Conference on Absolute Generality

September 8-9, 2008, ENS, 75005 Paris, France

Organized by Oystein Linnebo (Bristol) and David Nicolas (IJN)
with the financial support of Institut Jean Nicod (ENS-EHESS-CNRS),
Departement d'Etudes Cognitives (ENS), and GDR Semantique & Modelisation (CNRS)

Program [click on each title for downloading a pdf version of the slides or handout]

Tuesday, Sept 8: Salle de conference, 46 rue d'Ulm
09:30 - 11:00: Michael Glanzberg (UC Davis): Unrestricted quantification and extraordinary context dependence? (pdf)
11:15 - 12:30: Martin Filin Karlsson (Gothenburgh): Unrestricted quantification and model-theoretic semantics based on NFU (pdf)

14:00 - 15:30: David Nicolas (IJN): Semantics for plurals (pdf)
15:45 - 17:15: Gabriel Uzquiano (Oxford): How many angels can dance on the point of a needle? (pdf)

Wednesday, Sept 9: Salle Paul Lapie, 29 rue d'Ulm
09:30 - 11:00: Oystein Linnebo (Bristol): Modality and absolute generality (pdf)
11:15 - 12:30: James Studd (Oxford): The iterative conception of set: a modal reading (pdf)

14:00 - 15:30: Agustin Rayo (MIT): Confessions


Michael Glanzberg (UC Davis)
Title: Unrestricted quantification and extraordinary context dependence?
Abstract: One of the responses to a well-known family of paradoxes, including Russell's paradox and the Liar paradox, is to claim that quantification is never absolutely unrestricted. I have defended a contextualist version of this response, which argues that the lack of absolutely unrestricted quantifiers is an effect of context dependence of quantifiers on the background domain. In earlier work, however, I raised the concern that this sort of context dependence is distinct from the ordinary context dependence we see with quantifier domain restriction. I thus proposed an `extraordinary' form of context dependence. In this paper, I shall reconsider how extraordinary the context dependence required by the contextualist response to the paradox really is. Relying on recent work on the semantics of quantifiers, especially, the `distributive-universal' quantifiers, I shall show that some cases of context dependence of background domain can be assimilated to the ordinary context dependence of quantifier domain restriction. Thus, in a least some cases, the contextualist response to the paradoxes can be seen as an appeal to ordinary context dependence.

Martin Filin Karlsson (Gothenburgh)
Title: Unrestricted quantification and model-theoretic semantics based on NFU
Abstract: I argue that we should not give up the idea of a model-theoretic semantics, constructed in a first-order metatheory, for (first-order) object languages with unrestricted quantifiers. In particular, I argue that NFU is a suitable metatheory for constructing such a semantics, but only after having discussed the most common objections to this idea.

Oystein Linnebo (Bristol)
Title: Modality and absolute generality
Abstract: Various challenges to the possibility of absolutely general quantification have been developed. I show that these challenges turn on the phenomenon of indefinite extensibility, which I argue is best understood in a modal framework. The original question about the possibility of absolute generality then splits into two. One question concerns the possibility of absolutely general intra-world quantification. The standard challenges are easily seen to pose no threat to such quantification. A harder question concerns the possibility of absolutely general inter-world quantification. I develop a conception of such quantification and defend it against the standard challenges.

David Nicolas (IJN)
Title: Semantics for plurals
Abstract: First- and higher-order logic contain singular quantifiers, like the existential and universal quantifiers (something, everything). But many natural languages have plurals and collective predicates, and as a result, plural sentences that cannot be reduced to ordinary singular sentences. How can their semantics be characterized? While most natural language semanticists are happy to use first- or higher-order logic together with sets or sums, various philosophers and logicians maintain that we should instead use logics enriched with plural quantifiers. I compare these approaches, presenting and discussing several arguments put forward by the partisans of plural logic, notably in relation with the question of absolutely general quantification.

Agustin Rayo (MIT)
Title: Confessions
Abstract: Years ago, when I was young and reckless, I thought it made sense to talk about absolutely everything. In my talk I shall recant such heresy.

James Studd (Oxford)
Title: The iterative conception of set: a modal reading
Abstract: The iterative conception of set is naturally presented in tensed language: all members of a stage will form sets at some later stage, and so on. While it is implausible to take this tense at face value, we need not eschew modal readings altogether. In fact, a bi-modal language, governed by a tenselike logic, allows for a natural formalisation of the iterative conception, sufficing to recover (a modal analogue of) Zermelo set theory. This is of particular significance for relativists about generality, for under a suitable reading of the modality, it shows that the failure of quantifiers to encompass absolutely everything need not hinder, and arguably improves, the development of set theory.

Gabriel Uzquiano (Oxford)
Title: How many angels can dance on the point of a needle?
Abstract: This is joint work with John Hawthorne. We argue that certain modal questions raise serious problems for a modal metaphysics on which we are permitted to quantify unrestrictedly over absolutely all possibilia. For example, we argue that, on reasonable assumptions, each of David Lewis' modal realism and Timothy Williamson's necessitarianism are saddled with the remarkable conclusion that there is some cardinal number k such that there could not be more than k angels in existence. In the talk, I will draw a moral for the recent debate over absolute generality.