On the Explanatory Role of Mathematics in Empirical Science

This paper examines contemporary attempts to explicate the explanatory role of mathematics in the physical sciences. Most such approaches involve developing so-called mapping accounts of the relationships between the physical world and mathematical structures. The paper argues that the use of idealizations in physical theorizing poses serious difficulties for such mapping accounts. A new approach to the applicability of mathematics is proposed. 1. Introduction2. Mathematical Explanations I: Entities3. Mathematical Explanations II: Operations4. Mapping Accounts: Strengths5. Mapping Accounts: Idealizations 5.1. Pincock and matching models5.2. Bueno, Colyvan, and the inferential conception6. Mapping Accounts: Limitations7. Suggestions for a New Approach8. Conclusion Introduction Mathematical Explanations I: Entities Mathematical Explanations II: Operations Mapping Accounts: Strengths Mapping Accounts: Idealizations 5.1. Pincock and matching models5.2. Bueno, Colyvan, and the inferential conception Pincock and matching models Bueno, Colyvan, and the inferential conception Mapping Accounts: Limitations Suggestions for a New Approach Conclusion

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