v. 1. The methodology of scientific research programmes.--v. 2. Mathematics, science, and epistemology.

Henri Poincaré’s views on the foundations of mechanics and the nature of mechanical explanation were influenced by the work of two of the most renowned nineteenth century scientists, James Clerk Maxwell and Heinrich Hertz. In order then to unravel Poincaré’s views and own contribution to the subject it is important to see the connection between Maxwell ’s and Hertz’s researches on the one hand and Poincaré’s on the other. Consequently, I start this paper with a brief account of Poincaré’s encounter (...) with Maxwell ’s work in electromagnetism. Then, in section 2, I move on to show how Hertz’s work on the foundations of mechanics shaped Poincaré own views. In sections 3 and 4, I formulate Poincaré’s own conventionalist philosophy of mechanics and show how several methodological considerations, especially the search for unity, mitigated his conventionalism. Having thus examined Poincaré’s views on the foundations of mechanics, in section 5 I turn my attention to his notion of mechanical explanation and his proof that a mechanical explanation of a set of phenomena is possible if the principle of conservation of energy is satisfied. I then go on to show how Poincaré secured the possibility of a mechanical explanation of electromagnetic phenomena, and also how, having done so, he ended up with an unlimited number of configurations of matter in motion that could underpin electromagnetic phenomena. The upshot of this paper will be that Poincaré departed from the traditional conceptions on mechanical explanation and defended a purely structural conception, the strong point of which was that it promoted — as the motto of this paper says — the true and only aim of science, namely unity. (shrink)

The logical positivists adopted Poincare's doctrine of the conventionality of geometry and made it a key part of their philosophical interpretation of relativity theory. I argue, however, that the positivists deeply misunderstood Poincare's doctrine. For Poincare's own conception was based on the group-theoretical picture of geometry expressed in the Helmholtz-Lie solution of the space problem, and also on a hierarchical picture of the sciences according to which geometry must be presupposed be any properly physical theory. But both of this pictures (...) are entirely incompatible with the radically new conception of space and geometry articulated in the general theory of relativity. The logical positivists's attempt to combine Poincare's conventionalism with Einstein's new theory was therefore, in the end, simply incoherent. Underlying this problem, moreover, was a fundamental philosophical difference between Poincare's and the positivists concerning the status of synthetic a priori truths. (shrink)