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)

The aim of this paper is to argue that there existed relevant interactions between mechanics and geometry during the first half of the nineteenth century, following a path that goes from Gauss to Riemann through Jacobi. By presenting a rich historical context we hope to throw light on the philosophical change of epistemological categories applied by these authors to the fundamental principles of both disciplines. We intend to show that presentations of the changing status of the principles of mechanics as (...) a mere epiphenomenon of the emergence of non-Euclidean geometries are inaccurate, that the relations between the two disciplines were richer than what is usually considered in the literature. These claims will be based on historical and philosophical arguments, starting from the fact that disciplinary boundaries at the time were not rigid as we are used today. It is widely known that the main figures we target worked in different areas, which is a first piece of evidence for the plausibility of our main thesis. (shrink)

In this paper I argue that Poincaré’s acceptance of the atom does not indicate a shift from instrumentalism to scientific realism. I examine the implications of Poincaré’s acceptance of the existence of the atom for our current understanding of his philosophy of science. Specifically, how can we understand Poincaré’s acceptance of the atom in structural realist terms? I examine his 1912 paper carefully and suggest that it does not entail scientific realism in the sense of acceptance of the fundamental existence (...) of atoms but rather, argues against fundamental entities. I argue that Poincaré’s paper motivates a non-fundamentalist view about the world, and that this is compatible with his structuralism. (shrink)

Everything you always wanted to know about structural realism but were afraid to ask Content Type Journal Article Pages 227-276 DOI 10.1007/s13194-011-0025-7 Authors Roman Frigg, Department of Philosophy, Logic and Scientific Method, London School of Economics and Political Science, Houghton Street, London, WC2A 2AE UK Ioannis Votsis, Philosophisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, Geb. 23.21/04.86, 40225 Düsseldorf, Germany Journal European Journal for Philosophy of Science Online ISSN 1879-4920 Print ISSN 1879-4912 Journal Volume Volume 1 Journal Issue Volume 1, Number 2.

There is a basic division in the philosophy of mathematics between realist, ‘platonist’ theories and anti-realist ‘constructivist’ theories. Platonism explains how mathematical truth is strongly objective, but it does this at the cost of invoking mind-independent mathematical objects. In contrast, constructivism avoids mind-independent mathematical objects, but the cost tends to be a weakened conception of mathematical truth. Neither alternative seems ideal. The purpose of this paper is to show that in the philosophical writings of Henri Poincaré there is a coherent (...) argument for an interesting position between the two traditional poles in the philosophy of mathematics. Relying on a semi-Kantian framework, Poincaré combines an epistemological and metaphysical constructivism with a more realist account of the nature of mathematical truth. (shrink)