Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-22T04:31:04.221Z Has data issue: false hasContentIssue false
  • English
  • Français

There Are No Mathematical Explanations

Published online by Cambridge University Press:  01 January 2022

Jaakko Kuorikoski
Get access Rights & Permissions [Opens in a new window]

Abstract

If ontic dependence is the basis of explanation, there cannot be mathematical explanations. Accounting for the explanatory dependency between mathematical properties and empirical phenomena poses insurmountable metaphysical and epistemic difficulties, and the proposed amendments to the counterfactual theory of explanation invariably violate core commitments of the theory. Instead, mathematical explanations are either abstract mechanistic constitutive explanations or reconceptualizations of the explanandum phenomenon in which mathematics as such does not have an explanatory role. Explanation-like reasoning within mathematics, distinction between explanatory and nonexplanatory proofs, and comparative judgments of mathematical depth can be fully accounted for by a concept of formal understanding.

Type
Research Article
Information
Philosophy of Science , Volume 88 , Issue 2 , April 2021 , pp. 189 - 212
Copyright
Copyright © 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
Bangu, Sorin. 2013. “Indispensability and Explanation.” British Journal for the Philosophy of Science 64:255–77.CrossRefGoogle Scholar
Baron, Sam. 2019. “Mathematical Explanation by Law.” British Journal for the Philosophy of Science 70 (3): 683–717.CrossRefGoogle Scholar
Baron, Sam, Colyvan, Mark, and Ripley, David. 2017. “How Mathematics Can Make a Difference.” Philosophers’ Imprint 17 (3): 1–29.Google Scholar
Batterman, Robert. 2010. “On the Explanatory Role of Mathematics in Empirical Science.” British Journal for the Philosophy of Science 61 (1): 1–25.CrossRefGoogle Scholar
Brogaard, Berit, and Salerno, Joe. 2013. “Remarks on Counterpossibles.” Synthese 190:639–60.CrossRefGoogle Scholar
D’Alessandro, William. 2020. “Viewing-As Explanations and Ontic Dependence.” Philosophical Studies 177 (3): 769–92.CrossRefGoogle Scholar
Detlefsen, Michael, and Arana, Andrew. 2011. “Purity of Methods.” Philosophers’ Imprint 11 (2): 1–20.Google Scholar
Fine, Kit. 1994. “Ontological Dependence.” Proceedings of the Aristotelian Society 95:269–90.Google Scholar
Frans, Joachim, and Weber, Erik. 2014. “Mechanistic Explanation and Explanatory Proofs in Mathematics.” Philosophia Mathematica 22:231–48.CrossRefGoogle Scholar
Glazier, Douglas S. 2010. “A Unifying Explanation for Diverse Metabolic Scaling in Animals and Plants.” Biological Reviews 85:111–38.CrossRefGoogle ScholarPubMed
Huneman, Philippe. 2010. “Topological Explanations and Robustness in Biological Sciences.” Synthese 177 (2): 213–45.CrossRefGoogle Scholar
Jansson, Lena, and Saatsi, Juha. 2019. ”Explanatory Abstractions.” British Journal for the Philosophy of Science 70:817–44.CrossRefGoogle Scholar
Kahneman, Daniel. 2002. Autobiography written for the Riksbank Memorial Prize for Alfred Nobel. https://www.nobelprize.org/prizes/economic-sciences/2002/kahneman/biographical/.Google Scholar
Koslicki, Kathrin. 2012. “Varieties of Ontological Dependence.” In Metaphysical Grounding: Understanding the Structure of Reality, ed. Correira, Fabrice and Schnieder, Benjamin, 186–213. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kuorikoski, Jaakko. 2012. “Mechanisms, Modularity and Constitutive Explanation.” Erkenntnis 77 (3): 361–80.CrossRefGoogle Scholar
Kuorikoski, Jaakko, and Marchionni, Caterina. 2014. “Unification and Mechanistic Detail as Drivers of Model Construction: Models of Networks in Economics and Sociology.” Studies in History and Philosophy of Science A 48:97–104.CrossRefGoogle ScholarPubMed
Kuorikoski, Jaakko, and Ylikoski, Petri. 2013. “How Organization Explains.” In EPSA11 Perspectives and Foundational Problems in Philosophy of Science, ed. Karakostas, Vasillios and Dieks, Dennis, 69–80. Cham: Springer.CrossRefGoogle Scholar
Kuorikoski, Jaakko, and Ylikoski, Petri. 2015. “External Representations and Scientific Understanding.” Synthese 192:3817–37.CrossRefGoogle Scholar
