Quantifier variance

The term quantifier variance refers to a position in meta-ontology that claims there is no uniquely best ontological language with which to describe the world. According to Hirsch, it is an outgrowth of Urmson's dictum: "“If two sentences are equivalent to each other, then while the use of one rather than the other may be useful for some philosophical purposes, it is not the case that one will be nearer to reality than the other...We can say a thing this way, and we can say it that way, sometimes...But it is no use asking which is the logically or metaphysically right way to say it.”"

- James Opie Urmson

The rather technical term "quantifier variance" arose from the philosophical term 'quantifier', more particularly existential quantifier. A 'quantifier' in logic originally was the part of statements involving the logic symbols ∀ (for all) and ∃ (there exists) as in an expression like "for all‘such-and-such’ P is true" (∀ x: P(x)) or "there exists at least one ‘such-and-such’ such that P is true" (∃ x: P(x)) where ‘such-and-such’, or x, is an element of a set and P is a proposition or assertion. However, the idea of a quantifier has since been generalized. There are a variety of statements involving quantifiers that serve the same purpose in various ontologies, and they are accordingly all quantifier expressions. Quantifier variance is then one argument concerning exactly what expressions can be construed as quantifier expressions, and just which arguments in a quantifier expression are acceptable, that is, which substitutions for ‘such-and-such’, are permissible.

Mereology
An important question is the role of composite objects in quantifier variance. For example, a "school" of fish is something that exists in one formulation, while only "fish" exist in another.

A composite object is referred to as a mereological construction or mereological sum, or a fusion, or an aggregate. In an unrestricted view of mereology, any combination of any objects whatever — however arbitrary it may seem to consider them together — constitutes a composite object of which those objects are parts. There is debate over the utility of this notion, and what restrictions should be placed upon what kind of assemblies are meaningful. For example, perhaps it would be useful to place some requirement for one or another relationship between the parts.

There are unsettled issues regarding 'quantifier restriction', for example, the role of context in limiting the domain of a quantifier. According to Lewis, context means a quantifier cannot refer to just 'any' mereological sum. Hirsch disagrees with Lewis, and places quantifier variance outside this debate.

Without going into these details, it suffices here to note that quantifier variance does allow the flexibility to speak of the "existence" of an object that is an assembly of components in one formulation or 'language' (perhaps limited to some special kinds of assembly), while in another the assembly may be said not to exist, but only the components. "Putnam, for example, writes that “[T]he logical primitives themselves, and in particular the notions of object and existence, have a multitude of different uses rather than one absolute ‘meaning’.”[Putnam] This thesis — the thesis that there are many meanings for the existential quantifier that are equally natural and equally adequate for describing all the facts — is often referred to as “the doctrine of quantifier variance”[Hirsch], [Sider]"

- Ryan Wasserman

This flexibility of quantifier variance seemingly conflicts with the realist idea of things existing independent of language and thought. According to Hirsch and to Thomasson, there is no conflict: "But to say that the meaning of the term “object” or “exists”—or of sentences framed using those terms—depends on our conceptual scheme is not at all to say that objects (the term now being used in accord with the rules of an established language, say English) depend on our conceptual scheme." This view is known as the 'cookie-cutter' metaphor: the world is like dough, and concepts are like cookie cutters, carving cookies from the dough.

That viewpoint is not universally accepted, however. Just how do our perceptions and concepts color our view of reality? Answering this question is part of the subject–object problem and the role of things like mental representations.