[Date Index] [Thread Index] [FOM Postings] [FOM Home]

*To*: fom@math.psu.edu*Subject*: FOM: NYC logic conference/Wide Perspective*From*: Harvey Friedman <friedman@math.ohio-state.edu>*Date*: Tue, 28 Dec 1999 12:12:29 -0500*Sender*: owner-fom@math.psu.edu

Simpson 10:55PM 12/26/99 wrote: >The next day after the panel discussion, Gregory Cherlin in private >conversation raised an objection to my point about Riemannian >manifolds, Lebesgue measure, etc. According to Cherlin, the >development of these and many other mathematical concepts ought to be >viewed as foundational work. When I pressed him, he admitted that he >is entertaining the following proposition: All high-level conceptual >work in mathematics ought to be considered part of f.o.m. in the best >sense. I was also able to get Cherlin to admit that the >Frege-Hilbert-G"odel line is foundational in a different sense of the >word ``foundational''. But according to Cherlin, core mathematicians >view this ``traditional f.o.m.'' line as dull, passe, uninteresting, >etc. I said that this is a mistake on the part of the core >mathematicians, as witness their shock over the fact G"odel and Turing >are the only two mathematicians on the Time Magazine list of great >20th century thinkers. > >Basically I think Cherlin is going back to the position of denying the >interest of f.o.m. This was of course the view taken by Cherlin's >fellow applied model theorists (van den Dries et al) in the early days >of FOM. It is partly a matter of just how wide the perspective is that one is concerned with. It is my impression that, for instance, physicists have their own special view of what "foundations of physics" is which is quite different from what mathematicians have in mind. When mathematicians look at mathematical foundations of physics, they are looking for general formulations that transcend particular conceptual issues that physicists normally think of. Mathematicians look for exactness where physicists do not - and in fact the physicists will question the point of even having such exactness. When f.o.m. researchers look at f.o.m., they are looking for general formulations that transcend particular conceptual issues that mathematicians normally think of. F.o.m. researchers look for exactness where mathematicians do not - and in fact the mathematicians will question the point of even having such exactness. Take a look at Godel's second incompleteness theorem. It is a finding that transcends any particular conceptual development in mathematics. And it has to be exact where mathematicians aren't normally exact. Take a look at the programs of concrete independence results, enormous integers, reverse mathematics, etc. The issues and phenomena transcend any particular conceptual issues in core mathematics. Yet the examples cut across a huge variety of core mathematical topics. And more and more core mathematical contexts are being treated from these perspectives. These programs are clearly destined to eventually say something of clear interest in every mathematical context whatsoever. Yet the overall messages are of a character transcendent to any one of these contexts, and in fact transcendent to all of mathematics. They fit into a wider framework - that of foundational studies, which involves all subjects. Simpson mentions "their shock over the fact G"odel and Turing are the only two mathematicians on the Time Magazine list of great 20th century thinkers". There is nothing definitive about Time Magazine's list, of course. But it is an indication that there is greater general interest in what Godel and Turing did than what went on in core mathematics, regardless of how deep and intricate it was. If the core mathematicians wish to compete with Godel and Turing in the general intellectual culture of our times, they will want to cast their subjects in more generally intellectually attractive and generally understandable terms.

[Date Prev] [Date Next] [Thread Prev] [Thread Next]

[Date Index] [Thread Index] [FOM Postings] [FOM Home]