FOM: Lakatos

Reuben Hersh rhersh at
Sun Dec 14 11:59:22 EST 1997

You can find comment and critique on Lakatos, with a good deal of 
overlap,  in these places:

Mathematical Intelligencer, the first or 2d issue.

THe Mathematial Experience, P J Davis & R Hersh, Birkhauser, now available 
in a seond edition.

  What is Mathematics Really, R. Hersh, Oxford U. Press.  

Also there is a 
whole book about Lakatos, I forget the author & title, recently reviewed 
in Philosophia Mathematica.

Paul Ernest reviewed Lakatos in Math Reviews, shortly after it was

He also treats Lakatos in two books, Philosophy of Mathematics Education
and Constructivism as a Philosophy of Mathematics.

Cambridge or is it Oxford published a 2-volume collexted works of Lakatos.

The Boston Seminar (Symposium?) on philosophy of science published
a memorial volume for him.

Reuben 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
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> Computer Science Dept, McMaster University, Hamilton, Ont. L8S 4K1, Canada
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