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155Parsimony and inference to the best mathematical explanationSynthese 193 (2). 2016.Indispensability-based arguments for mathematical platonism are typically motivated by drawing an analogy between abstract mathematical objects and concrete scientific posits. In this paper, I argue that mathematics can sometimes help to reduce our concrete ontological, ideological, and structural commitments. My focus is on optimization explanations, and in particular the case study involving periodical cicadas. I argue that in this case, stronger mathematical apparatus yields explanations that…Read more
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147Mathematics and Explanatory GeneralityPhilosophia Mathematica 25 (2): 194-209. 2017.According to one popular nominalist picture, even when mathematics features indispensably in scientific explanations, this mathematics plays only a purely representational role: physical facts are represented, and these exclusively carry the explanatory load. I think that this view is mistaken, and that there are cases where mathematics itself plays an explanatory role. I distinguish two kinds of explanatory generality: scope generality and topic generality. Using the well-known periodical-cicad…Read more
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Complex Thinking: the Emergence of Everything?The Baltic International Yearbook of Cognition, Logic and Communication 2. 2006.
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819Indexing and Mathematical ExplanationPhilosophia Mathematica 19 (3): 323-334. 2011.We discuss a recent attempt by Chris Daly and Simon Langford to do away with mathematical explanations of physical phenomena. Daly and Langford suggest that mathematics merely indexes parts of the physical world, and on this understanding of the role of mathematics in science, there is no need to countenance mathematical explanation of physical facts. We argue that their strategy is at best a sketch and only looks plausible in simple cases. We also draw attention to how frequently Daly and Langf…Read more
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480Are there genuine mathematical explanations of physical phenomena?Mind 114 (454): 223-238. 2005.Many explanations in science make use of mathematics. But are there cases where the mathematical component of a scientific explanation is explanatory in its own right? This issue of mathematical explanations in science has been for the most part neglected. I argue that there are genuine mathematical explanations in science, and present in some detail an example of such an explanation, taken from evolutionary biology, involving periodical cicadas. I also indicate how the answer to my title questi…Read more
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56Russell Marcus. Autonomy Platonism and the Indispensability ArgumentPhilosophia Mathematica 24 (3): 422-424. 2016.
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561Mathematical Explanation in ScienceBritish Journal for the Philosophy of Science 60 (3): 611-633. 2009.Does mathematics ever play an explanatory role in science? If so then this opens the way for scientific realists to argue for the existence of mathematical entities using inference to the best explanation. Elsewhere I have argued, using a case study involving the prime-numbered life cycles of periodical cicadas, that there are examples of indispensable mathematical explanations of purely physical phenomena. In this paper I respond to objections to this claim that have been made by various philos…Read more
Swarthmore, Pennsylvania, United States of America
Areas of Specialization
Philosophy of Mathematics |
General Philosophy of Science |
PhilPapers Editorships
Epistemology of Mathematics |