Quantification and Leibniz's Law

Abstract

It is held by most logicians and philosophers of language that (L) is a principle fundamental to the intent of objectual quantification. It is widely believed, furthermore, that quantificational devices of English involving 'all', 'every' and analogous universal quantifiers, as well as English devices of existential quantification, are objectual quantifiers. And thus, it is widely believed that (L), or at least a somewhat more carefully formulated analogue, in which talk of variables is replaced or supplemented by talk of pronomial reference, is true of English. In this paper, I argue that (L) is not in any way fundamental to objectual quantification. All of the quantifiers of a language may be objectual, and yet sentences of the language which are instances of (L) may be false. I argue further that there are reasons for thinking that English is a language whose quantifiers are objectual, but for which (L) fails.' I will begin by presenting a putative counterexample to (L) in English. Suppose that John says to you: