Philosophy Faculty Publications and Presentations

Numbers as properties

Document Type

Article

Publication Date

10-3-2023

Abstract

Although number sentences are ostensibly simple, familiar, and applicable, the justification for our arithmetical beliefs has been considered mysterious by the philosophical tradition. In this paper, I argue that such a mystery is due to a preconception of two realities, one mathematical and one nonmathematical, which are alien to each other. My proposal shows that the theory of numbers as properties entails a homogeneous domain in which arithmetical and nonmathematical truth occur. As a result, the possibility of arithmetical knowledge is simply a consequence of the possibility of ordinary knowledge.

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Publication Title

Synthese

DOI

10.1007/s11229-023-04330-z

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