Week 8, 3 March 2014 (16:00-18:00, 52 Pritchatts Road LT1)

Neil Barton (Birkbeck)

Title: Proper Classes, Forcing Extensions, and Universism


"Universism" about Set Theory (the view that there is a single, unique, maximal interpretation of set-theoretic discourse) has come under fire in recent years, partly because of the way in which Set Theory is practised. The characterisation of large cardinals in terms of proper-class-sized elementary embeddings is fairly common and provides a cohesive way of understanding higher axioms of infinity. However, proper classes in general, especially of the non-definable variety needed for interpreting certain embeddings, seem to invite paradox on the Univesist's picture. Forcing over V , on the other hand seems perfectly cogent, whilst the Universist is forced to deny its coherency. My talk explores these issues, analysing some recent presentations of technical material and using them to inform the philosophical debate. My aims are twofold:

  1. Show that there is a deep relationship between representations of forcing extensions within a ground model and the class theory countenanced.
  2. Show that these criticisms of Universism both depend upon a maxim concerning modality in the context of mathematics, a principle the Universist is likely to reject.

About the seminar

The Midlands Logic Seminar was founded in 2011 and aims to cover all areas of mathematical logic, as well as related areas of theoretical computer science and philosophy of mathematics.


All meetings for Term 2, 2014-15 will be Tuesday from 16:00-18:00 in room LT1, 52 Pritchatts Road on the campus of the University of Birmingham.
  • campus map
  • google maps
    To get to campus, take the train from Birmingham New Street to the University stop (7 minutes).


    Dr Richard Kaye
    School of Mathematics
    University of Birmingham


    Dr Walter Dean
    Department of Philosophy
    University of Warwick