- Can the Cumulative Hierarchy Be Categorically Characterized?
- Logique et Analyse
- Volume | Issue number
- 59 | 236
- Pages (from-to)
- Document type
- Interfacultary Research Institutes
- Institute for Logic, Language and Computation (ILLC)
Mathematical realists have long invoked the categoricity of axiomatizations
of arithmetic and analysis to explain how we manage to fix
the intended meaning of their respective vocabulary. Can this strategy
be extended to set theory? Although traditional wisdom recommends
a negative answer to this question, Vann McGee (1997) has
offered a proof that purports to show otherwise. I argue that one of
the two key assumptions on which the proof rests deprives McGee’s
result of the significance he and the realist want to attribute to it. I
consider two strategies to deal with the problem — one of which is
outlined by McGee himself (2000) — and argue that both of them fail.
I end with some remarks on the prospects for mathematical realism
in the light of my discussion.
- go to publisher's site
- Final publisher version
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library, or send a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.