Erkenntnis 86 (1):113-127 (2021)

Authors
John Wigglesworth
University of Vienna
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.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
ISBN(s)
DOI 10.1007/s10670-018-0096-3
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Translate to english
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 61,109
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

The Foundations of Arithmetic.Gottlob Frege - 1953 - Evanston: Ill., Northwestern University Press.
Ontology and Ideology.W. V. Quine - 1951 - Philosophical Studies 2 (1):11 - 15.
Scientific Theories.Hans Halvorson - 2016 - In Paul Humphreys (ed.), The Oxford Handbook of Philosophy of Science. Oxford University Press. pp. 585-608.
The Semantic View, If Plausible, Is Syntactic.Hans Halvorson - 2013 - Philosophy of Science 80 (3):475-478.

View all 19 references / Add more references

Citations of this work BETA

Identifying Finite Cardinal Abstracts.Sean C. Ebels-Duggan - 2021 - Philosophical Studies 178 (5):1603-1630.

Add more citations

Similar books and articles

The Structuralist Thesis Reconsidered.Georg Schiemer & John Wigglesworth - 2017 - British Journal for the Philosophy of Science:axy004.
Structuralism and Metaphysics.Charles Parsons - 2004 - Philosophical Quarterly 54 (214):56--77.
Say My Name. An Objection to Ante Rem Structuralism.Tim Räz - 2015 - Philosophia Mathematica 23 (1):116-125.
What We Talk About When We Talk About Numbers.Richard Pettigrew - 2018 - Annals of Pure and Applied Logic 169 (12):1437-1456.
Bad Company Generalized.Gabriel Uzquiano - 2009 - Synthese 170 (3):331 - 347.
Non-Ontological Structuralism†.Michael Resnik - 2019 - Philosophia Mathematica 27 (3):303-315.
Bad Company Tamed.Øystein Linnebo - 2009 - Synthese 170 (3):371 - 391.
The Identity Problem for Realist Structuralism.J. Keranen - 2001 - Philosophia Mathematica 9 (3):308--330.
Which Abstraction Principles Are Acceptable? Some Limitative Results.Øystein Linnebo & Gabriel Uzquiano - 2009 - British Journal for the Philosophy of Science 60 (2):239-252.
Mathematical Structuralism Today.Julian C. Cole - 2010 - Philosophy Compass 5 (8):689-699.

Analytics

Added to PP index
2018-12-19

Total views
32 ( #333,250 of 2,440,225 )

Recent downloads (6 months)
8 ( #82,559 of 2,440,225 )

How can I increase my downloads?

Downloads

My notes