Article ID: CBB550734458

Frege’s Unification (2019)


What makes certain definitions fruitful? And how can definitions play an explanatory role? The purpose of this paper is to examine these questions via an investigation of Frege’s treatment of definitions. Specifically, I pursue this issue via an examination of Frege’s views about the scientific unification of logic and arithmetic. In my view, what interpreters have failed to appreciate is that logicism is a project of unification, not reduction. For Frege, unification involves two separate steps: (1) an account of the content expressed by arithmetical claims and (2) the justification of that content. The distinction between these steps allows us to see that there are two notions of definition at play in Frege’s logicist work, viz., one concerned with conceptual analysis, the other concerned with the construction of gap-free proof. I then use this discussion to explain how Frege employs his definitions to defend an epistemological thesis about arithmetic, and to clarify Grundlagen’s fruitfulness condition of definitions, and thereby address two interpretive puzzles from the recent literature.

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Authors & Contributors
Centrone, Stefania
Weltya, Ivan
Weiner, Joan
Tappenden, Jamie
Schirn, Matthias
Reada, Stephen
History and Philosophy of Logic
Logica Universalis
Theoria (0495-4548)
Pacific Philosophical Quarterly
Nuncius: Annali di Storia della Scienza
Oxford University Press
Open Court
Philosophy of mathematics
Frege, Gottlob
Thomas Aquinas, Saint
Bolzano, Bernard
Van Heijenoort, Jean
Enriques, Federigo
Time Periods
19th century
20th century, early
20th century, late
20th century

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