[FOM] Re: pom/fom. directions

Jon Williamson jon.williamson at kcl.ac.uk
Wed Oct 22 07:28:11 EDT 2003

Is this the point of dispute?

Corfield thinks that philosophers of maths should study and understand

Friedman thinks that philosophers of maths should only study those bits of
maths of general intellectual interest, or of traditional philosophical

> There are two standard ways that people who know some modern mathematics
> to convince people that there is some value to modern mathematics.
> 1. It is beautiful.
> 2. It is deep.
> 3. It is extremely difficult.
> 4. It ties up with physics.
> 5. It is useful.
> Obviously 2,3 are related, and 4,5 are related.
> But note that none of these "reasons" has any prima facie connection with
> what traditionally has been of concern for philosophers.

> However, there is one clearly impressive achievement that perhaps some
> think that philosophers could achieve with regard to modern mathematics.
> Can it be cast in such a way that not only is it more understandable to
> people, but actually assumes a compelling kind of obvious general
> intellectual interest?
> For this, things like 1-5 just won't do. I mean a way of casting it so
> it can arguably take an equal place alongside the great awe inspiring
> intellectual achievements of all time?

The difficulties I can see with Friedman's view are these:

1. it is hard to see how much of post-1930s FOM has been of general
intellectual interest. In contrast, there have been a number of topics in
recent maths of general intellectual interest, e.g. nonlinear dynamics and
the general interest in chaos theory; number theory and the general interest
in cryptography and in Fermat's last theorem,; many areas of recent maths
and the general interest in fundamental physics.

2. how should one delimit `traditional philosophical interest'? The
philosophical interests of the Pythagorean school? Of Plato? Of Kant? In any
case, why be so backward-looking?

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