Pluralism in the foundations of mathematics, ASL invited address, joint APA/ASL meeting, New York, January 2024

This will be an invited ASL address at the joint meeting of the ASL with the APA Eastern Division conference, held in New York 15-18 January 2024. My talk will be 16 January 2024 11:00 am.

Note the plurality of Empire State Buildings...

Abstract. I shall give an account of the debate on set-theoretic pluralism and pluralism generally in the foundations of mathematics, including arithmetic. Is there ultimately just
one mathematical universe, the final background context, in which every mathematical
question has an absolute, determinate answer? Or do we have rather a multiverse of
mathematical foundations? Some mathematicians and philosophers favor a hybrid notion, with pluralism at the higher realms of set theory, but absoluteness for arithmetic.
What grounds are there for these various positions? How are we to adjudicate between
them? What ultimately is the purpose of a foundation of mathematics?

Natures of Proof, Pacific APA, San Francisco, April 2023

I am a commentator at the Pacific APA 2023 conference in San Francisco in a Book Symposium session focused on the book of Catarina Duthil Novaes, The Dialogical Roots of Deduction.

I think very highly of Novaes’s book (my book review is here) and I nominated it for the Lakatos prize, which I am very glad to say that she won. This is particularly appropriate in my view in light of Lakatos’s own use of dialogues in expressing his perspectives on the philosophy of mathematics and the nature of proof.

I shall be a speaker at the book symposium, intending to place the dialogical perspective on proof in the context of a variety of other views of proof. I shall conclude with a few criticisms of the book, which I hope might lead to interesting discussion.

My remarks will follow this outline: