Collapse and the Varieties of Quantifier Variance

The aim of this chapter is to bring clarity regarding the doctrine of quantifier variance (due to Eli Hirsch), and two prominent arguments against this doctrine, the collapse argument and the Eklund-Hawthorne argument. Different versions of the doctrine of quantifier variance are distinguished, and it is shown that the effectiveness of the arguments against it depends on what version of the doctrine is at issue. The metaontological significance of the different versions of the doctrine is also assessed. Roughly, quantifier variance concerns there being different possible existential quantifier meanings, and often the doctrine involves a claim to the effect there is no unique “best” quantifier meaning. Much of the discussion in the chapter concerns what it is to be an existential quantifier meaning in the sense at issue.

Metaontology, Existence, and Reference

This chapter presents and defends a conventionalist-friendly metaontology, thereby showing how conventionalism manages to vindicate trivial ontological realism in mathematics. After clarifying and demonstrating this entailment of conventionalism, it clarifies the metaontology involved. The chapter then defends metadeflationism about quantifiers, which entails a version of quantifier pluralism. This is a form of what has recently been called “modest quantifier variance” in joint work with Eli Hirsch. After laying out this view, it is defended from several objections. With this groundwork set out, the chapter then explains how this answers Kant’s challenge for trivial realism that was explained in the previous chapter. Finally, the chapter closes by discussing the metaphysics of mathematical objects, in conventionalist terms, addressing the Julius Caesar problem and structuralism, among other things.

Variance Theses in Ontology and Metaethics

The chapter illustrates conceptual engineering by bringing up a number of issues in metaontology and metaethics. A prominent debate in metaontology relates to whether some existence concept is metaphysically privileged. On the one hand, ontological realists say yes, and, on the other hand, friends of quantifier variance say no. The chapter brings up the corresponding question in metaethics by asking, is some rightness concept normatively privileged? It investigates this question, and compares the metaethics case and the metaontology case. One aim is to arrive at conclusions regarding possible limits to the project of conceptual engineering.

Is Social Ontology Prior to Social Scientific Methodology?

In this article, I examine “Ontology Matters!” (OM!) arguments. OM! arguments conclude that ontology can contribute to empirical success in social science. First, I capture the common form between different OM! arguments. Second, I describe quantifier variance as discussed in metaontology. Third, I apply quantifier variance to the common form of OM! arguments. I then present two ways in which ontology is prior to social science methodology, one realist and one pragmatic. I argue that a pragmatic interpretation of ontology’s priority gives proponents of realist OM! arguments a special burden that they must meet to render their argument successful.