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Dynamical Systems Theory and Explanatory Indispensability

Published online by Cambridge University Press:  01 January 2022

Juha Saatsi
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Abstract

I examine explanations’ realist commitments in relation to dynamical systems theory. First I rebut an ‘explanatory indispensability argument’ for mathematical realism from the explanatory power of phase spaces. Then I critically consider a possible way of strengthening the indispensability argument by reference to attractors in dynamical systems theory. The take-home message is that understanding of the modal character of explanations (in dynamical systems theory) can undermine Platonist arguments from explanatory indispensability.

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Type
Explanation
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Philosophy of Science , Volume 84 , Issue 5 , December 2017 , pp. 892 - 904
Copyright
Copyright © The Philosophy of Science Association

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References

Baker, A. 2009. “Mathematical Explanation in Science.” British Journal for the Philosophy of Science 60 (3): 611–33.CrossRefGoogle Scholar
Baker, A., and Colyvan, M. 2011. “Indexing and Mathematical Explanation.” Philosophia Mathematica 19 (3): 323–34.CrossRefGoogle Scholar
Bishop, R. 2015. “Chaos.” In Stanford Encyclopedia of Philosophy, ed. Zalta, Edward N. Stanford, CA: Stanford University. https://plato.stanford.edu/entries/chaos/.Google Scholar
Chihara, C. 1990. Constructibility and Mathematical Existence. Oxford: Oxford University Press.Google Scholar
Daly, C., and Langford, S. 2009. “Mathematical Explanation and Indispensability Arguments.” Philosophical Quarterly 59 (237): 641–58.CrossRefGoogle Scholar
Field, H. 1980. Science without Numbers. Oxford: Oxford University Press.Google Scholar
Hellman, G. 1989. Mathematics without Numbers: Towards a Modal-Structural Interpretation. Oxford: Clarendon.Google Scholar
Hilborn, R. C. 2000. Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers. Oxford: Oxford University Press.CrossRefGoogle Scholar
Koperski, J. 2001. “Has Chaos Been Explained?” British Journal for the Philosophy of Science 52 (4): 683–700.CrossRefGoogle Scholar
Lyon, A. 2012. “Mathematical Explanations of Empirical Facts, and Mathematical Realism.” Australasian Journal of Philosophy 90 (3): 559–78.CrossRefGoogle Scholar
Lyon, A., and Colyvan, M. 2007. “The Explanatory Power of Phase Spaces.” Philosophia Mathematica 16 (2): 227–43.CrossRefGoogle Scholar
Malament, D. 1982. “Science without Numbers by Hartry H. Field.” Journal of Philosophy 79 (9): 523–34.CrossRefGoogle Scholar
Melia, J. 2000. “Weaseling Away the Indispensability Argument.” Mind 109 (435): 455–80.CrossRefGoogle Scholar
Psillos, S. 2010. “Scientific Realism: Between Platonism and Nominalism.” Philosophy of Science 77 (5): 947–58.CrossRefGoogle Scholar
Psillos, S. 2011. “Living with the Abstract: Realism and Models.” Synthese 180 (1): 3–17.CrossRefGoogle Scholar
Reutlinger, A. 2015. “Is There a Monist Theory of Causal and Non-causal Explanations? The Counterfactual Theory of Scientific Explanation.” Philosophy of Science 83:733–45.Google Scholar
Saatsi, J. 2016a. “On Explanations from Geometry of Motion.” British Journal for the Philosophy of Science. doi:10.1093/bjps/axw007.CrossRefGoogle Scholar
Saatsi, J. 2016b. “On the Indispensable Explanatory Role of Mathematics.” Mind 125 (500): 1045–70.. doi:10.1093/mind/fzv175.CrossRefGoogle Scholar
Saatsi, J., and Pexton, M. 2013. “Reassessing Woodward’s Account of Explanation: Regularities, Counterfactuals, and Noncausal Explanations.” Philosophy of Science 80 (5): 613–24.CrossRefGoogle Scholar
Smith, P. 1998. Explaining Chaos. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Strogatz, S. H. 1994. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Cambridge, MA: Perseus.Google Scholar
Woodward, J. 2003. Making Things Happen: A Causal Theory of Explanation. Oxford: Oxford University Press.Google Scholar