[FOM] Reply to Rupert MCallum on Voplin and consistency

Gabriel Stolzenberg gstolzen at math.bu.edu
Fri Nov 3 16:13:43 EST 2006

   Re a copy of Volpin's consistency proof manuscript, I would first
try David Isles in the math department at Tufts.

   Also, if you know enough to do so (I don't), it might be helpful
to explain to the members of the fom list how Alik thought he could
"prove the unprovable" by making finer distinctions (of a certain
kind) than traditionally is done.  (E.g., distinguishing between
the "near" and "distant" future, which I recall him claiming is a
distinction that exists in Russian.)  I myself never had more than
a very sketchy idea of what Alik was up to.  Or against.

   For someone seemingly (and, in some ways, truly) unworldly, Alik
seemed very knowledgable.  A long time ago, I asked both Alik and
Kleene (not at the same time) for the simplest theorem that came to
mind in the proof of which the law of excluded middle was really doing
some work.

   Alik gave a reasonable answer.  (I think he said the Intermediate
Value Theorem.)  Kleene did not.  Which suggested to me that he hadn't
thought about this before, whereas Alik had.  In the proof of the theorem
he chose, the law of excluded middle wasn't really doing any work.  (I
don't remember which theorem he offered but the proof was a fake proof
by contradiction, like standard proof of the infinitude of primes or the
traditional proof that square root of 2 is irrational.)

   Gabriel Stolzenberg

   P.S.  My all-time favorite "proof" of the consistency of mathematics,
which I learned from Fred Richman, goes like this:  Suppose not.  Then
we have a contradiction.

On Thu, 2 Nov 2006, Rupert McCallum wrote:

> Yes, he claimed to have a proof of the consistency of ZF with any
> finite number of inaccessible cardinals. Unfortunately it seems to be
> hard to get hold of a copy of this proof. I would really like to know
> in which axiomatic theory he claimed it could be done.
> --- Gabriel Stolzenberg <gstolzen at math.bu.edu> wrote:

> >    Alik Volpin's "ultra-finitist" program had the aim of proving
> > the consistency of mathematics.

More information about the FOM mailing list