Non-eliminative Structuralism, Fregean Abstraction, and Non-rigid Structures

Erkenntnis 86 (1):113-127 (2018)
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Abstract

Linnebo and Pettigrew have recently developed a version of non-eliminative mathematical structuralism based on Fregean abstraction principles. They recognize that this version of structuralism is vulnerable to the well-known problem of non-rigid structures. This paper offers a solution to the problem for this version of structuralism. The solution involves expanding the languages used to describe mathematical structures. We then argue that this solution is philosophically acceptable to those who endorse mathematical structuralism based on Fregean abstraction principles.

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John Wigglesworth
University of York

Citations of this work

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Identifying finite cardinal abstracts.Sean C. Ebels-Duggan - 2020 - Philosophical Studies 178 (5):1603-1630.
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References found in this work

The foundations of arithmetic.Gottlob Frege - 1884/1950 - Evanston, Ill.,: Northwestern University Press.
Philosophy of mathematics: structure and ontology.Stewart Shapiro - 1997 - New York: Oxford University Press.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford, England: Oxford University Press USA.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2000 - Philosophical Quarterly 50 (198):120-123.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2002 - Philosophy and Phenomenological Research 65 (2):467-475.

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