Abstractionism and Mathematical Singular Reference

Philosophia Mathematica 27 (2):177-198 (2019)
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Abstract

ABSTRACT Is it possible to effect singular reference to mathematical objects in the abstractionist framework? I will argue that even if mathematical expressions pass the relevant syntactic and inferential tests to qualify as singular terms, that does not mean that their semantic function is to refer to a particular object. I will defend two arguments leading to this claim: the permutation argument for the referential indeterminacy of mathematical terms, and the argument from the semantic idleness of the terms introduced by abstraction principles.

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Bahram Assadian
University of Leeds

Citations of this work

Thin entities.Matti Eklund - 2023 - Theoria 89 (3):356-365.

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References found in this work

The Varieties of Reference.Gareth Evans - 1982 - Oxford: Oxford University Press. Edited by John Henry McDowell.
On Denoting.Bertrand Russell - 1905 - Mind 14 (56):479-493.
The foundations of arithmetic.Gottlob Frege - 1884/1950 - Evanston, Ill.,: Northwestern University Press.
On Denoting.Bertrand Russell - 2005 - Mind 114 (456):873 - 887.

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