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

Authors
Bahram Assadian
University of Amsterdam
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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DOI 10.1093/philmat/nkz003
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References found in this work BETA

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

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Citations of this work BETA

Thin Entities.Matti Eklund - forthcoming - Theoria.

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