Which explanatory role for mathematics in scientific models? Reply to “The Explanatory Dispensability of Idealizations”

Silvia De Bianchi*

*Corresponding author for this work

Research output: Contribution to journalArticleResearch

5 Citations (Scopus)


In The Explanatory Dispensability of Idealizations, Sam Baron suggests a possible strategy enabling the indispensability argument to break the symmetry between mathematical claims and idealization assumptions in scientific models. Baron’s distinction between mathematical and non-mathematical idealization, I claim, is in need of a more compelling criterion, because in scientific models idealization assumptions are expressed through mathematical claims. In this paper I argue that this mutual dependence of idealization and mathematics cannot be read in terms of symmetry and that Baron’s non-causal notion of mathematical difference-making is not effective in justifying any symmetry-breaking between mathematics and idealization. The function of making a difference that Baron attributes to mathematics cannot be referred to physical facts, but to the features of quantities, such as step lengths or time intervals taken into account in the models. It appears, indeed, that it does not follow from Baron’s argument that idealizations do not help to carry the explanatory load at least for two reasons: (1) mathematics is not independent of idealizations in modelling and (2) idealizations help mathematics to carry the explanatory load of a model in different degrees.

Original languageEnglish
Pages (from-to)-
Number of pages15
Issue number2
Publication statusPublished - 1 Feb 2016


  • Difference-making
  • Explanation
  • Idealization
  • Mathematics
  • Scientific models


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