25 17:13:43 EST 2006

   This is about Allen Hazen's message, "Re: on bill tait's answers
to GS's questions" of March 23.

   In it, AH quotes an exchange between WT (Bill Tait) and GS (yours
truly).  I begin by quoting part of it here.

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"?

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

AH: 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.)

   Thank you, Allen.  My all-time favorite dream was Freud validating
my perceptions.

AH: ...I remember as a student (in the 1970s) being very puzzled by
expositions of intuitionism...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?

   In my case, it was the mid 1960's, when Bishop inexplicably began
lecturing on this stuff.  (Before FCA.)  My impression was that if it
ever took over, it would destroy everything good and beautiful about
mathematics.  But I wasn't as articulate (or metaphysical) as you.  I
had only a vague impression of what was going on.

AH:  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.)

    Re Dummett, when he gave the William James lectures at Harvard,
I was astonished to discover that here was an analytic philosopher
who could at least talk the talk.  As for the difference between GS
at Bishop's lecture and GS, less than 10 years later, at Dummett's,
some may call it "brain-washing."  I call it "a Gestalt switch."

   Re Dummett's account:  In my view, what Dummett was (and maybe
still is) attempting to do with anti-realism, while retaining his
analytic philosopher's beliefs about rationality (and the habits of
thought that go with them), is like trying to square the circle.

   Finally, isn't there a risk that your message may subject you to
ritual execution in Melbourne?  At least, in the philosophy department?

   With best regards,

   Gabriel Stolzenberg

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