>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