Bunge’s Mathematical Structuralism Is Not a Fiction

In Michael Robert Matthews (ed.), Mario Bunge: A Centenary Festschrift. New York, NY, USA: Springer Verlag. pp. 587-608 (2019)
  Copy   BIBTEX

Abstract

In this paper, I explore Bunge’s fictionism in philosophy of mathematics. After an overview of Bunge’s views, in particular his mathematical structuralism, I argue that the comparison between mathematical objects and fictions ultimately fails. I then sketch a different ontology for mathematics, based on Thomasson’s metaphysical work. I conclude that mathematics deserves its own ontology, and that, in the end, much work remains to be done to clarify the various forms of dependence that are involved in mathematical knowledge, in particular its dependence on mental/brain states and material objects.

Links

PhilArchive

External links

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

Through your library

Similar books and articles

Mathematical representation: playing a role.Kate Hodesdon - 2014 - Philosophical Studies 168 (3):769-782.
Structuralism and Its Ontology.Marc Gasser - 2015 - Ergo: An Open Access Journal of Philosophy 2:1-26.
Category Theory and Mathematical Structuralism.Andrei Rodin - 2008 - Proceedings of the Xxii World Congress of Philosophy 41:37-40.
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 and Meta-Mathematics.Simon Friederich - 2010 - Erkenntnis 73 (1):67 - 81.
Why Pragmaticism is Neither Mathematical Structuralism nor Fictionalism.AhtiVeikko Pietarinen - 2008 - Proceedings of the Xxii World Congress of Philosophy 41:19-25.
Non-ontological Structuralism†.Michael Resnik - 2019 - Philosophia Mathematica 27 (3):303-315.
Structuralism and the notion of dependence.Øystein Linnebo - 2008 - Philosophical Quarterly 58 (230):59-79.
Structuralism and metaphysics.Charles Parsons - 2004 - Philosophical Quarterly 54 (214):56--77.
Moderate mathematical fictionism.Mario Bunge - 1997 - In Evandro Agazzi & György Darvas (eds.), Philosophy of Mathematics Today. Kluwer Academic Publishers. pp. 51--71.

Analytics

Added to PP
2019-07-26

Downloads
571 (#31,422)

6 months
67 (#71,141)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Jean-Pierre Marquis
Université de Montréal

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references