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The Structuralist Thesis Reconsidered

Schiemer, Georg and Wigglesworth, John (2017) The Structuralist Thesis Reconsidered. The British Journal for the Philosophy of Science.


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Øystein Linnebo and Richard Pettigrew ([2014]) have recently developed a version of non-eliminative mathematical structuralism based on Fregean abstraction principles. They argue that their theory of abstract structures proves a consistent version of the structuralist thesis that positions in abstract structures only have structural properties. They do this by defining a subset of the properties of positions in structures, so-called fundamental properties, and argue that all fundamental properties of positions are structural. In this paper, we argue that the structuralist thesis, even when restricted to fundamental properties, does not follow from the theory of structures that Linnebo and Pettigrew have developed. To make their account work, we propose a formal framework in terms of Kripke models that makes structural abstraction precise. The formal framework allows us to articulate a revised definition of fundamental properties, understood as intensional properties. Based on this revised definition, we show that the restricted version of the structuralist thesis holds.

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Item Type: Published Article or Volume
Schiemer, Georg
Wigglesworth, Johnjmwigglesworth@gmail.com0000-0002-7305-6844
Keywords: mathematical structuralism, structural abstraction, structural properties
Subjects: Specific Sciences > Mathematics
Depositing User: Dr John Wigglesworth
Date Deposited: 25 Sep 2017 16:19
Last Modified: 25 Sep 2017 16:19
Item ID: 13485
Journal or Publication Title: The British Journal for the Philosophy of Science
Subjects: Specific Sciences > Mathematics
Date: 11 September 2017

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