Pincock C. Mathematics and Explanation 2023 torrent

Textbook in PDF format

This Element answers four questions. Can any traditional theory of scientific explanation make sense of the place of mathematics in explanation? If traditional monist theories are inadequate, is there some way to develop a more flexible, but still monist, approach that will clarify how mathematics can help to explain? What sort of pluralism about explanation is best equipped to clarify how mathematics can help to explain in science and in mathematics itself? Finally, how can the mathematical elements of an explanation be integrated into the physical world? Some of the evidence for a novel scientific posit may be traced to the explanatory power that this posit would afford, were it to exist. Can a similar kind of explanatory evidence be provided for the existence of mathematical objects, and if not, why not?
Introduction
The Challenge to Traditional Theories of Scientific Explanation
Derivation and Unification
Causation
Conclusion
Counterfactual Accounts of Mathematical Explanation
Counterfactuals Involving Only Possible Worlds: Reutlinger
Counterfactuals Involving Impossible Worlds
Baron, Colyvan, and Ripley’s Counterfactual Approach
Baron’s Counterfactual Schemes
Povich’s Ontic Counterfactual Account
Conclusion
Explanatory Pluralism
Explanatory Proofs in Mathematics
Steiner on Explanatory Proofs
Lange on Explanatory Proofs
Pluralist Accounts of Genuine Mathematical Explanations
Steiner on Genuine Mathematical Explanations
Lange on Genuine Mathematical Explanations
Pluralism and the Value of Explanation
Conclusion
Autonomy, Indispensability, and Inference to the Best Explanation
Putnam on the Autonomy of the Special Sciences
Explanatory Indispensability Arguments for Mathematical
Platonism
Inference to the Best Mathematical Explanation
Conclusion
References