<p>This paper is a study of <i>Objectual Quantifier Theory</i>, the view that quantificational noun phrases, such as <i>every woman</i> and <i>some pig</i>, denote generic individuals, such as the arbitrary woman and the indefinite pig. We explore the motivations for this view and various ways of developing it, taking inspiration from and expanding upon Kit Fine’s work on arbitrary objects (Fine, <i>Proceedings of the Aristotelian Society, Supplementary Volumes,</i> <i>57</i>, 55–77 1983; <i>Journal of Philosophical Logic,</i> <i>14</i>(1), 57–107 1985; <i>Reasoning with Arbitrary Objects</i> 1985). Our discussion centres around the task of delivering a compositional treatment of quantifier phrases in natural language. In the first part of the paper, we explore the potential for applying and extending Fine’s framework in the interpretation of quantifier expressions, developing desiderata for a successful theory. In the second part of the paper, we develop our positive theory, which we call <i>Objectual Quantifier Theory</i>, as a theory of quantification in natural language. We argue that Objectual Quantifier Theory is at least as empirically powerful as Generalized Quantifier Theory.</p>