What Can Our Best Scientific Theories Tell Us About The Modal Status of Mathematical Objects?

Joe Morrison*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Indispensability arguments are used as a way of working out what there is: our best science tells us what things there are. Some philosophers think that indispensability arguments can be used to show that we should be committed to the existence of mathematical objects (numbers, functions, sets). Do indispensability arguments also deliver conclusions about the modal properties of these mathematical entities? Colyvan (in Leng, Paseau, Potter (eds) Mathematical knowledge, OUP, Oxford, 109-122, 2007) and Hartry Field (Realism, mathematics and modality, Blackwell, Oxford, 1989) each suggest that a consequence of the empirical methodology of indispensability arguments is that the resulting mathematical objects can only be said to exist (or not exist) contingently. Kristie Miller has argued that this line of thought doesn’t work (Miller in Erkenntnis, 77 (3), 335-359, 2012). Miller argues that indispensability arguments are in direct tension with contingentism about mathematical objects, and that they cannot tell us about the modal status of mathematical objects. I argue that Miller’s argument is crucially imprecise, and that the best way of making it clearer no longer shows that the indispensability strategy collapses or is unstable if it delivers contingentist conclusions about what there is.

Original languageEnglish
Early online date28 May 2021
Publication statusEarly online date - 28 May 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V.

Copyright 2021 Elsevier B.V., All rights reserved.


  • Contingentism
  • Indispensability arguments
  • Inference to the best explanation
  • Metaphysics of science
  • Naturalism
  • Philosophy of mathematics
  • Philosophy of science

ASJC Scopus subject areas

  • Philosophy
  • Logic


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