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We explore the motivations for this view and various ways of developing it, taking inspiration from and expanding upon Kit Fine\u2019s work on arbitrary objects (Fine, <jats:italic>Proceedings of the Aristotelian Society, Supplementary Volumes,<\/jats:italic>\n            <jats:italic>57<\/jats:italic>, 55\u201377 1983; <jats:italic>Journal of Philosophical Logic,<\/jats:italic>\n            <jats:italic>14<\/jats:italic>(1), 57\u2013107 1985; <jats:italic>Reasoning with Arbitrary Objects<\/jats:italic> 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\u2019s 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 <jats:italic>Objectual Quantifier Theory<\/jats:italic>, as a theory of quantification in natural language. We argue that Objectual Quantifier Theory is at least as empirically powerful as Generalized Quantifier Theory.<\/jats:p>","DOI":"10.1007\/s10992-025-09803-9","type":"journal-article","created":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T04:46:45Z","timestamp":1751950005000},"page":"793-855","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Objectual Quantifier Theory"],"prefix":"10.1007","volume":"54","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3175-3334","authenticated-orcid":false,"given":"James Ravi","family":"Kirkpatrick","sequence":"first","affiliation":[]},{"given":"Lukas","family":"Lewerentz","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,8]]},"reference":[{"key":"9803_CR1","unstructured":"Abney, S. (1987). The English NP in its sentential aspect. 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