Batterman () raises a number of concerns for the inferential conception of the applicability of mathematics advocated by Bueno and Colyvan (). Here, we distinguish the various concerns, and indicate how they can be assuaged by paying attention to the nature of the mappings involved and emphasizing the significance of interpretation in this context. We also indicate how this conception can accommodate the examples that Batterman draws upon in his critique. Our conclusion is that ‘asymptotic reasoning’ can be straightforwardly accommodated within the inferential conception.
2Immersion, Inference and Partial Structures
3Idealization and Surplus Structure
4Renormalization and the Stability of Mathematical Representations
5Explanation and Eliminability
6Requirements for Explanation
7Interpretation and Idealization
8Explanation, Empirical Regularities and the Inferential Conception