Conversations on Mind, Matter, and Mathematics

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Princeton University Press, 1998 - 260 pages
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Do numbers and the other objects of mathematics enjoy a timeless existence independent of human minds, or are they the products of cerebral invention? Do we discover them, as Plato supposed and many others have believed since, or do we construct them? Does mathematics constitute a universal language that in principle would permit human beings to communicate with extraterrestrial civilizations elsewhere in the universe, or is it merely an earthly language that owes its accidental existence to the peculiar evolution of neuronal networks in our brains? Does the physical world actually obey mathematical laws, or does it seem to conform to them simply because physicists have increasingly been able to make mathematical sense of it? Jean-Pierre Changeux, an internationally renowned neurobiologist, and Alain Connes, one of the most eminent living mathematicians, find themselves deeply divided by these questions.

The problematic status of mathematical objects leads Changeux and Connes to the organization and function of the brain, the ways in which its embryonic and post-natal development influences the unfolding of mathematical reasoning and other kinds of thinking, and whether human intelligence can be simulated, modeled,--or actually reproduced-- by mechanical means. The two men go on to pose ethical questions, inquiring into the natural foundations of morality and the possibility that it may have a neural basis underlying its social manifestations. This vivid record of profound disagreement and, at the same time, sincere search for mutual understanding, follows in the tradition of Poincaré, Hadamard, and von Neumann in probing the limits of human experience and intellectual possibility. Why order should exist in the world at all, and why it should be comprehensible to human beings, is the question that lies at the heart of these remarkable dialogues.

  

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Review: Conversations on Mind, Matter, and Mathematics

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I think we can both agree that nobody's opinion is changed after having these conversations. Consulter l'avis complet

Table des matières

Mathematics and the Brain
iii
Plato as Materialist?
13
Nature Made to Order
29
The Neuronal Mathematician
62
Darwin among the Mathematicians
110
Thinking Machines
141
The Real and the Rational
167
Ethical Questions
198
Glossary of Mathematical Terms
225
Glossary of Neurobiological Terms
235
Index
241
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À propos de l'auteur (1998)

Changeux is Director of the Molecular Neurobiology Laboratory at the Institute Pasteur in Paris and Professor at the College de France.

Michel Tardieu holds the Chair in the Syncretisms of Late Antiquity at the College de France. His many books include "La Formation des canons scriptuaires," M. B. DeBevoise has translated or edited some thirty works from the French and Italian.

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