Unrestricted Quantification and the Structure of Type Theory

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• Salvatore Florio and Nicholas K Jones, University of Birmingham (Philosophy)
• Friday 15 February 2019, 11:00-12:00
• Computer Science, The Sloman Lounge (UG).

If you have a question about this talk, please contact Noam Zeilberger.

Semantic theories based on a hierarchy of types have prominently been used to defend the possibility of unrestricted quantification. However, they also pose a prima facie problem for it: each quantifier ranges over at most one level of the hierarchy and is therefore not unrestricted. It is difficult to evaluate this problem without a principled account of what it is for a quantifier to be unrestricted. Drawing on an insight of Russell’s about the relationship between quantification and the structure of predication, we offer such an account. We use this account to examine the problem in three different type-theoretic settings, which are increasingly permissive with respect to predication. We conclude that unrestricted quantification is available in all but the most permissive kind of type theory.

This talk is part of the Theoretical computer science seminar series.

This talk is included in these lists:

• Computer Science Departmental Series
• Computer Science Distinguished Seminars
• Computer Science, The Sloman Lounge (UG)
• Theoretical computer science seminar
• computer sience

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