An Inferential Conception of the Application of Mathematics

Noûs 45 (2):345-374 (2011)
  Copy   BIBTEX

Abstract

A number of people have recently argued for a structural approach to accounting for the applications of mathematics. Such an approach has been called "the mapping account". According to this view, the applicability of mathematics is fully accounted for by appreciating the relevant structural similarities between the empirical system under study and the mathematics used in the investigation ofthat system. This account of applications requires the truth of applied mathematical assertions, but it does not require the existence of mathematical objects. In this paper, we discuss the shortcomings of this account, and show how these shortcomings can be overcome by a broader view of the application of mathematics: the inferential conception.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,227

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

Can Mathematics Explain Physical Phenomena?Otávio Bueno & Steven French - 2012 - British Journal for the Philosophy of Science 63 (1):85-113.
Outline of a dynamical inferential conception of the application of mathematics.Tim Räz & Tilman Sauer - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 49:57-72.
Logic, Reasoning and the Logical Constants.Pascal Engel - 2006 - Croatian Journal of Philosophy 6 (2):219-235.
Mathematics without truth (a reply to Maddy).Hartry Field - 1990 - Pacific Philosophical Quarterly 71 (3):206-222.
Dirac and the dispensability of mathematics.Otavio Bueno - 2005 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (3):465-490.
On The Infinite / Sur L’infini.Marcel Bodea - 2001 - Studia Philosophica 1.
Legal concepts as inferential nodes and ontological categories.Giovanni Sartor - 2009 - Artificial Intelligence and Law 17 (3):217-251.
New waves in philosophy of mathematics.Otávio Bueno & Øystein Linnebo (eds.) - 2009 - New York: Palgrave-Macmillan.
An introduction to the philosophy of mathematics.Mark Colyvan - 2012 - Cambridge: Cambridge University Press.
Deflationary representation, inference, and practice.Mauricio Suárez - 2015 - Studies in History and Philosophy of Science Part A 49 (C):36-47.

Analytics

Added to PP
2009-03-04

Downloads
947 (#14,984)

6 months
14 (#183,612)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Otávio Bueno
University of Miami
Mark Colyvan
University of Sydney

Citations of this work

Models and fictions in science.Peter Godfrey-Smith - 2009 - Philosophical Studies 143 (1):101 - 116.
Mathematical Explanation by Law.Sam Baron - 2019 - British Journal for the Philosophy of Science 70 (3):683-717.
Indexing and Mathematical Explanation.Alan Baker & Mark Colyvan - 2011 - Philosophia Mathematica 19 (3):323-334.
How Theories Represent.Otávio Bueno & Steven French - 2011 - British Journal for the Philosophy of Science 62 (4):857-894.

View all 95 citations / Add more citations

References found in this work

How the laws of physics lie.Nancy Cartwright - 1983 - New York: Oxford University Press.
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Realism, Mathematics & Modality.Hartry H. Field - 1989 - New York, NY, USA: Blackwell.
The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford, England: Oxford University Press.

View all 35 references / Add more references