The Center for the Advancement of Logic, its Philosophy, History and Applications presents

"The Geometry Behind Poincaré's Conventionalism"
with Jeremy Heis, Department of Logic & Philosophy of Science, UC Irvine
Wednesday January 8, 2014
11:00 a.m.
Social Science Tower, Room 777

Commentators have wondered whether Poincaré's argument for conventionalism in the philosophy of geometry depends on any specific geometrical facts. Some readers (e.g. Gimbel 2004) see his view as simply a "general epistemological brand of conventionalism" -- just an application of Duhemian underdetermination, or even as an instance of Grünbaum's Trivial Semantic Conventionalism. Even commentators who resist these readings, like Ben-Menahem 2006, argue that Poincaré needs only the fact that there are Euclidean models of hyperbolic space. These readings contrast strongly with a much earlier reaction from Bertrand Russell's Essay on the Foundations of Geometry (1897). Russell claimed that Poincaré's conventionalism stands or falls with a very particular (and in Russell's mind, mistaken) feature of Poincaré's mathematical work: his reliance on the Cayley-Klein definition of distance. (This reading also contrasts with contemporary readings, like Zahar 1997 and Torretti 2010, that explain how Poincaré's use of hyperbolic geometry in the theory of Fuchsian functions provided the "initial motivation," though not a necessary premise, for his conventionalism.) In this talk, Heis will argue that Russell's reading of Poincaré's argument is closer to the truth than many contemporary readings. He will show this by situating Poincaré's geometrical work in its mathematical context, explaining why conventionalism was inevitable for Poincaré, even though it was not a live option for other turn of the century geometers.

For further information, please contact Patty Jones, or 949-824-1520.


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