Foundational pro jects disagree on whether pure and applied mathematics should be explained together. Proponents of unified accounts like neologicists defend Frege’s Constraint (FC), a principle demanding that an explanation of applicability be provided by mathematical definitions. I reconsider the philo- sophical import of FC, arguing that usual conceptions are biased by ontological assumptions. I explore more reasonable weaker variants — Moderate and Mod- est FC — arguing against common opinion that ante rem structuralism (and other) views can meet them. I dispel doubts that such constraints are ‘tooth- less’, showing they both assuage Frege’s original concerns and accommodate neo-logicist intents by dismissing ‘arrogant’ definitions.

On the Philosophical Significance of Frege’s Constraint

Sereni, Andrea
2019

Abstract

Foundational pro jects disagree on whether pure and applied mathematics should be explained together. Proponents of unified accounts like neologicists defend Frege’s Constraint (FC), a principle demanding that an explanation of applicability be provided by mathematical definitions. I reconsider the philo- sophical import of FC, arguing that usual conceptions are biased by ontological assumptions. I explore more reasonable weaker variants — Moderate and Mod- est FC — arguing against common opinion that ante rem structuralism (and other) views can meet them. I dispel doubts that such constraints are ‘tooth- less’, showing they both assuage Frege’s original concerns and accommodate neo-logicist intents by dismissing ‘arrogant’ definitions.
Neo-Logicism, structuralism, applicability of mathematics, Frege's Constraint
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12076/5561
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