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Since the mid-sixties, Paul Benacerraf's work has been at the heart of the concerns of philosophers of mathematics. His conception of the epistemological difficulties of Platonism is crucial to the dispensability arguments at the root of contemporary nominalism, but also to the naturalism inherited from Quine. His reflection on the criterion of identity of numbers (in terms of objects, sets or properties) is important for structuralism, and his critique of logicism for any discussion of Hume's principle at work in Frege. His article on super-tasks has renewed reflections on non-constructive procedures, linked to more general considerations of finitism and feasibility. The aim of this symposium is to consider all these major contributions from a critical perspective.

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