Philosophical Studies 168 (1):261-282 (2014)

Authors
Katharina Felka
Uppsala University
Abstract
A realist view of numbers often rests on the following thesis: statements like ‘The number of moons of Jupiter is four’ are identity statements in which the copula is flanked by singular terms whose semantic function consists in referring to a number (henceforth: Identity). On the basis of Identity the realists argue that the assertive use of such statements commits us to numbers. Recently, some anti-realists have disputed this argument. According to them, Identity is false, and, thus, we may deny that the relevant statements commit us to numbers. The present paper argues that the correct linguistic analysis of the relevant number statements supports the anti-realist view that Identity is false. However, as will further be shown, pace the anti-realist, this analysis does not establish that such statements do not commit us to numbers after all
Keywords Ontological commitment  Abstract objects  Number words  Frege  Specificational sentences  Nominalizations
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DOI 10.1007/s11098-013-0129-3
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References found in this work BETA

On Denoting.Bertrand Russell - 1905 - Mind 14 (56):479-493.
On Denoting.Bertrand Russell - 2005 - Mind 114 (456):873 - 887.
Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
Platonism and Anti-Platonism in Mathematics.Mark Balaguer - 1998 - New York, NY, USA: Oxford University Press.

View all 24 references / Add more references

Citations of this work BETA

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Nominalization, Specification, and Investigation.Richard Lawrence - 2017 - Dissertation, University of California, Berkeley

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