A Nominalist Alternative to Reference by Abstraction

Theoria 1:1-12 (2022)
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Abstract

Theoria, EarlyView. In his recent book Thin Objects, Øystein Linnebo (2018) argues for the existence of a hierarchy of abstract objects, sufficient to model ZFC, via a novel and highly interesting argument that relies on a process called dynamic abstraction. This paper presents a way for a nominalist, someone opposed to the existence of abstract objects, to avoid Linnebo's conclusion by rejecting his claim that certain abstraction principles are sufficient for reference (RBA). Section 1 of the paper explains Linnebo's argument for RBA. It offers a reading of Linnebo's work upon which he has two arguments for RBA: one deductive and one abductive, and argues that whilst the deductive argument is unsound the abductive one is prima facie plausible. The nominalist must therefore find a way to respond to the abductive argument. Section 2 outlines just such a response, by offering an alternative explanation of the cases Linnebo wishes to argue from. Most interestingly, it shows that abstraction in Linnebo's most difficult case (the “reference to ordinary bodies” case) can be achieved using mereological means, rather than relying on RBA.

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Gareth Rhys Pearce
University of Vienna

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References found in this work

Mereology.Achille C. Varzi - 2016 - Stanford Encyclopedia of Philosophy.
Thin Objects: An Abstractionist Account.Øystein Linnebo - 2018 - Oxford: Oxford University Press.
On what there is.W. V. Quine - 1953 - In Willard Van Orman Quine (ed.), From a Logical Point of View. Cambridge: Harvard University Press. pp. 1-19.
Inference to the Best explanation.Peter Lipton - 2004 - In Martin Curd & Stathis Psillos (eds.), The Routledge Companion to Philosophy of Science. Routledge. pp. 193.
A Subject with no Object.Zoltan Gendler Szabo, John P. Burgess & Gideon Rosen - 1999 - Philosophical Review 108 (1):106.

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