Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-21T19:26:44.231Z Has data issue: false hasContentIssue false

Dynamical Systems Theory and Explanatory Indispensability

Published online by Cambridge University Press:  01 January 2022

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.

Type
Explanation
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, 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): 683700.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): 317.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