Philosophy of Mathematics Seminar

Abstract: The iterative conception of set has held centre-stage for a lot of the discussion in the philosophy of sets. For a long time, the “typical” way of thinking of this conception has been to take all possible subsets of sets living at previous layers when moving from one layer to another, thus forming layers by iterating the power-set operation (taking unions at limits). Call this the strong iterative conception. On the other hand, call the conception which holds that sets are formed in layers, but takes no stand on whether we get all subsets at additional layers, the weak iterative conception. 

In this talk we propose an axiomatization of the most immediate instance of the weak conception, namely that represented by Gödel’s “constructible universe” L. To do so, we adapt an approach to the semantics of L based on what is known as the “condensation sentence” σ. While this method was pioneered by Hilary Putnam and his students Leslie Tharp and George Boolos in the 1960s, we frame it within the contemporary level-theoretic setting developed by Michael Potter and Tim Button. The outcome is a theory of constructible levels (CLT) that sheds new light on the conception as an intrinsic justification of the axioms of set theory and on its ability to pin down a determinate universe of sets.

This is partly joint work with Neil Barton (National University of Singapore)

Registration: If you do not hold a University card which gives access to the upper floors of the Schwarzman Centre, please write to admin@philosophy.ox.ac.uk copied to daniel.isaacson@philosophy.ox.ac.uk at least two working days before a seminar to register your attendance.  

Please note: A notice will be sent out for each talk with the Zoom link.

_{Philosophy of Mathematics Seminar Convenors: Daniel Isaacson and Beau Mount}