In Conventionalism, Yemima Ben-Menahem traces the 20th century development of two strands of conventionalism from their roots in Poincaré’s Science and Hypothesis. Ben-Menahem views later developments of these two conventionalist strands — into the view that all so-called necessary truths are mere conventions, and the view that all scientific theories are subject to underdetermination — as underargued extrapolations of more specific theses present in Poincaré’s work on geometry. Ben-Menahem’s thoughtful analysis of the story of conventionalism, a story she tells us, ‘of a highly edifying philosophical failure’ (p. 5), is a welcome contribution to the understanding of twentieth century analytic philosophy.

Poincaré’s conventionalism starts with an account of the status of the axioms of alternative geometries. Prior to the development of non-Euclidean geometries, the axioms of Euclidean geometry could be viewed as necessary truths. According to Kant, these truths, though substantial and therefore synthetic,...

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