In This Article Expand or collapse the "in this article" section Indispensability of Mathematics

  • Introduction

Philosophy Indispensability of Mathematics
Sorin Bangu
  • LAST REVIEWED: 10 November 2022
  • LAST MODIFIED: 27 March 2014
  • DOI: 10.1093/obo/9780195396577-0241


Philosophers speak of the “indispensability of mathematics” in association with a family of arguments, taking as their starting point two claims. First, a descriptive claim: science and everyday discourse is permeated by mathematics and mathematical terms. Second, a more controversial normative claim: mathematics enjoys a special status within our body of beliefs, because it plays an essential, indeed indispensable, role in our understanding of the world. Although the descriptive thesis is usually regarded as unproblematic, the normative thesis has attracted a good deal of attention. Most importantly, it gave rise to an important metaphysical project, the proposal of a novel argument for an old idea, mathematical realism. The very possibility that such an argument might be successful has led many to reconsider the viability of a realist metaphysics of mathematics traceable to Plato (“mathematical Platonism”), according to which mathematical objects (numbers, sets, etc.) genuinely exist (as opposed to being mere useful fictions), and mathematical truths are objective (as opposed to expressing mere conventions). Several versions of the indispensability argument have been proposed in order to support several forms of realism, and all of them have been subject to sustained criticism, from various angles (although, interestingly, not all objectors are anti-realists, or “nominalists”). The debate around the plausibility of such arguments is connected in subtle ways with other doctrines and positions in the philosophy of science, metaphysics, and epistemology. The work done in this area can be divided into three periods: the pre-Quinean attempt to take the indispensability idea seriously (most notably by Gottlob Frege); the period consisting of the first attempts to articulate such an argument (presented by Willard V. O. Quine and Hilary Putnam, roughly localizable in the period between the 1950s and the 1970s); and finally the “post-Quinean” period (the 1980s to the early 21st century), in which this family of arguments became a relatively well-defined object of philosophical exploration.

General Overviews

General overviews of the indispensability argument fall into two categories. Some present only the essentials, whereas others go into much more detail and articulate the position more fully, for instance, by examining the possible objections or by discussing the indispensability strategy in relation to other philosophical concerns.

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