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What is in a Definition? Understanding Frege’s Account

Kanterian, Edward (2018) What is in a Definition? Understanding Frege’s Account. Siegener Beiträge zur Geschichte und Philosophie der Mathematik, 9 . pp. 7-46. ISSN 2197-5590. (KAR id:70115)

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Abstract

Joan Weiner (2007) 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.

Item Type: Article
Subjects: B Philosophy. Psychology. Religion > B Philosophy (General)
Divisions: Faculties > Humanities > School of European Culture and Languages > Philosophy
Depositing User: Edward Kanterian
Date Deposited: 16 Nov 2018 12:12 UTC
Last Modified: 21 Feb 2020 12:28 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/70115 (The current URI for this page, for reference purposes)
Kanterian, Edward: https://orcid.org/0000-0003-2666-6655
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