Against Fregean Quantification

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Abstract

There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth and reference. We argue that the Fregean approach faces the same choice: abandon compositionality or abandon the centrality of truth and reference to semantic theory. Indeed, we argue that developing a fully compositional semantics in the tradition of Frege leads to a typographic variant of the most radical of Tarskian views: variabilism, the view that names should be modeled as Tarskian variables. We conclude with the consequences of this result for Frege's distinction between sense and reference.

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Author Profiles

Bryan Pickel
University of Glasgow
Brian Rabern
University of Edinburgh

Citations of this work

Semantic Monsters.Brian Rabern - 2021 - In Heimir Geirsson & Stephen Biggs (eds.), The Routledge Handbook of Linguistic Reference. Routledge. pp. 515-532.

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References found in this work

General Semantics.David K. Lewis - 1970 - Synthese 22 (1-2):18--67.
Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.

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