Batterman ([2010]) raises a number of concerns for the inferential conception of the applicability of mathematics advocated by Bueno and Colyvan ([2011]). 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.

  • 1Introduction

  • 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

  • 9Conclusion

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