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Making the Lightness of Being Bearable: Arithmetical Platonism, Fictional Realism and Cognitive Command

Published online by Cambridge University Press:  01 January 2020

Bill Wringe
Bill Wringe*
Affiliation:
Bilkent University, 06800 Bilkent, Ankara, Turkey
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Extract

In this paper I wish to defend a minimalist version of arithmetical Platonism — which I shall refer to as ‘minimal Platonism’ — from an objection which alleges that an advocate of this view is committed to an unduly capacious ontology. The objection, which I shall call the ‘Lightness of Being’ objection, runs as follows. The minimal Platonist is committed to the claim that arithmetical objects, such as numbers, exist provided that two conditions are met. The first is that terms for numerals are singular terms — where something's being a singular term is judged on the basis of purely syntactic criteria. The second is that some sentences in which these singular terms feature are non-trivially true. However, the names of fictional characters are also singular terms (when judged by the metaphysically lightweight criteria used by advocates of minimal Platonism).

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 38 , Issue 3 , September 2008 , pp. 453 - 487
Copyright
Copyright © The Authors 2008

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