David J. Stump

In a response to my recent article in this journal, Shahram Shahryari argues that I fail to present a third position between absolutism and relativism. He makes two points: first, that fallibilism is insufficient as an alternative, because it is compatible with both relativism and absolutism. The second point is that my argument that experience can lead to objective judgment without being a new absolute fails. I discuss these in turn, showing that both critiques fail and that pragmatism is a genuine alternative between absolutism and relativism.

I will present two examples of influential (and incorrect) interpretations of Poincaré, pinpointing their errors and documenting some of their diffusion. The first example, which appears to have been initiated by Moritz Schlick, is the widespread misinterpretation of Poincaré’s argument for geometric conventionalism by basing it on the underdetermination of theories in science. The second example, having to do with Poincaré’s claim that Euclidean and non-Euclidean geometries are inter-translatable, stems from Louis Rougier and was spread in the English language literature by Max Black. I will then reflect on whether it is possible to avoid fragmentation in the interpretation of Poincaré, using Jeremy Gray’s admirable attempt at completeness in his intellectual biography of Poincaré as an example. Finally, I will propose one possible new direction for study of Poincaré that might enrich our view of him substantially by achieving a level of detail that has so far been lacking.

Much like contemporary philosophers of science, Poincare attempts to develop a philosophy of science that is able to account for genuine historical change in science but also allows science to be seen as progressive. Poincare is famous for his thesis that there is no true metric of space. He claims that we may choose either Euclidean or non-Euclidean geometry in mechanics and the choice is not objectively right or wrong. However, his conventionalism is not total, as some have charged. He holds that only geometry is conventional and he argues that science does discover truth, despite a conventional element in our theories. I review Poincare's general philosophy of science, clarify the burden of proof required to establish his thesis of the conventionality of metric, and provide an interpretation of his arguments for the conventionality of metric which is consistent with his general views. Poincare does not accept physical geometry in the ordinary sense, because he holds the purely relationalist view that space is a mere abstraction that we use to describe the world. Even inertial effects are to be described solely in terms of the relations of physical objects. Were such relationalism true, Poincare could defend his thesis of conventionality of metric without the introduction of ad hoc "universal forces" in physics. Relationalism is disconfirmed by currently accepted scientific theories of space, so we must admit that Poincare's defense of his conventionalist thesis is inadequate. ;The debate over conventionalism has often taken place with global arguments that purport to show that everything is conventional or that all conventions reduce to a trivial change in notation, or charges that conventionalism is a form of relativism. Both global support for conventionalism and global refutations of conventionalism are inadequate. Discussion of conventionalism should center on specific elements of physical theory rather than a priori objections that the view is inconsistent or trivial. I argue that Poincare does not depend on global arguments to defend his conventionalist thesis and that in this regard his philosophical method is quite correct