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

Abstract

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.

Combining finite and infinite elements: Why do we use infinite idealizations in engineering?

“…15 Here I mean that infinite idealization is not explanatory if taken by itself and not in connection with FEM. See also De Bianchi (2016) for the general case of idealization as being not explanatory per se. 16 For a review of the applications of infinite element methods, see Gerdes (2000).…”

Tipología de modelos científicos de explicación. Ciencia y complejidad

“…Esta es la razón más determinante de que los modelos sean prerrogativas de la ciencia y no tanto de la filosofía. Manifiestamente, la filosofía contribuye a explicar y a comprender el mundo y la realidad, pero nunca en términos precisos de modelos (teóricos) (De Bianchi, 2016).…”

Mathematical Explanation as Part of an (Im)perfect Scientific Explanation: An Analysis of Two Examples

“… Cf., e.g., Pincock 2012: 205-206, Tallant 2013, Baker 2016, Barrantes 2019, Bianchi 2016, Colyvan 2018 …”