Changeux, J.-P.; Connes, A.: Conversations on mind, matter, and mathematics (1995)
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- Footnote
- Rez. in: Mathematical intelligencer 27(2005) no.4, S.48-56 (J. Petitot): "What exactly is the type of reality of mathematical ideal entities? This problem remains largely an open question. Any ontology of abstract entities will encounter certain antinomies which have been well known for centuries if not millennia. These antinomies have led the various schools of contemporary epistemology increasingly to deny any reality to mathematical ideal objects, structures, constructions, proofs, and to justify this denial philosophically, thus rejecting the spontaneous naive Platonism of most professional mathematicians. But they throw out the baby with the bath water. Contrary to such figures as Poincaré, Husserl, Weyl, Borel, Lebesgue, Veronese, Enriques, Cavaillès, Lautman, Gonseth, or the late Gödel, the dominant epistemology of mathematics is no longer an epistemology of mathematical content. For quite serious and precise philosophical reasons, it refuses to take into account what the great majority of creative brilliant mathematicians consider to be the true nature of mathematical knowledge. And yet, to quote the subtitle of Hao Wang's (1985) book Beyond Analytic Philosophy, one might well ask whether the imperative of any valid epistemology should not be "doing justice to what we know." The remarkable debate Conversations an Mind, Matter, and Mathematics between Alain Connes and JeanPierre Changeux, both scientific minds of the very first rank and professors at the College de France in Paris, takes up the old question of the reality of mathematical idealities in a rather new and refreshing perspective. To be sure, since it is designed to be accessible to a wide audience, the debate is not framed in technical terms; the arguments often employ a broad brush and are not always sufficiently developed. Nevertheless, thanks to the exceptional standing of the protagonists, the debate manages to be compelling and relevant. ...
Conclusion The debate between Jean-Pierre Changeux and Alain Connes is one of the most interesting to take place in recent years. lt re-frames in a very up-to-date context a whole series of traditional and difficult questions from the standpoint of the knowledge and experience of two of the leading protagonists of contemporary science. To the choice presented by the neurobiologist between a Platonist ontology and a neurocognitive psychology of mathematical activity, the mathematician replies with a conception that is objective (neither ontological nor psychological) of the thoroughly consistent universe of mathematical idealities. lt is indeed in this three-sided arena that the major difficulties play themselves out. One of the great virtues of the book is to cast a spotlight an this confrontation."
