Platonism is still very strong in mathematics. My friend Reuben Hersh, who
just published a book "What is Mathematics, really? " has already been
attacked by Martin Gardner--of Scientific American fame--for his social
practices view of the field.
It,too, is a good read.
Vera
On Mon, 3 Nov 1997, martin packer wrote:
> Jay writes from Tucson:
>
> >As to the critique of mathematics, certainly Valerie
> >Walkerdine, among others, has given us some directions to pursue, and I
> >have recently found an excellent critique of the philosophical idealism
> >still dominant in Mathematics in the work of Brian Rotman at LSU.
>
> I want to second Jay's recommendation of the work of Brian Rotman. Many
> months ago on xmca I briefly sketched Rotman's analysis of the ways the
> formal assertions of mathematics are sustained by the social practices of
> its practitioners. This in his 1993 book, "Ad infinitum: The ghost in
> Turing's machine - taking god out of mathematics and putting the body back
> in".
>
> And I recently stumbed across an older book: "Jean Piaget: Psychologist of
> the real." (1977, Ithaca: Cornell University Press.) There Rotman
> considers, with the care and subtlety of a trained mathematician, Piaget's
> epistemological claims. He shows, amongst other things, that the notion of
> equilibrium can't give direction to development (because there can be
> multiple equilibrium states for a system in change); that Piaget's
> understanding of evolution is based on a misplaced, pre-Darwinian emphasis
> on the individual, not the species; that his focus on the Bourbaki group's
> reconstruction of mathematics leads him to gravely missrepresent the
> history of mathematics (stopping with the Greeks, in some cases!); that the
> concept of internalization is vague; that his conceptualization of language
> is inadequate, and leads to further misunderstanding of mathematics; that
> Piaget fuzzes the relationship between individual and society in order to
> insist that cognitive change is not subject to social influences; and that
> his social organicism is nineteenth century in style.
>
> A good read! Two thumbs up!
>
> Martin
>
>
> ================
> Martin Packer
> Associate Professor
> Department of Psychology
> Duquesne University
> Pittsburgh PA 15282
>
> (412) 396-4852
> fax: (412) 396-5197
>
> packer who-is-at duq3.cc.duq.edu
> http://www.duq.edu/liberalarts/psychology/packer.html
>
>
---------------------------------
Vera P. John-Steiner
Department of Linguistics
Humanities Bldg. 526
University of New Mexico
Albuquerque, NM 87131
(505) 277-6353 or 277-4324
Internet: vygotsky who-is-at unm.edu
---------------------------------