FOM: social construction and general intellectual interest

[Torkel Franzen]

  Michael Detlefsen says:

   >Now for the substantive point. In this I am in distinct sympathy with
   >Harvey ... and for theoretical reasons.

  Actually it's not clear from your subsequent comments to what extent
you are in sympathy with Friedman. This is because of the ambiguities
pointed out by Colin Mclarty.

  One theme in Friedman's comments has been the view that number
theorists and other mainstream mathematicians somehow promote or stand
for an "indefensible and inappropriate approach to intellectual
life". This idea has little to recommend it, but seems an invitation
to pointless, even nasty, squabbling.

  A second theme is the notion that (the basic ideas of) P=NP and the
foundations of mathematics will be interesting and easily
understandable to all sorts of people. Here again I don't see anything
to brawl about. By all means let us try to make foundations
interesting to all sorts of people. Any little disappointments that we
may experience when we fail to encounter the understanding and enthusiasm
that we think is our due will perhaps only be good for us.

  My comments below, therefore, are predicated on the following colorless
understanding of the point at issue: does the subject of foundations have
a general intellectual interest, and if so, in what terms should we
present that interest to people?

  Your remark that

   >Surely, in posing limits to so magnificent a social vision as Leibniz' (who
   >thought it should even end the lust for warfare through pitting people in a
   >'computational' struggle over logical materiel rather than the more usual
   >types of blood-letting like the Thirty Years War) fom-type results like
   >Church's Theorem show themselves to be of the greatest "general
   >intellectual interest".

seems to presuppose that Leibniz' vision is of the greatest general
intellectual interest. This, surely, is not obvious. There are lots of
magnificent visions that are of interest only to a select few (the
visions of Grothendieck), or are not generally considered of
intellectual interest (the visions of L. Ron Hubbard). Further argument
is needed.

   >The modern-day Leibnizian, as she seeks to minimize the
   >'discouragement' to Leibniz' Program (the term I use for the above-sketched
   >logico-socio-political program of Leibniz) of Church's Theorem and the
   >like, will take a natural and well-motivated interest in the P=NP
   >completeness problem (and research in computational complexity and related
   >foundational matters in general). Thus the large potential for "general
   >intellectual interest" in the latter.

  Surely there aren't all that many modern-day Leibnizians around? What
can we say to those who are not modern-day Leibnizians?

   I don't want to sound too critical here, for I don't myself have any good
reply to my question, even though I think foundations are very interesting
and that it should be possible to make the subject interesting to many
people who are not now familiar with it. Clearly it is a lot easier to
bring out the interest of Church's theorem than it is to bring out the
interest of constructible sets.