The ineliminability of non-nominal quantification

Abstract

Objectual interpretations of non-nominal quantification seems to offer a non-substitutional treatment of quantification which respects differences of grammatical category in the object language whilst only employing nominal quantification in the metalanguage. I argue that the satisfaction conditions of such interpretations makes use concepts that must themselves be explained through non-nominal quantification. As a result, the interpretation misrepresents the structure of non-nominal quantification and the relationship between nominal and non-nominal forms of generality.