Metaphysics Work-in-Progress Group (Tuesday - Week 8, TT21)
What is absolutely unrestricted quantification? According to the account we developed in “Unrestricted Quantification and the Structure of Type Theory”, a generalisation of the form ‘everything is F’ expresses absolute generality exactly when the domain of quantification contains everything that can be meaningfully said to be F. The approach underlying our account treats the notion of absolute domain as relational: a domain is absolute for a generalisation. An alternative approach treats it as monadic: a domain is absolute simpliciter, without parameters. We compare the two approaches and argue that they capture different theoretical roles for absolute generality. While these approaches and roles coincide in the standard setting presupposed by most prior literature on absolute generality, they diverge in more complex settings, such as cumulative type theory. A central lesson is that there are (at least) two legitimate conceptions of absolute generality, and that the differences between them emerge only under certain views about the structure of meaningful predication.
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Metaphysics Work-in-Progress convenors: Alex Moran and Alex Kaiserman