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.

Which explanatory role for mathematics in scientific models? Reply to 'The Explanatory Dispensability of Idealizations' / S. De Bianchi. - In: SYNTHESE. - ISSN 0039-7857. - 193:2(2015), pp. 387-401.

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

S. De Bianchi
2015

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.
Mathematics; Explanation; Idealization; Difference-making; Scientific models
Settore M-FIL/02 - Logica e Filosofia della Scienza
Article (author)
File in questo prodotto:
File Dimensione Formato  
Bianchi2016_Article_WhichExplanatoryRoleForMathema.pdf

accesso riservato

Tipologia: Publisher's version/PDF
Dimensione 439.12 kB
Formato Adobe PDF
439.12 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/838588
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 5
social impact