paradigm where probability reigns. In The Value of Science, Poincaré writes and repeats his enthusiasm for two lines of research : statistical laws (taking the place of differential laws), and relativistic mechanics (taking the place of Newtonian mechanics). Nevertheless, he did not take into account the ideas of Planck. This latter had in 1900 published the spectral laws governing blackbody radiation, which were the foundation of quantum mechanics. In 1905, the same year as the publication of The Value of Science, Albert Einstein published a decisive article on the photoelectric effect, which he based on the work of Planck. Despite the doubts of Poincaré, which were no doubt related to his vision of physics as an approximation of reality (in contrast to the exactness of mathematics), the probabilistic rules of quantum mechanics were clearly the response to the second crisis of mathematical physics, at the end of the nineteenth century. (One can point out that in 1902, Poincaré envisaged a relativistic physics which closely matched, in its theoretical development, the one developed and propounded by Einstein several years later.) Objective value of science "What is the purpose of science?" is the question repeatedly asked in Poincaré's book. To this teleological problem, Poincaré responds by taking the opposite position from that of Édouard Le Roy, philosopher and mathematician, who argued in a 1905 article (Sur la logique de l'invention, "On the logic of invention") that science is intrinsically anti-intellectual (in the sense of Henri Bergson) and nominalistic. In contrast to Le Roy, Poincaré follows the thought of Pierre Duhem. He explains that the notion that science is anti-intellectual is self-contradictory, and that the accusation of nominalism can be strongly criticized, because it rests on confusions of thoughts and definitions. He defends the idea of conventional principles, and the idea that scientific activity is not merely a set of conventions arranged arbitrarily around the raw observations of experiment. He wishes rather to demonstrate that objectivity in science comes precisely from the fact that the scientist does no more than translate raw facts into a particular language: "(...) tout ce que crée le savant dans un fait, c'est le langage dans lequel il l'énonce". The only contribution of science would be the development of a more and more mathematized language, a coherent language because it offers predictions which are useful – but not certain, as they remain forever subject to comparisons with real