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.

The classes will focus primarily on the *-ed readings.

The reading list below is also available with links to electronic resources at Search for: absolute generality.

Week 1: An introduction to the absolute generality debate 

[Questions for the class]

*Williamson, 2003, Everything, Philosophical Perspectives 17, 415–465, Sections I–III. Optional: Section IV. (We’ll return to further sections later in term.)

*Studd, 2019, Everything, More or Less (OUP), Chapter 1. (Optional: Sections 2.1 and 2.3 provide some helpful background for later weeks.) For a pre-print of Chapter 1, please see my research page.

Parsons, 2006, The problem of absolute universality, in Rayo and Uzquiano (eds) Absolute Generality (OUP).

Week 2: Indefinite Extensibility I

[Questions for the class]

*Dummett, 1994, What is mathematics about?, in George (ed) Mathematics and Mind, George (OUP), 11–26. Reprinted in Dummett’s The Seas of Language.

*Cartwright, 1994, Speaking of everything, Nous 28, 1–20.

Everything, More or Less, Section 2.5 OR Studd, 2017, Generality, Extensibility, and Paradox, Proceedings of the Aristotelian Society 117, 81–101, Section II

Boolos, 1993, Whence the contradiction? Aristotelian Society Supplementary Volume, 67, 213–233. Reprinted in Boolos’s Logic, Logic and Logic.

Dummett, 1994, Chairman’s address: Basic Law V, Proceedings of the Aristotelian Society 94, 243–251.

Week 3. Encoding the semantics of quantifiers

[Questions for the class]

Barwise and Cooper, 1981, Generalized quantifiers and natural language, Linguistics and Philosophy 4, 159–219. Especially Sections 0–2.

*Everything, More or Less, Chapter 3.

Rayo and Uzquiano, 1999, Toward a theory of second-order consequence, Notre Dame Journal of Formal Logic 40, 315–325.

Week 4. Quantifier domain restriction and restrictionism

[Questions for the class]

*Glanzberg, 2004, Quantification and realism, Philosophy and Phenomenological Research, 69, 541–572, Sections I–III. (Section IV is optional.)

*Williamson, Everything, Section VII (the objection from semantic theorizing). Optional: Section VI (the objection from kind generalizations).

Everything, More or Less, Sections 4.2–4.3.

Glanzberg, 2006, Context and unrestricted quantification, in Rayo and Uzquiano (eds) Absolute Generality.

Stanley and Szabo, 2000, On quantifier domain restriction, Mind & Language 15, 219–261.

Week 5. Metasemantics and expansionism

[Questions for the class]

*Warren, 2017, Quantifier variance and indefinite extensibility, Philosophical Review, 126(1), 81–122. Sections 1–3. (Section 4 is optional but you may like to return to it in week 7.)

Everything, More or Less, Sections 4.1 and 4.4–4.5.

Fine, 2006, Relatively unrestricted quantification, in Rayo and Uzquiano (eds) Absolute Generality.

Week 6. Ineffability and schematic generality

[Questions for the class]

*Williamson, Everything, Section V (the objection from ineffability).

*Everything, More or Less, Chapter 5

Lavine, 2006, Something about everything: Universal quantification in the universal sense of universal quantification. In Rayo and Uzquiano (eds) Absolute Generality. Focus on Sections 5.7, 5.9, 5.10

Week 7. Potentialism and modal generality

[Questions for the class]

*Linnebo, 2010, Pluralities and sets, The Journal of Philosophy 107, 144–164.

*Hewitt, 2015. When do some things form a set? Philosophia Mathematica 23, 311–337. Sections 2.4–2.8

Everything, More or Less, Sections 6.1–6.4

Week 8. Indefinite extensibility II

[Questions for the class]

*Everything, More or Less, Sections 7.1–7.3. (Optional: Sections 7.4–7.5.)

Hewitt, When do some things form a set?, Section 3.

*Soysal, 2017, Why is the universe of sets not a set?, Synthese, 1–23.

Uzquiano, 2015, Varieties of indefinite extensibility, Notre Dame Journal of Formal Logic 56, 147–166.