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What are numbers?

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Abstract

This paper argues that (cardinal) numbers are originally given to us in the context ‘Fs exist n-wise’, and accordingly, numbers are certain manners or modes of existence, by addressing two objections both of which are due to Frege. First, the so-called Caesar objection will be answered by explaining exactly what kind of manner or mode numbers are. And then what we shall call the Functionality of Cardinality objection will be answered by establishing the fact that for any numbers m and n, if there are exactly m Fs and also there are exactly n Fs, then m = n.

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  1. Department of Philosophy and Religious Studies, Western Illinois University, Macomb, IL, 61455, USA

    Joongol Kim

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  1. Joongol Kim
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Correspondence to Joongol Kim.

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Kim, J. What are numbers?. Synthese 190, 1099–1112 (2013). https://doi.org/10.1007/s11229-011-9883-y

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  • DOI: https://doi.org/10.1007/s11229-011-9883-y

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