Joel David Hamkins : Pluralism in the ontology of mathematics

Séminaire mamuphi (Ircam, Paris, 12 février 2022)
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What is the nature of mathematical ontology-what does it mean to make existence assertions in mathematics? Is there an ideal mathematical realm, a mathematical universe, that those assertions are about? Perhaps there is more than one. Does every mathematical assertion ultimately have a definitive truth value? I shall lay out some of the back-and-forth in what is currently a vigorous debate taking place in the philosophy of set theory concerning pluralism in the set-theoretic foundations, concerning whether there is just one set-theoretic universe underlying our mathematical claims or whether there is a diversity of possible set-theoretic conceptions.