[FOM] Example of beef: nonrigorous heuristics

[Stephen G Simpson]

Timothy Y. Chow 27 Oct 2003 writes:

 > Simpson asks, "Where's the beef?"  Let me flesh out my previous
 > article on the "unreasonable effectiveness of nonrigorous
 > heuristics" to provide an illustration of the kind of beef that I
 > think Corfield is talking about.
 > 
 > One can imagine carrying out the following program.
 > [...]

The program sounds interesting.  However, until somebody carries it
out, or at least makes a start, there is no beef here.  What you are
calling beef is purely imaginary.

Some of Corfield's pronouncements here on FOM seem to have this same
quality.  They sound interesting, but it is hard to discern any actual
progress or novel insight, mathematical or philosophical.

Furthermore, Corfield seems to be prejudiced against f.o.m., while I
believe that any genuine, serious progress on the issues that he
raises is likely to involve f.o.m. techniques.

 > Since I just came up with this "research program" on a bus ride this
 > morning, it has little chance of being stunningly successful.  However,
 > I do not see any immediate reason why it must *necessarily* fail, and
 > so I think it succeeds as an illustration of a *possible* line of work
 > that
 > 
 > a. is of philosophical, and even general intellectual interest, inasmuch
 > as it might yield insights into the structure and growth of mathematical
 > knowledge; [...]

I don't see any compelling philosophical or general intellectual
interest in what you are saying here, unless and until somebody makes
some progress and achieves some genuine insight.

Stephen G. Simpson
Professor of Mathematics
Pennsylvania State University
http://www.math.psu.edu/simpson/