Poincarae's Philosophy: From Conventionalism to Phenomenology

By Elie Zahar | Go to book overview

3
Poincaré's Philosophy of
Geometry

Geometry has pride of place in Poincaré's philosophy of science. The received view is that his 'conventionalism' can be traced back to his work on non-Euclidean geometries: through constructing models of any one geometry within any other, Poincaré was allegedly led to the view that the choice of a geometry, as well as of certain basic scientific postulates, is a matter of arbitrary convention. In this chapter, I propose to show that the expression 'geometric conventionalism' already constitutes a misnomer. that in conformity with his global philosophy of science, Poincaré adopted a realist, albeit a fundamentally fallibilist, attitude regarding the status of physical geometry.


3.1 CONVENTIONALISM AND GEOMETRY

Were it not for my Popperian qualms about asking 'What is' questions, I should have entitled this chapter 'What is Geometrical Conventionalism'?' I shall in fact be inquiring into the various meanings of the word 'conventionalism', but only with a view to answering the following question: are there aspects of our knowledge which depend solely on arbitrary decisions and can therefore refer to no external reality?

In one sense, the answer is trivially affirmative: in deciding to formulate his hypothesis in one natural language rather than in another, the scientist is guided, not by epistemological, but by pragmatic considerations such as: should I write my articles in English and thus be understood by a wide public, or should I use my mother tongue in which I feel more at ease? Note that I am here talking about science, not about philosophy. Some philosophers are known to have claimed that deep philosophical insights can be rendered only by very special languages, such as Greek and German (see for example Heidegger 1953). I take it for granted that scientific thought is equivalently expressible in all natural languages. We shall see that the triv-

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