In the work of both Matti Eklund and John Hawthorne there is an influential semantic argument for a maximally expansive ontology that is thought to undermine even modest forms of quantifier variance. The crucial premise of the argument holds that it is impossible for an ontologically "smaller" language to give a Tarskian semantics for an ontologically "bigger" language. After explaining the Eklund-Hawthorne argument (in section I), we show this crucial premise to be mistaken (in section II) by developing a Tarskian (...) semantics for a mereological universalist language within a mereological nihilist language (a case which we, and Eklund and Hawthorne, take as representative). After developing this semantics we step back (in section III) to discuss the philosophical motivations behind the Eklund- Hawthorne argument’s demand for a semantics. We ultimately conclude that quantifier variantists can meet any demand for a semantics that might reasonably be imposed upon them. (shrink)

Quantifier variance holds that different languages can have unrestricted quantifier expressions that differ in meaning, where an expression is a “quantifier” just in case it plays the right inferential role. Several critics argued that J.H. Harris’s “collapse” argument refutes variance by showing that identity of inferential role is incompatible with meaning variance. This standard, syntactic collapse argument has generated several responses. More recently, Cian Dorr proved semantic collapse theorems to generate a semantic collapse argument against variance. The argument is significantly (...) different from standard collapse, so it requires a new response. Here I clarify and analyze the semantic collapse argument, and explain how variantists can and should respond to it. The paper also includes an appendix showing the difficulties of positing identity variance without quantifier variance. The argument in the appendix has yet to appear in print, but is familiar to specialists. (shrink)

ABSTRACT Generality relativism is the view that any domain of quantification can always be expanded. The view promises to resolve a broad range of paradoxes, but, without an explanation of how domains expand, it sounds very mysterious. Proponents of linguistic versions of generality relativism try to demystify the view by likening domain expansions to semantic change. They think that domains expand when we re-interpret certain terms so that, upon re-interpretation, the quantifiers range over more things. This article makes trouble for (...) linguistic approaches. According to the so-called charge of ineffability, generality relativism cannot be asserted in a coherent manner—given that asserting the view requires generalising over absolutely all domains of quantification. Generality relativists typically try to answer the charge with the help of modal operators; but linguistic approaches interpret these operators in semantically and syntactically idiosyncratic ways. I argue that, because of these commitments, linguistic approaches ultimately do not have a good response to the charge of ineffability. (shrink)

There are various well-known paradoxes of modal recombination. This paper offers a solution to a variety of such paradoxes in the form of a new conception of metaphysical modality. On the proposed conception, metaphysical modality exhibits a type of indefinite extensibility. Indeed, for any objective modality there will always be some further, broader objective modality; in other terms, modal space will always be open to expansion.