Mathematical Explanations Of Empirical Facts, And Mathematical Realism

Australasian Journal of Philosophy 90 (3):559-578 (2012)
  Copy   BIBTEX

Abstract

A main thread of the debate over mathematical realism has come down to whether mathematics does explanatory work of its own in some of our best scientific explanations of empirical facts. Realists argue that it does; anti-realists argue that it doesn't. Part of this debate depends on how mathematics might be able to do explanatory work in an explanation. Everyone agrees that it's not enough that there merely be some mathematics in the explanation. Anti-realists claim there is nothing mathematics can do to make an explanation mathematical ; realists think something can be done, but they are not clear about what that something is. I argue that many of the examples of mathematical explanations of empirical facts in the literature can be accounted for in terms of Jackson and Pettit's [1990] notion of program explanation, and that mathematical realists can use the notion of program explanation to support their realism. This is exactly what has happened in a recent thread of the debate over moral realism. I explain how the two debates are analogous and how moves that have been made in the moral realism debate can be made in the mathematical realism debate. However, I conclude that one can be a mathematical realist without having to be a moral realist

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 94,698

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

Mathematics and Program Explanations.Juha Saatsi - 2012 - Australasian Journal of Philosophy 90 (3):579-584.
Scientific Realism and the Indispensability Argument for Mathematical Realism: A Marriage Made in Hell.Jacob Busch - 2011 - International Studies in the Philosophy of Science 25 (4):307-325.
Importance and Explanatory Relevance: The Case of Mathematical Explanations.Gabriel Târziu - 2018 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 49 (3):393-412.
Mathematical Explanation in Science.Alan Baker - 2009 - British Journal for the Philosophy of Science 60 (3):611-633.
Mathematical explanation and indispensability.Vineberg Susan - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):233-247.
Mathematical explanation and indispensability.Susan Vineberg - 2018 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 33 (2):233-247.
Multiple realization and expressive power in mathematics and ethics.David Liggins - 2016 - In Uri D. Leibowitz & Neil Sinclair (eds.), Explanation in Ethics and Mathematics: Debunking and Dispensability. Oxford, England: Oxford University Press UK.

Analytics

Added to PP
2011-08-26

Downloads
188 (#109,190)

6 months
23 (#152,487)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Aidan Lyon
Leiden University

Citations of this work

Explanatory Abstractions.Lina Jansson & Juha Saatsi - 2019 - British Journal for the Philosophy of Science 70 (3):817–844.
The Narrow Ontic Counterfactual Account of Distinctively Mathematical Explanation.Mark Povich - 2021 - British Journal for the Philosophy of Science 72 (2):511-543.
Abstract Explanations in Science.Christopher Pincock - 2014 - British Journal for the Philosophy of Science 66 (4):857-882.
Mathematical Explanation by Law.Sam Baron - 2019 - British Journal for the Philosophy of Science 70 (3):683-717.

View all 68 citations / Add more citations

References found in this work

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Mind, Language and Reality: Philosophical Papers.Hilary Putnam - 1975 - New York: Cambridge University Press.
On the origin of species.Charles Darwin - 1964 - New York: Oxford University Press. Edited by Gillian Beer.
The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford, England: Oxford University Press.

View all 36 references / Add more references