Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
Bertrand Russell (1872–1970)In the last chapter we saw one of the main cases for Platonism, namely, the indispensability argument. In this chapter we look at a few anti-realist philosophies of mathematics. Each of these positions can be understood as a response to the indispensability argument. They are also motivated by the Benacerraf epistemic challenge to Platonism and the hope that it's easier to be rid of troublesome mathematical entities than it is to provide a Platonist epistemology.
Fictionalism
Fictionalism in the philosophy of mathematics is the view that mathematical statements, such as ‘7+5 = 12’ and ‘πis irrational’, are to be interpreted at face value and, thus interpreted, are false. Fictionalists are typically driven to reject the truth of such mathematical statements because these statements imply the existence of mathematical entities, and, according to fictionalists, there are no such entities. Fictionalism is a nominalist (or antirealist) account of mathematics in that it denies the existence of a realm of abstract mathematical entities. It should be contrasted with mathematical realism (or Platonism), where mathematical statements are taken to be true and, moreover, are taken to be truths about mathematical entities. Fictionalism should also be contrasted with other nominalist philosophical accounts of mathematics that propose a reinterpretation of mathematical statements, according to which the statements in question are true but no longer about mathematical entities.
Review the options below to login to check your access.
Log in with your Cambridge Aspire website account to check access.
If you believe you should have access to this content, please contact your institutional librarian or consult our FAQ page for further information about accessing our content.