Poincaré's conception of the objectivity of mathematics

Philosophia Mathematica 2 (3):202-227 (1994)
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Abstract

There is a basic division in the philosophy of mathematics between realist, ‘platonist’ theories and anti-realist ‘constructivist’ theories. Platonism explains how mathematical truth is strongly objective, but it does this at the cost of invoking mind-independent mathematical objects. In contrast, constructivism avoids mind-independent mathematical objects, but the cost tends to be a weakened conception of mathematical truth. Neither alternative seems ideal. The purpose of this paper is to show that in the philosophical writings of Henri Poincaré there is a coherent argument for an interesting position between the two traditional poles in the philosophy of mathematics. Relying on a semi-Kantian framework, Poincaré combines an epistemological and metaphysical constructivism with a more realist account of the nature of mathematical truth.

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Janet Folina
Macalester College

Citations of this work

On mathematical error.David Sherry - 1997 - Studies in History and Philosophy of Science Part A 28 (3):393-416.

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References found in this work

Philosophical Investigations.Ludwig Wittgenstein - 1953 - New York, NY, USA: Wiley-Blackwell. Edited by G. E. M. Anscombe.
The Structure of Scientific Revolutions.Thomas S. Kuhn - 1962 - Chicago, IL: University of Chicago Press. Edited by Ian Hacking.
The Structure of Scientific Revolutions.Thomas Samuel Kuhn - 1962 - Chicago: University of Chicago Press. Edited by Otto Neurath.
Philosophical investigations.Ludwig Wittgenstein & G. E. M. Anscombe - 1953 - Revue Philosophique de la France Et de l'Etranger 161:124-124.

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