Is there just one mathematical universe? DRIFT, Amsterdam, May 2019

This will be a talk for the Wijsgerig Festival DRIFT 2019, held in Amsterdam May 11, 2019. The theme of the conference is: Ontology.

Kamanasish Debnath [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)]

Abstract. What does it mean to make existence assertions in mathematics?
Is there a mathematical universe, perhaps an ideal mathematical reality, that the assertions are about? Is there possibly more than one such universe? 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 worlds.

One thought on “Is there just one mathematical universe? DRIFT, Amsterdam, May 2019

  1. An interesting item in this topic is synthetic differential geometry, which works beautifully, but only when the underlying logic does not have the law of the excluded middle.

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