Frege's Definition of Number: No Ontological Agenda?

Hungarian Philosophical Review 54 (4):76-92 (2010)
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Abstract

Joan Weiner has argued that Frege’s definitions of numbers constitute linguistic stipulations that carry no ontological commitment: they don’t present numbers as pre-existing objects. This paper offers a critical discussion of this view, showing that it is vitiated by serious exegetical errors and that it saddles Frege’s project with insuperable substantive difficulties. It is first demonstrated that Weiner misrepresents the Fregean notions of so-called Foundations-content, and of sense, reference, and truth. The discussion then focuses on the role of definitions in Frege’s work, demonstrating that they cannot be understood as mere linguistic stipulations, since they have an ontological aim. The paper concludes with stressing both the epistemological and the ontological aspects of Frege’s project, and their crucial interdependence.

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Edward Kanterian
University of Kent

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References found in this work

Frege.Michael Dummett - 1981 - Cambridge: Harvard University Press.
Collected Papers on Mathematics, Logic, and Philosophy.Gottlob Frege - 1991 - Wiley-Blackwell. Edited by Brian McGuinness.
Der Gedanke.Gottlob Frege - 1918 - Beiträge Zur Philosophie des Deutschen Idealismus 2:58-77.
Frege in Perspective.Joan Weiner - 2018 - Cornell University Press.

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