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The directionality of distinctively mathematical explanations
1Philosophy and Philosophy-Neuroscience-Psychology Program, Washington University in St. Louis, 1 Brookings Dr., St. Louis, MO 63130, USA.
Studies in History and Philosophy of Science
|June 21, 2017
Summary
This study argues that mathematical explanations of natural phenomena are not distinct. It shows that the mathematical facts in these explanations lack the necessary directionality, which is crucial for scientific understanding.
Area of Science:
- Philosophy of Science
- Philosophy of Mathematics
- Scientific Explanation
Background:
- Philosophical debates on the nature of scientific explanation.
- Lange's (2013b) argument for distinctively mathematical explanations.
- The role of modal strength in scientific explanations.
Purpose of the Study:
- To critique Lange's (2013b) account of distinctively mathematical explanations.
- To demonstrate the inadequacy of mathematics in providing normative directionality in explanations.
- To re-evaluate the relationship between mathematical and natural scientific explanations.
Main Methods:
- Analysis of Lange's examples of distinctively mathematical explanations.
- Examination of the role of implicit directionality in scientific explanations.
- Philosophical argumentation regarding the normative function of mathematical facts.
Main Results:
- Lange's examples fail to establish the existence of distinctively mathematical explanations.
- The implicit directionality in explanations requires appeal to ontic facts, not mathematical ones.
- Mathematics cannot fulfill the normative role Lange assigns to it in these explanations.
Conclusions:
- Distinctively mathematical explanations, as argued by Lange, do not exist.
- Superficially natural scientific explanations often rely on relations of stronger-than-natural necessity.
- Mathematical and natural scientific explanations represent different facets of scientific explanation, not opposing kinds.
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