An Inferential Conception of the Application of Mathematics

Noûs 45 (2):345-374 (2011)

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.

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Author Profiles

Otávio Bueno
University of Miami
Mark Colyvan
University of Sydney

References found in this work

How the Laws of Physics Lie.Nancy Cartwright - 1983 - Oxford, England: Oxford University Press.
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Realism, Mathematics, and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford, England: Oxford University Press.

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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.

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