FOM: Lakatos
Jeffery Zucker
zucker at maccs.dcss.McMaster.CA
Sat Dec 13 22:00:05 EST 1997
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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