This will be a talk on November 6, 2017 for the Logic and Metaphysics workshop at the CUNY Graduate Center, run by Graham Priest.

## The modal principles of potentialism in mathematics

**Abstract.** Potentialism is the view in the philosophy of mathematics that one’s mathematical universe, whether in arithmetic or set theory, is never fully completed, but rather unfolds gradually as new parts of it increasingly come into existence or become accessible or known to us. As in the classical dispute between actual versus potential infinity, the potentialist holds that objects in the upper or outer reaches have potential as opposed to actual existence, in the sense that one can imagine forming or discovering always more objects from that realm, as many as desired, but the task is never completed. Recent work has emphasized the modal aspect of potentialism, and in this talk, I shall describe a general model-theoretic account of the modal logic of potentialism, identifying specific modal principles that hold or fail depending on features of the potentialist system under consideration. This work makes use of modal control statements, such as buttons, switches, dials and ratchets and the connection of these kinds of statements with the modal theories S4, S4.2, S4.3 and S5. I shall take the various natural kinds of arithmetic and set-theoretic potentialism as illustrative cases.

This is joint work with Øystein Linnebo, University of Oslo (see our paper The modal logic of set-theoretic potentialism and the potentialist maximality principles), and further joint work in progress with Victoria Gitman and Roman Kossak, and very recent joint work in progress with W. Hugh Woodin.

What time and exactly where will this be held? Are “outsiders” welcome to attend/observe? I am the former chair of the Math Dept at The Beekman School in NYC, now semi-retired, and have always had an interest in Logic and the Philosophy of Mathematics.

=Charlie Sitler

charlies@beekmanschool.org

212 755 6666

The seminar will run Mondays 4.15-6.15 at the CUNY Graduate Center (365 Fifth Avenue, across the corner from the Empire State Building), but the room is not yet assigned. I believe outsiders are welcome, but you can contact the organizer Graham Priest (CUNY) to confirm this. I’ll try to post the room details here when the information becomes available.