Against Categoricity

Research output: Contribution to conferenceAbstract


According to the universism position in set theory, there is only aSingle Universe for set theory and all the models we build throughforcing have instrumental value: they are useful only until we findthe “true” one. The belief that this universe actually exists and theconsequent dismissal of a pluralist conception is based on two mainarguments: first, already inVwe can simulate different universes, sothere is no need to assume the existence of other universes: second, settheory is actually categorical, i.e. all the different models stemmingfrom it are in fact isomorphic. I argue that both arguments are offtarget
Original languageEnglish
Number of pages6
Publication statusPublished - 10 Jul 2020
EventJoint Session of the Mind Association and Aristotelean Society: Open sessions - University of Kent, Canterbury, United Kingdom
Duration: 10 Jul 202012 Jul 2020
Conference number: 94


ConferenceJoint Session of the Mind Association and Aristotelean Society
Abbreviated titleJoint Session
CountryUnited Kingdom
Internet address

Fields of Science and Technology Classification 2012

  • 603 Philosophy, Ethics, Religion
  • 101 Mathematics


  • Philosophy of Mathematics
  • Set theoretic multiverse
  • Forcing
  • Categoricity
  • Foundations of Mathematics

Cite this

de Ceglie, M. (2020). Against Categoricity. Abstract from Joint Session of the Mind Association and Aristotelean Society, Canterbury, United Kingdom.