Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-08T18:30:39.626Z Has data issue: false hasContentIssue false

The Metarepresentational Role of Mathematics in Scientific Explanations

Published online by Cambridge University Press:  12 January 2022

Colin McCullough-Benner*
Affiliation:
School of Philosophy, Religion, and History of Science, University of Leeds, Leeds, UK

Abstract

Several philosophers have argued that to capture the generality of certain scientific explanations, we must count mathematical facts among their explanantia. I argue that we can better understand these explanations by adopting a more nuanced stance toward mathematical representations, recognizing the role of mathematical representation schemata in representing highly abstract features of physical systems. It is by picking out these abstract but nonmathematical features that explanations appealing to mathematics achieve a high degree of generality. The result is a rich conception of the role of mathematics in scientific explanations that does not require us to treat mathematical facts as explanantia.

Type
Article
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of the Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baker, Alan. 2005. “Are There Genuine Mathematical Explanations of Physical Phenomena?Mind 114 (454):223–38.CrossRefGoogle Scholar
Baker, Alan. 2017. “Mathematics and Explanatory Generality.” Philosophia Mathematica 25 (2):194209.Google Scholar
Baker, Alan, and Colyvan, Mark. 2011. “Indexing and Mathematical Explanation.” Philosophia Mathematica 19 (3):323–34.Google Scholar
Baron, Sam. 2020. “Counterfactual Scheming.” Mind 129 (514):535–62.CrossRefGoogle Scholar
Bueno, Otávio, and Colyvan, Mark. 2011. “An Inferential Conception of the Application of Mathematics.” Noûs 45 (2):345–74.CrossRefGoogle Scholar
Colyvan, Mark. 2002. “Mathematics and Aesthetic Considerations in Science.” Mind 111 (441):6974.CrossRefGoogle Scholar
Colyvan, Mark. 2013. “Road Work Ahead: Heavy Machinery on the Easy Road.” Mind 121 (484):1031–46.CrossRefGoogle Scholar
Daly, Chris, and Langford, Simon. 2009. “Mathematical Explanation and Indispensability Arguments.” Philosophical Quarterly 59 (237):641–58.CrossRefGoogle Scholar
Goles, Eric, Schulz, Oliver, and Markus, Mario. 2001. “Prime Number Selection of Cycles in a Predator-Prey Model.” Complexity 6 (4):3338.CrossRefGoogle Scholar
Jansson, Lina, and Saatsi, Juha. 2019. “Explanatory Abstractions.” British Journal for the Philosophy of Science 70 (3):817–44.CrossRefGoogle Scholar
Kitcher, Philip. 1989. “Explanatory Unification and the Causal Structure of the World.” In Scientific Explanation, edited by Philip, K. and Salmon, W. C., 410505. Minneapolis: University of Minnesota Press.Google Scholar
Knowles, Robert, and Saatsi, Juha. 2021. “Mathematics and Explanatory Generality: Nothing But Cognitive Salience.Erkenntnis 86 (5):11191137.CrossRefGoogle Scholar
Lange, Marc. 2013. “What Makes a Scientific Explanation Distinctively Mathematical?British Journal for the Philosophy of Science 64 (3):485511.Google Scholar
Lyon, Aidan. 2012. “Mathematical Explanations of Empirical Facts, and Mathematical Realism.” Australasian Journal of Philosophy 90 (3):559–78.CrossRefGoogle Scholar
Mancosu, Paolo. 2018. “Explanation in Mathematics.” In The Stanford Encyclopedia of Philosophy, edited by Zalta, E. N.. Stanford: Stanford University Press. https://plato.stanford.edu/archives/sum2018/entries/mathematics-explanation/.Google Scholar
McCullough-Benner, Colin. 2020. “Representing the World with Inconsistent Mathematics.” British Journal for the Philosophy of Science 71 (4):1331–58.CrossRefGoogle Scholar
Melia, Joseph. 2000. “Weaseling Away the Indispensability Argument.” Mind 109 (435):458–79.CrossRefGoogle Scholar
Nguyen, James, and Frigg, Roman. 2021Mathematics Is Not the Only Language in the Book of Nature.” Synthese 198:59415962.CrossRefGoogle Scholar
Pincock, Christopher. 2012. Mathematics and Scientific Representation. Oxford: Oxford University Press.CrossRefGoogle Scholar
Plebani, Matteo. 2016. “Nominalistic Content, Grounding, and Covering Generalizations: Reply to ‘Grounding and the Indispensability Argument.’Synthese 193 (2):549–58.CrossRefGoogle Scholar
Reutlinger, Alexander , and Saatsi, Juha, eds. 2018. Explanation Beyond Causation: Philosophical Perspectives on Non-Causal Explanations. Oxford: Oxford University Press.CrossRefGoogle Scholar
Saatsi, Juha. 2011. “The Enhanced Indispensability Argument: Representational Versus Explanatory Role of Mathematics in Science.” British Journal for the Philosophy of Science 62 (1):143–54.CrossRefGoogle Scholar
Saatsi, Juha. 2016. “On the ‘Indispensable Explanatory Role’ of Mathematics.” Mind 125 (500):1045–70.CrossRefGoogle Scholar
Wakil, Samantha, and Justus, James. 2017. “Mathematical Explanation and the Biological Optimization Fallacy.” Philosophy of Science 84 (5):916–30.CrossRefGoogle Scholar