[FOM] Re: pom/fom. directions

[Jon Williamson]

Is this the point of dispute?

Corfield thinks that philosophers of maths should study and understand
maths;

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

> There are two standard ways that people who know some modern mathematics
try
> 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
might
> 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
more
> 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
that
> 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?