Philosophy of Science 84 (5):892-904 (2017)
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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 (Lyon and Colyvan 2007). 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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| Keywords | Indispensability argument Explanation Platonism Chaos |
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| Reprint years | 2017 |
| DOI | 10.1086/693965 |
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References found in this work BETA
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Mathematics Without Numbers: Towards a Modal-Structural Interpretation.Geoffrey Hellman - 1989 - Oxford, England: Oxford University Press.
Mathematical Explanation in Science.Alan Baker - 2009 - British Journal for the Philosophy of Science 60 (3):611-633.
Is There A Monist Theory of Causal and Non-Causal Explanations? The Counterfactual Theory of Scientific Explanation.Alexander Reutlinger - 2016 - Philosophy of Science 83 (5):733-745.
Constructibility and Mathematical Existence.Charles S. Chihara - 1990 - Oxford, England: Oxford University Press.
View all 27 references / Add more references
Citations of this work BETA
Mathematics and Explanatory Generality: Nothing but Cognitive Salience.Juha Saatsi & Robert Knowles - 2021 - Erkenntnis 86 (5):1119-1137.
Taking Reductionism to the Limit: How to Rebut the Antireductionist Argument From Infinite Limits.Juha Saatsi & Alexander Reutlinger - 2017 - Philosophy of Science (3):455-482.
Mathematical Explanation and the Biological Optimality Fallacy.Samantha Wakil & James Justus - 2017 - Philosophy of Science 84 (5):916-930.
Unification and Mathematical Explanation in Science.Sam Baron - 2021 - Synthese 199 (3-4):7339-7363.
The Indispensability Argument and the Nature of Mathematical Objects.Matteo Plebani - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):249-263.
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