FOM: FoM and Set Theory in Philosophy

[A.P. Hazen]

Charles Silver's reply in the "f.o.m./TIME Magazine" string suggests two
problems for getting academic philosophers interested in f.o.m.  One is
that set theory is presented as THE foundation (as if there was no longer a
philosophically interesting QUESTION about f.o.m.).  I think this may be
less so now than it used to be: set theoretic "triumphalism" peaked in the
1960s and 1970s and isn't as strong now.  (View based on personal
observation: no scientific survey methodology!)
Second problem was that set theory is technical and HARD, and even if it is
not THE foundation of mathematics, an understanding of it is required for
anyone with a serious interest in f.o.m.  Here it would help if there were
some good high-level popularizations ("non-technical expositions" if we are
embarrassed to say p*p*l*rization) that the philosophers could read.  I
read and enjoyed Frankel, Bar-Hillel and Levy (with Van Dalen)'s
"Foundations of Set Theory" when I was a graduate student; I might never
have gone any further if I hadn't first had this introduction.  Another
book to slip to one's philosophy colleagues to get them interested might be
Rudy Rucker's "Infinity and the Mind": a lot of it is wild and woolly*, at
a significantly more speculative and less disciplined level than Frankel et
al., but the appendix on large cardinal axioms is the chapter on large
cardinals I'd want included if an expaned edition of "Foundations of Set
Theory" was going to be re-issued.
---
* The way I describe it to my colleagues in philosophy is "Sure, some of
the ideas are half-baked, but that's o.k.-- they're dough, and our job as
professional philosophers is to bake them!"

Allen Hazen
Philosophy Department
University of Melbourne
(interested in logic, philosophy of mathematics, and related stuff)