FOM: Whither FOM? (and a note about FOM archives)

[Stephen G Simpson]

Michael Thayer writes:
 > I am a computer consultant who reads mathematics and philosophy for
 > pleasure, and am interesting in some of the (as yet undelivered)
 > promises of this list.

Michael, I appreciate your remarks, and I have to agree with your
implicit criticism.  The fact is that the FOM list has only barely
begun to deliver on its promise of serious discussion of current
exciting issues and programs in foundations of mathematics.  I'm
trying to remedy this by soliciting genuine f.o.m. contributions and
by clearing the air, so that genuine f.o.m. contributions can be
discussed in a focussed and fruitful way.

 > >>I want to try to clear the air.  ...
 >  This is a good idea.

Thanks, I'm glad you agree that there is a need for this.

 > >    http://www.math.psu.edu/simpson/Hierarchy.html
 ...
 > For my self, I see nothing in point 1. of Steve's paper that is
 > even plausible.

That's OK.  I'm not concerned about whether you and other FOM
subscribers can accept my philosophical base.  The only thing that you
and I need to care about is:

  Can we have a serious discussion of genuine f.o.m. issues?

I sincerely believe that we can.  But in order to do so, we need to
avoid getting bogged down in irrelevancy (Lang conjectures,
cohomology, barbers, Scientific American readers, etc.)  And in order
to avoid getting bogged down, we need to have a focussed, working
concept of what f.o.m. is all about.  I think that my definition of
f.o.m. can serve that purpose, even if not everybody agrees with its
philosophical underpinning.

Michael, let me put the question to you in concrete terms.  Where do
you want the FOM list to go?  Do you want the FOM list to discuss
f.o.m. as I have defined it (analysis of basic mathematical concepts
such as number, shape, set, proof, axiom, ... with an eye to the unity
of human knowledge)?  Or do you want the FOM list to discuss
cohomology, symplectic manifolds, and everything else under the sun?
That is the choice in front of us, as I see it.

 > My personal offering would be that something is of foundaitonal
 > interst when it shows that something which has always been thought
 > of in one way, can also be concieved in a totally different way.

OK.  You are saying that X is of foundational interest if and only if
X shows that something which has always been thought of in one way can
also be conceived in a totally different way.  Well, fine, and I think
I know where you are coming from -- surprising connections between
branches of mathematics, etc etc.  However, I have to say that, in my
opinion, your stated formulation is much too vague to serve as a basis
for focussed discussion of f.o.m.  I'm afraid that if we adopt
something like this as our definition of "foundational", then
everybody will interpret it their own way and we will end up
discussing everything under the sun, with little time or energy left
for genuine f.o.m.  This will continue for a few weeks or months, and
then, after everybody has made all the points they want to make, the
FOM list will die.  I don't want that to happen, and I assume that you
also don't want that to happen.

Let me close with a censored quotation from Student A illustating the
attitude of some math students who have expressed an interest in the
FOM list.  I'm keeping this anonymous, so that Student A won't have to
worry about reprisals from professors who just don't get it.  Please
read this carefully:

   I would love to subscribe!  I am passionately interested in the
   foundations of mathematics, yet I find that it is discouragingly
   unpopular with most of my professors here at [name of university
   omitted]. I look forward to reading what the professionals who
   *are* interested have to say about the present situation in the
   foundations of mathematics ....
   
Michael, let me ask you, how do you interpret Student A's remarks?  Do
you think Student A is saying that he/she wants the FOM list to
discuss topics such as the foundational role of cohomology in geometry
and algebra, or the unifying role of the Lang conjectures in number
theory and algebraic geometry?  I don't think so.  Or, do you think
that Student A is excited about the
Frege-Russell-Hilbert-Brouwer-G"odel-... line and similarly motivated
issues and programs in genuine f.o.m.?  That's what I think, and I'm
trying to steer FOM in a direction that will be useful for people like
Student A.  I'd appreciate all the help I can get.

Sincerely,
-- Steve

PS 

An administative note:

Individual FOM postings through October 31 are now available for
browsing and downloading at

  http://www.math.psu.edu/simpson/Foundations.html

The monthly FOM archive files for September, October, and November are
also available.