rhersh at math.unm.edu
Sun Dec 14 12:01:41 EST 1997
ALso Sol Feferman, in an article called something like Math Logic vs
Logic of Math Discovery, referenced in the two books by Hersh.
On Sat, 13 Dec
1997, Jeffery Zucker wrote:
> I recently read "Proofs and Refutations" by Imre Lakatos.
> Many subscribers to this list will be familiar with this
> classic work, but I'll summarise it briefly.
> It grew out of Lakatos' 1961 Cambridge PhD thesis under
> R. Braithwaite, and was strongly influenced by Karl Popper.
> It was edited and published posthumously by John Worrall
> and Elie Zahar in 1976.
> I'll quote briefly from the author's Introduction:
> "Its modest aim is to elaborate the point that informal,
> quasi-empirical, mathematics does not grow through
> a monotonous increase of the number of indubitably
> established theorems but through the incessant
> improvement of guesses by speculation and criticism,
> by the logic of proofs and refutations"
> The bulk of the book is in the form of a case study
> (in dialogue form), in which Euler's celebrated theorem for
> polyhedra (V-E+F=2) is subjected to a series of successive
> proofs and refutations, the latter being dealt with (not only
> by revisions of the proofs, but also) by successive
> re-formulations of the theorem, involving re-definitions of
> the notion of "polygon".
> I was impressed, not only by the author's philosophical
> brilliance (as it seems to me), but also by the
> dazzling erudition displayed in his historical footnotes.
> I have two questions, with which members of this list
> may be able to help me:
> (1) In spite of Lakatos's strong (to me) arguments,
> his work seems to have had little, if any, discernible effect
> on mathematical pedagogy, including the style of textbooks.
> Why is this?
> (2) What has been written in response to this work
> (for or against)?
> BTW, Moshe Machover (whom the editors acknowledge for
> his help) may have some interesting insights on this.
> Jeff Zucker
> Computer Science Dept, McMaster University, Hamilton, Ont. L8S 4K1, Canada
> zucker at mcmaster.ca || http://www.dcss.mcmaster.ca/~zucker/z.html
> (905) 525-9140 x 23438 || fax (905) 546-9995
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