Grad Class: Absolute Generality

 

TT19, M. 11, Ryle Room.

Almost no systematic theorizing is generality-free. Scientists test general hypotheses; set theorists prove theorems about every set; metaphysicians espouse theses about all things regardless of their kind. But how general can we be? Do we ever succeed in theorizing about ABSOLUTELY EVERYTHING in some interestingly final, all-caps-worthy sense of ‘absolutely everything’?

Not according to generality relativism. In its most promising form, this kind of relativism maintains that what ‘everything’ and other quantifiers encompass is always open to expansion: no matter how broadly we may generalize, a more inclusive ‘everything’ is always available.

The importance of the issue comes out, in part, in relation to the foundations of mathematics. Generality relativism opens the way to avoid Russell’s paradox without imposing ad hoc limitations on which pluralities of items may be encoded as a set. On the other hand, generality relativism faces numerous challenges from generality absolutists: What are we to make of seemingly absolutely general theories? What prevents our achieving absolute generality simply by using ‘everything’ unrestrictedly? How are we to characterize relativism without making use of exactly the kind of generality this view foreswears?

The absolute generality debate bears on a wide-range of issues in logic, metaphysics, the philosophy of mathematics, and the philosophy of language. Over the course of term, we’ll engage with the following topics:

  • semantics for determiners and quantifiers
  • model-theoretic semantics for non-set-sized domains
  • the semantics/pragmatics of quantifier domain restriction
  • the metasemantics of quantifiers
  • plural logic
  • the set-theoretic paradoxes
  • the foundations of Zermelo–Fraenkel set theory
  • indefinite extensibility
  • potentialism and actualism about the set-theoretic hierarchy

This is a somewhat technical subject; but the class won’t presuppose that you’re already familiar with the formal apparatus (beyond standard first-order logic).

The course will be loosely structured around a monograph I wrote on this topic, with compulsory (= *’ed) and optional readings drawn from a wide-spectrum of views across the debate.

Reading for week 1.

Williamson, T., 2003, Everything, Philosophical Perspectives 17, 415–465, Sections I–IV.

*Studd, J. P., 2019, Everything, More or Less (OUP), Chapter 1.

The readings for weeks 2–8 will be posted here before the first class.