Lange, Marc. 2013. “What Makes a Scientific Explanation Distinctively Mathematical?” British Journal for the Philosophy of Science 64 (3): 485–511.CrossRefGoogle Scholar
Lange, Marc. 2014. “Aspects of Mathematical Explanation: Symmetry, Unity, and Salience.” Philosophical Review 123:485–531.CrossRefGoogle Scholar
Lange, Marc. 2015. “Depth and Explanation in Mathematics.” Philosophia Mathematica 23:196–214.CrossRefGoogle Scholar
Lange, Marc. 2017. Because without Cause. Oxford: Oxford University Press.Google Scholar
Lyon, Aidan. 2012. “Mathematical Explanations of Empirical Facts, and Mathematical Realism.” Australasian Journal of Philosophy 90 (3): 559–78.CrossRefGoogle Scholar
Lyon, Aidan, and Colyvan, Mark. 2008. “The Explanatory Power of Phase Spaces.” Philosophia Mathematica 16:227–43.Google Scholar
Lyon, Ardon. 1977. “The Immutable Laws of Nature.” Proceedings of the Aristotelian Society 77 (1): 107–26.CrossRefGoogle Scholar
Pincock, Christopher. 2015. “Abstract Explanations in Science.” British Journal for the Philosophy of Science 66:857–82.CrossRefGoogle Scholar
Pincock, Christopher. 2018. “Accommodating Explanatory Pluralism.” In Explanation beyond Causation: Philosophical Perspectives on Non-causal Explanations, ed. Reutlinger, Alexander and Saatsi, Juha, 39–56. Oxford: Oxford University Press.Google Scholar
Povich, Mark. 2019. “The Narrow Ontic Counterfactual Account of Distinctively Mathematical Explanation.” British Journal for the Philosophy of Science. https://doi.org/10.1093/bjps/axz008.CrossRefGoogle Scholar
Raerinne, Jani. 2013. “Explanatory, Predictive, and Heuristic Roles of Allometries and Scaling Relationships.” BioScience 63 (3): 191–98.CrossRefGoogle Scholar
Reutlinger, Alexander. 2016. “Is There a Monist Theory of Causal and Noncausal Explanations? The Counterfactual Theory of Scientific Explanation.” Philosophy of Science 83 (5): 733–45.CrossRefGoogle Scholar
Reutlinger, Alexander. 2018. “Extending the Counterfactual Theory of Explanation.” In Explanation beyond Causation: Philosophical Perspectives on Non-causal Explanations, ed. Reutlinger, Alexander and Saatsi, Juha, 74–95. Oxford: Oxford University Press.CrossRefGoogle Scholar
Rice, Collin. 2015. “Moving beyond Causes: Optimality Models and Scientific Explanation.” Noûs 49 (3): 589–615.CrossRefGoogle Scholar
Saatsi, Juha. 2011. “The Enhanced Indispensability Argument: Representational versus Explanatory Role of Mathematics in Science.” British Journal for the Philosophy of Science 62:143–54.CrossRefGoogle Scholar
Saatsi, Juha. 2012. “Mathematics and Program Explanations.” Australasian Journal of Philosophy 90 (3): 579–84.CrossRefGoogle Scholar
Saatsi, Juha. 2016. “On the ‘Indispensable Explanatory Role’ of Mathematics.” Mind 125:1045–70.CrossRefGoogle Scholar
Saatsi, Juha, and Pexton, Mark. 2013. “Reassessing Woodward’s Account of Explanation: Regularities, Counterfactuals, and Noncausal Explanations.” Philosophy of Science 80 (5): 613–24.CrossRefGoogle Scholar
Salmon, Wesley. 1998. Causality and Explanation. Oxford: Oxford University Press.CrossRefGoogle Scholar
Skow, Bradford. 2016. Reasons Why. Oxford: Oxford University Press.CrossRefGoogle Scholar
Sota, Teiji, Yamamoto, Satoshi, Cooley, John, Hill, Kathy, Simon, Chris, and Yoshimura, Jin. 2013. “Independent Divergence of 13- and 17-Y Life Cycles among Three Periodical Cicada Lineages.” Proceedings of the National Academy of Sciences of the USA 110:6919–24.CrossRefGoogle ScholarPubMed
Steiner, Mark. 1978. “Mathematical Explanation.” Philosophical Studies 34:135–51.CrossRefGoogle Scholar
Strevens, Michael. 2018. “The Mathematical Route to Causal Understanding.” In Explanation beyond Causation: Philosophical Perspectives on Non-causal Explanations, ed. Reutlinger, Alexander and Saatsi, Juha, 96–116. Oxford: Oxford University Press.Google Scholar
Woodward, James. 2003. Making Things Happen. Oxford: Oxford University Press.Google Scholar
Woodward, James. 2016. “The Problem of Variable Choice.” Synthese 193 (4): 1047–72.CrossRefGoogle Scholar
Ylikoski, Petri, and Kuorikoski, Jaakko. 2010. “Dissecting Explanatory Power.” Philosophical Studies 148 (2): 201–19.CrossRefGoogle Scholar