Poincaré's conventionalism and the logical positivists

Foundations of Science 1 (2):299-314 (1995)
The logical positivists adopted Poincare's doctrine of the conventionality of geometry and made it a key part of their philosophical interpretation of relativity theory. I argue, however, that the positivists deeply misunderstood Poincare's doctrine. For Poincare's own conception was based on the group-theoretical picture of geometry expressed in the Helmholtz-Lie solution of the space problem, and also on a hierarchical picture of the sciences according to which geometry must be presupposed be any properly physical theory. But both of this pictures are entirely incompatible with the radically new conception of space and geometry articulated in the general theory of relativity. The logical positivists's attempt to combine Poincare's conventionalism with Einstein's new theory was therefore, in the end, simply incoherent. Underlying this problem, moreover, was a fundamental philosophical difference between Poincare's and the positivists concerning the status of synthetic a priori truths.
Keywords Conventionalism  Geometry  Logical positivism  Relativity theory  Group theory  Synthetic a priori
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    Steven Bland (2013). Scepticism, Relativism, and the Structure of Epistemic Frameworks. Studies in History and Philosophy of Science Part A 44 (4):539-544.
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