Linnebo on reference by abstraction

Analytic Philosophy 2 (4):603-615 (2023)
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Abstract

According to Øystein Linnebo's account of abstractionism, abstraction principles, received as Fregean criteria of identity, can be used to reduce facts about singular reference to objects such as directions and numbers to facts that do not involve such objects. In this article, first I show how the resources of Linnebo's metasemantics successfully handle Dummett's challenge against the referentiality of the singular terms formed by abstraction principles. Then, I argue that Linnebo's metasemantic commitments do not provide us with tools for dispelling the threat of a version of referential indeterminacy, according to which nothing in our use of a singular term, even when it is guided by an associated criterion of identity, could determine which particular object it refers to. I end by examining the bearing of the indeterminacy challenge to Linnebo's treatment of Frege's Caesar Problem: in the absence of an argument against the indeterminacy of reference, it is unclear how numerical expressions could qualify as genuine singular terms.

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reprint Assadian, Bahram (2023) "Linnebo on reference by abstraction". Analytic Philosophy 65(4):603-615

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Bahram Assadian
University of Leeds

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References found in this work

Ontological Relativity and Other Essays.Willard Van Orman Quine - 1969 - New York: Columbia University Press.
Putnam’s paradox.David Lewis - 1984 - Australasian Journal of Philosophy 62 (3):221 – 236.
The Varieties of Reference.Gareth Evans & John Mcdowell - 1986 - Philosophy 61 (238):534-538.
Can there be vague objects?Gareth Evans - 1978 - Analysis 38 (4):208.
Frege’s Conception of Numbers as Objects.Crispin Wright - 1983 - Critical Philosophy 1 (1):97.

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