Philosophical Studies 168 (3):769-782 (2014)

Authors
Kate Hodesdon
University of Bristol
Abstract
The primary justification for mathematical structuralism is its capacity to explain two observations about mathematical objects, typically natural numbers. Non-eliminative structuralism attributes these features to the particular ontology of mathematics. I argue that attributing the features to an ontology of structural objects conflicts with claims often made by structuralists to the effect that their structuralist theses are versions of Quine’s ontological relativity or Putnam’s internal realism. I describe and argue for an alternative explanation for these features which instead explains the attributes them to the mathematical practice of representing numbers using more concrete tokens, such as sets, strokes and so on
Keywords Mathematical structuralism  Representation  Ontological relativity  Model-theoretic arguments  Empiricist structuralism  Van Fraassen
Categories (categorize this paper)
Reprint years 2014
ISBN(s)
DOI 10.1007/s11098-013-0160-4
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

References found in this work BETA

Laws and Symmetry.Bas C. van Fraassen - 1989 - Oxford University Press.
Reason, Truth and History.Hilary Putnam - 1981 - Cambridge University Press.
Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.

View all 39 references / Add more references

Citations of this work BETA

Identifying Finite Cardinal Abstracts.Sean C. Ebels-Duggan - 2021 - Philosophical Studies 178 (5):1603-1630.
John Corcoran.José M. Sagüillo, Michael Scanlan & Stewart Shapiro - 2021 - History and Philosophy of Logic 42 (3):201-223.

Add more citations

Similar books and articles

Category Theory and Mathematical Structuralism.Andrei Rodin - 2008 - Proceedings of the Xxii World Congress of Philosophy 41:37-40.
Mathematical Structuralism Today.Julian C. Cole - 2010 - Philosophy Compass 5 (8):689-699.
Three Varieties of Mathematical Structuralism.Geoffrey Hellman - 2001 - Philosophia Mathematica 9 (2):184-211.
Structuralism and Metaphysics.Charles Parsons - 2004 - Philosophical Quarterly 54 (214):56--77.
Why Pragmaticism is Neither Mathematical Structuralism nor Fictionalism.AhtiVeikko Pietarinen - 2008 - Proceedings of the Xxii World Congress of Philosophy 41:19-25.
Indefiniteness of Mathematical Objects.Ken Akiba - 2000 - Philosophia Mathematica 8 (1):26--46.

Analytics

Added to PP index
2013-06-30

Total views
211 ( #46,669 of 2,439,465 )

Recent downloads (6 months)
17 ( #41,404 of 2,439,465 )

How can I increase my downloads?

Downloads

My notes