Poincaré’s conventionalism has been interpreted in many writings as a philosophical position emerged by reflection on certain scientific problems, such as the applicability of geometry to physical space or the status of certain scientific principles. In this paper I would like to consider conventionalism as a philosophical position that emerged from Poincaré’s scientific practice. But not so much from dealing with scientific problems, as from the use of two specific methodologies proper to modern mathematics and the modern natural sciences: methodological (...) structuralism and the hypothetical-deductive method—thus, as a philosophical position which emerged from a way (or rather, two ways) ofdoingscience. With this approach, I try to deepen the analysis of connections between Poincaré’s scientific practice and his philosophy. (shrink)

Much of the focus on Poincaré’s philosophy of science has been on the notion of convention, a crucial concept that has become distinctive of his position. However, other notions have received much less attention. That is the case of verifiable hypotheses. This kind of hypotheses seems to be constituted from the generalization of several observable facts. So, in order to understand what these hypotheses are, we need to know what a fact to Poincaré is. He divides facts into brute and (...) scientific facts. The characterization of this duality is not trivial at all, and leads us to the following questions that we will discuss in this paper: which the part of construction that exists in a scientific fact and which the part of translation, that is, what remains from the brute fact in the scientific one?; and when we conceive a generalized hypothesis, are we supposed to do it from scientific or from brute facts? The clarification of these questions could lead to distinguish the part of construction and the part of translation in the first steps of science, which is essential to get a better understanding of Poincaré’s conception of science. (shrink)

In the introduction to his famous book, La Science et l’hypothèse, Poincaré remarks on the necessary role and legitimacy of hypotheses. He establishes a triple classification of hypotheses, dividing them into verifiable, useful, and apparent. However, in chapter 9, entitled ‘Les hypothèses en physique’, he gives a slightly different triadic classification: natural hypotheses, indifferent hypotheses, and real generalizations. The origin of this second classification is a lecture given at the International Congress of Physics, Paris, 1900. What are the similarities and (...) differences between these two classifications? My main purpose is to provide a possible equivalence between the two classifications in order to clarify the role of hypotheses in Poincaré’s epistemology of natural science. The discussion will be based on the two fundamental texts mentioned above and on the contrast between Poincaré’s use of the notion of hypothesis and that of some of his contemporaries. (shrink)