Book chapter in Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics, and Language (ed.  Alessandro Torza), Synthese Library 2015, pp 339-366

Abstract: Semantic pessimism has sometimes been used to argue in favour of absolutism about quantifiers, the view, to a first approximation, that quantifiers in natural or artificial languages sometimes range over a domain comprising absolutely everything.
Williamson argues that, by her lights, the relativist who opposes this view cannot state the semantics she wishes to attach to quantifiers in a suitable metalanguage. This chapter argues that this claim is sensitive to both the version of relativism in question and the sort of semantic theory in play. Restrictionist and expansionist variants of relativism should be distinguished. While restrictionists face the difficulties Williamson presses in stating the truth-conditions she wishes to ascribe to quantified sentences in the familiar quasi-homophonic style associated with Tarski and Davidson, the expansionist does not. In fact, not only does the expansionist fare no worse than the absolutist with respect to semantic optimism, for certain styles of semantic theory, she fares better. In the case of the extensional semantics of so called ‘generalised quantifiers’, famously applied to natural language by Barwise and Cooper, it is argued that expansionists enjoy optimism and absolutists face a significant measure of pessimism.