[FOM] John Baez on David Corfield's book

[David Corfield]

Stephen G Simpson wrote:

> If you have no objection to "foundationalism", then how are we to
> understand remarks such as the following?
>
>   "Not only does the foundationalist filter fail to detect the pulse
>   of contemporary mathematics, it also screens off the past to us as
>   not-yet-achieved.  Our job is to dismantle it ...."
>
> And, what exactly do you mean by "the foundationalist filter"?  Am I
> wrong in assuming it has something to do with foundations of
> mathematics (f.o.m.), the topic of this mailing list?

By the pulse of contemporary mathematics I mean the development of the
kind of mathematics relating to Fields Medals: Langlands conjectures,
Weil conjectures, Topological quantum field theory, knot theory, Thurston
on 3-manifolds, Monstrous moonshine, etc., and the extraordinary connections
between these topics. Presumably, we agree that your work on foundations
has no bearing on the way mathematicians view the proper organisation of
mathematical ideas.

Where we may differ is that I believe there is a task for philosophers to
treat
this organisation. In doing so I can appeal beyond Lakatos to Frege and
Plato.
Miles Burnyeat wrote an excellent paper on the role of mathematics in The
Republic. Plato clearly has a sense about the organisation of the whole of
existing mathematics. For the philosopher-king, after 10 years of being
taught math between the ages of 20 and 30, the next 5 years is to be spent
on dialectical discussion, part of the job of which is to question the
founding
assumptions of mathematics, e.g., have we got the definitions of geometry
right?
In many ways the true Platonist of the 20th century is Lakatos - conceptual
development via dialogue.

David Corfield