Henri Poincare
French mathematician. He was great not only as a mathematician or a mathematical physicist but also as a philosopher of science. He propounded a kind of conventionalism with respect to geometry. He claimed that axioms of geometry are neither a synthetic a priori truth nor an empirical truth, and that they are a convention in a disguised form; we choose an appropriate convention in the light of our experience, and thus the question is not whether it is true or not but whether it is convenient or simple. He conjetured that Euclidean geometry will remain the most convenient and the simplest.
Although this conjecture was in a sense "falsified" by the subsequent development of relativistic physics, the thesis of conventionalism seems to have survived in some form; without introducing some conventional elements, we cannot determine the metrical structure of (physical) space and time.
Also, he was one of the ealiest who noticed "chaos" in a mechanical, deterministic system ("chaos" is a phenomenon such that even if the system behaves deterministically, it quickly becomes unpredictable because of its very sensitive dependence on initial conditions). This insight seems to have stemmed from his own formulation of the initial-value problem of dynamics (see, e.g., Science and Hypothesis, ch. 5, sect.5): Given an initial state of a dynamical system and the direction of its change, can we determine the history of the system completely, or what sort of information do we need in order to be able to do this? He was a relativist in the sense that he thought that only relative motions should be relevant in dynamics, and we should discard absolute space and time; but he also noticed the difficulty of this position. His popular books such as Science and Hypothesis are still attractive, and provide good materials for philosophical consideration.
See my Notes on Poincare (Japanese).
