Synthese 197 (9):3823-3850 (2020)

Authors
Neil Barton
Universität Konstanz
Abstract
Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent work in numerical cognition and ontogenetic studies.
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DOI 10.1007/s11229-019-02220-x
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The Origin of Concepts.Susan Carey - 2009 - Oxford University Press.
Parts of Classes.David Lewis - 1990 - Blackwell.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
Seeing And Knowing.Fred I. Dretske - 1969 - Chicago: University Of Chicago Press.
Realism in Mathematics.Penelope Maddy - 1990 - Oxford, England and New York, NY, USA: Oxford University Prress.

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