Non-ontological Structuralism†

Philosophia Mathematica 27 (3):303-315 (2019)
  Copy   BIBTEX

Abstract

ABSTRACT Historical structuralist views have been ontological. They either deny that there are any mathematical objects or they maintain that mathematical objects are structures or positions in them. Non-ontological structuralism offers no account of the nature of mathematical objects. My own structuralism has evolved from an early sui generis version to a non-ontological version that embraces Quine’s doctrine of ontological relativity. In this paper I further develop and explain this view.

Categories

Keywords

Reprint years

DOI

10.1093/philmat/nky002

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,197

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Strukturalizm jako alternatywa dla platonizmu w filozofii matematyki.Izabela Bondecka-Krzykowska - 2004 - Filozofia Nauki 1.
Mathematical representation: playing a role.Kate Hodesdon - 2014 - Philosophical Studies 168 (3):769-782.
Particles vs. structures: Weak ontic structuralism.Aharon Kantorovich - unknown
Structuralism and metaphysics.Charles Parsons - 2004 - Philosophical Quarterly 54 (214):56--77.
Structuralism and Its Ontology.Marc Gasser - 2015 - Ergo: An Open Access Journal of Philosophy 2:1-26.
Scientific representation and perspective.Ioannis Votsis - unknown
How are Mathematical Objects Constituted? A Structuralist Answer.Wolfgang Spohn - unknown
Mathematical platonism meets ontological pluralism?Matteo Plebani - 2017 - Inquiry: An Interdisciplinary Journal of Philosophy:1-19.
Structuralism reconsidered.Fraser MacBride - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press. pp. 563--589.
Mathematical structuralism today.Julian C. Cole - 2010 - Philosophy Compass 5 (8):689-699.
Structuralism, Indispensability, and the Access Problem.Russell Marcus - 2007 - Facta Philosophica 9 (1):203-211.
Category Theory and Mathematical Structuralism.Andrei Rodin - 2008 - Proceedings of the Xxii World Congress of Philosophy 41:37-40.
Priority and Particle Physics: Ontic Structural Realism as a Fundamentality Thesis.Kerry McKenzie - 2014 - British Journal for the Philosophy of Science 65 (2):353-380.
Three varieties of mathematical structuralism.Geoffrey Hellman - 2001 - Philosophia Mathematica 9 (2):184-211.
The construction of ontological categories.Jan Westerhoff - 2004 - Australasian Journal of Philosophy 82 (4):595 – 620.

Analytics

Added to PP
2018-02-08

Downloads
94 (#183,744)

6 months
8 (#367,748)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Michael Resnik
University of North Carolina, Chapel Hill

Citations of this work

Add more citations

References found in this work

Naming and Necessity: Lectures Given to the Princeton University Philosophy Colloquium.Saul A. Kripke - 1980 - Cambridge, MA: Harvard University Press. Edited by Darragh Byrne & Max Kölbel.
Ontological relativity and other essays.Willard Van Orman Quine (ed.) - 1969 - New York: Columbia University Press.
The structure of empirical knowledge.Laurence BonJour - 1985 - Cambridge: Harvard University Press.
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.

View all 125 references / Add more references