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, Philosophical Analysis, p. 186

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 the topic 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.