[FOM] John Baez on David Corfield's book

[Stephen G Simpson]

Alexander M Lemberg Wed, 1 Oct 2003 15:36:37 -0600 writes:

 > I think it goes in both directions, but mainly in that opposite
 > from yours. Namely, it was the need for concepts such as TS which
 > influenced mathematicians to pursue set-theoretical
 > f.o.m. research. 

By TS I assume you mean "topological space". 

What is your evidence for this assertion?  On its face it seems
surprising, because set-theoretical f.o.m. research began long before
the concepts of general topology were on the horizon.  Are you
claiming that the modern concept of topological space was somehow "in
the air" already in the 1890's?  What is the evidence for this?

 > Similarly, questions arising from Fourier analysis influenced
 > Cantor to develop set theory.

Here you may have a better case, because trigonometric series long
predated set theory.  The case has also been made by Dauben in his
book about Cantor.

However, see also the new paper "Did Cantor Need Set Theory?", by
James Humphreys, to appear in the volume Reverse Mathematics 2001,
edited by me, to be published by the Association for Symbolic Logic.

Humphreys blends f.o.m. considerations -- specifically reverse
mathematics -- with philosophical and historical considerations to
argue against Dauben's point.  Humphreys shows that the trigonometric
series questions -- related to sets of uniqueness -- which Cantor was
studying, did not require transfinite ordinal and cardinal numbers for
their solution.  Thus, it is reasonable to ask whether Cantor's
invention or discovery of set theory had some other motive.

Martin Krieger Thu, 02 Oct 2003 18:19:29 -0700 writes:

 > I have read parts of Corfield's book and many of his articles over
 > the years. I must say that the discussion on the list bears little
 > resemblance to the book.

Corfield's comments here on the FOM list have been stridently
anti-f.o.m.  Is his book less so?
 
---

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