What is in a Definition? Understanding Frege’s Account


Joan Weiner has argued that Frege’s definitions of numbers are linguistic stipulations, with no content-preserving or ontological point: they don’t capture any determinate content of numerals, as they have none, and don’t present numbers as preexisting objects. I show that this view is based on exegetical and systematic errors. First, Idemonstrate that Weiner misrepresents the Fregean notions of ‘Foundations-content’, sense, reference, and truth. I then consider the role of definitions, demonstrating that they cannot be mere linguistic stipulations, since they have a content-preserving, ontological point, and a decompositional aspect; Frege’s project of logical analysis and systematisation makes no sense without definitions so understood. The pivotal ontological role of elucidations is also explained. Next, three aspects of definition are distinguished, the informal versus the formal aspect, and the aspect of definition achieved through the entire process of systematisation, which encompasses the previous two and is little discussed in the literature. It is suggested that these insights can contribute to resolving some of the puzzles concerning the tension between the epistemological aim of logicism and Frege’s presentation of definitions as arbitrary conventions. Finally, I stress the interdependence between the epistemological and ontological aspects of Frege’s project of defining number.

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Edward Kanterian
University of Kent

References found in this work

On Concept and Object.Gottlob Frege - 1951 - Mind 60 (238):168-180.
Frege: The Last Logicist.Paul Benacerraf - 1981 - Midwest Studies in Philosophy 6 (1):17-36.
Frege on Sense and Linguistic Meaning.Tyler Burge - 1990 - In David Bell & Neil Cooper (eds.), The Analytic Tradition. Oxford: Blackwell. pp. 30-60.
Singular Terms and Arithmetical Logicism.Ian Rumfitt - 2003 - Philosophical Books 44 (3):193--219.

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