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
Abstracts
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.