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Poincare on the Foundation of Geometry in the UnderstandingIn this paper I aim to clarify Poincaré’s views on the foundations of geometry. According to the received view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schema that provide implicit definitions of geometric terms. I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study of a group. In place of the received view I offer a revised view, according to which Poincare held that axioms in geometry are in fact assertions about invariants of groups.
McHenry County College