[FOM] shipman's challenge: the best defense

Gabriel Stolzenberg gstolzen at math.bu.edu
Tue Jan 8 13:08:02 EST 2008

   On Thu 03 Jan 2008, in Re: Formalization Thesis (Vol 61 Issue 5),
Joe Shipman wrote:

> I repeat my earlier challenge: can anyone who disputes Chow's
> Formalization Thesis respond with a SPECIFIC MATHEMATICAL STATEMENT
> which they are willing to claim is not, despite its expressiblity in
> English text on the FOM discussion forum, "faithfully representable"
> or "adequately expressible" as a sentence in the formal system ZFC?

   I would expect that, at least initially, in just about every case,
a more responsible attitude for a mathematician (e.g., me) to take
would be to refrain from answering either in the affirmative or the
negative.  I say this for two related reasons.  First, the expression,
"adequately expressible," is radically vague and subjective. Second,
because mathematicians are not trained to assess such matters (there
is no course of training because, as of now, there is nothing to be
taught), they should not assume that just because they do/don't have
any doubts about adequacy/inadequacy today, they will/won't have any

   Having said this, I invite Joe to think about the "adequacy" of
a formalization of the informal statement, "The set of real numbers
is uncountable."  The claim that it is a "faithful representation"
of the informal statement might well make a mathematician (e.g., me)
uncomfortable.  I believe this is a familiar point.

   Gabriel Stolzenberg

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