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*To*: fom*Subject*: FOM: whither mathematics; set theory; cultural studies; historicism*From*: Stephen G Simpson <simpson@math.psu.edu>*Date*: Fri, 30 Jan 1998 23:11:15 -0500 (EST)*In-Reply-To*: <34D259F7@courier.lmu.ac.uk>*References*: <34D259F7@courier.lmu.ac.uk>*Reply-To*: simpson@math.psu.edu*Sender*: owner-fom@math.psu.edu

David Corfield writes: > Does either side of this debate have ideas about where it wants to > see mathematics going, or the way it is taught? Speaking only for myself, I'd like to see mathematics and the philosophy of mathematics become more objective and reality-oriented. I would hope for the following: (1) better integration of pure and applied mathematics and various mathematical sciences; (2) healthy skepticism about Bourbakian "mathematical architecture"; (3) greater attention to and understanding of f.o.m. issues; (4) more emphasis on mathematical rigor, precise thinking, etc. I feel that all of these would have a very positive impact on mathematics education as well as philosophy of mathematics. > There have been consequences (possibly unintended) of the 'set > theory as foundation of math' picture. It has worked its way into > the minds of the larger part of Anglo-American philosophers. Are > FOM set theorists happy with that, or do they take their work to be > misappropriated? If the latter, should they not say so? I think one of the bad consequences was the "new math" of the 1960's and 1970's. This was a US educational fad which consisted of teaching set-theoretic f.o.m. to young school children in inappropriate ways. See Morris Kline's book "Why Johnny Can't Add". Though I see a lot of f.o.m. value in set theory, I'm not particularly wedded to it. In an ideal world, I would expect philosophers of mathematics to explore objective alternatives to set-theoretic f.o.m. In the real world that we live in, I'm alarmed about the subjectivist or postmodernist trend in current academic philosophy, and I don't see how anything good for mathematics can come of it. > David Corfield > School of Cultural Studies > Leeds Metropolitan University > U.K. > > Interests: Historicist philosophy of mathematics, cognitive psychology Hmmm, cultural studies. Does this smack of the subjectivist turn that I alluded to above? And what about "historicist philosophy"? Is it Hegelian? I'm not a big fan of Popper, but I think Popper's "The Poverty of Historicism" made some good points. An even better attack on historicism (not widely known, unfortunately) is Ludwig von Mises, "Theory and History". -- Steve Name: Stephen G. Simpson Position: Professor of Mathematics Institution: Penn State University Research interest: foundations of mathematics More information: www.math.psu.edu/simpson/

**References**:**Corfield, David [CES]**- FOM: Set vs topos debate

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