Peacocke on magnitudes and numbers

Philosophical Studies 178 (8):2717-2729 (2020)
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Abstract

Peacocke’s recent The Primacy of Metaphysics covers a wide range of topics. This critical discussion focuses on the book’s novel account of extensive magnitudes and numbers. First, I further develop and defend Peacocke’s argument against nominalistic approaches to magnitudes and numbers. Then, I argue that his view is more Aristotelian than Platonist because reified magnitudes and numbers are accounted for via corresponding properties and these properties’ application conditions, and because the mentioned objects have a “shallow nature” relative to the corresponding properties. The result is an asymmetric conception of abstraction, which contrasts with the neo-Fregeans’ but has important tenets in common with an approach that I have recently developed.

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Øystein Linnebo
University of Oslo

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References found in this work

The origin of concepts.Susan Carey - 2009 - New York: Oxford University Press.
Realism, Mathematics & Modality.Hartry H. Field - 1989 - New York, NY, USA: Blackwell.
The Construction of Logical Space.Agustín Rayo - 2013 - Oxford, England: Oxford University Press.
Realism, Mathematics, and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
Thin Objects: An Abstractionist Account.Øystein Linnebo - 2018 - Oxford: Oxford University Press.

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