29-30 March 2011
London, U.K.
Higher-order logic versus set theory -------------------------------------- 29 30 March 2011 in London Institute of Philosophy, Stewart House, Room ST274/275 From a mathematical point of view, higher-order logic (HOL) and set theory have a lot in common; for instance, both allow us to talk about collections of individuals, and there are partial translations in both directions. However, philosophers often argue that HOL and set theory differ in important ways, such as epistemic status and ontological commitments. This workshop aims to assess the relation between HOL and set theory, drawing in part on an examination of the history of these theories. Questions include the following. - In the early twentieth century, HOL competed with set theory as the best foundation for mathematics and lost. What were the reasons for preferring set theory? Do these reasons remain valid today? - Are higher-order logic and iterative set theory two ways of developing what are essentially the same ideas (as for instance G del argues)? - How should the important notion of ontological commitment be understood? Do HOLs carry ontological commitment? - Can and should HOL be extended to logics of infinite order? If so, how should this be done? - How closely do logics of infinite order resemble set theory? Does this teach us anything about the relation between HOL and set theory? Speakers Jose Ferreiros (Sevilla) Salvatore Florio (Birkbeck, University of London) Daniel Isaacson (Oxford) Ignasi Jane (Barcelona) Michael Potter (Cambridge) Stewart Shapiro (Ohio State University) Sean Walsh (Birkbeck, University of London) We aim to begin around noon on the first day and to end by 6pm on the second. The workshop is organized in connection with the European Research Council project "Plurals, predicates, and paradox" (http://www.bbk.ac.uk/philosophy/our-research/ppp). To register, please email s.florio@bbk.ac.uk