FOM: Truth in mathematics

[Alasdair Urquhart]

FOM subscribers who have been following the recent
debate on the nature of mathematical truth
should be interested in a recent valuable collection
of articles "Truth in Mathematics" edited by
Dales and Oliveri (Oxford 1998).  This is the record
of a conference in Mussomeli, Sicily, that was
unusual in bringing together philosophers and mathematicians.
It includes contributions by outstanding mathematicians,
among them Manin, Woodin and Martin.  

A particularly interesting piece is by Vaughan Jones,
whose philosophy is broadly anti-formalist.  He says,
among other things:

"Proofs are indispensable, but I would say they are necessary
but not sufficient for mathematical truth, at least truth as perceived
by the individual" (Dales and Oliveri, p. 208).

He goes on after this to discuss the reliability of proofs and
of programs in a way that complements Andrej Bauer's recent 
excellent posting.

The entire volume repays close study, and also refutes the
assertion that working mathematicians have no use for
the notion of truth.

Alasdair Urquhart