Quantifiers

The notion of quantification is clearly central to the absolutist’s characteristic claim that we sometimes quantify over an absolutely comprehensive domain. Barwise and Cooper give a widely accepted semantics for natural language quantifiers, building on the usual model-theoretic semantics for first-order languages. But only a relativist about quantifiers can take these semantic theories at face value. An absolutist who denies that absolutely general quantifiers range over a set-domain may seek to free these semantic theories from their set-theoretic trappings by employing plural and superplural resources. More radically, he may reject the Barwise–Cooper semantics altogether. This chapter argues that neither approach is cost-free.