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Keywords:

  • explanatory virtues;
  • inference to the best explanation;
  • indispensability argument for mathematical realism;
  • scientific realism;
  • naturalism

Abstract

When the indispensability argument for mathematical entities (IA) is spelled out, it would appear confirmational holism is needed for the argument to work. It has been argued that confirmational holism is a dispensable premise in the argument if a construal of naturalism, according to which it is denied that we can take different epistemic attitudes towards different parts of our scientific theories, is adopted. I argue that the suggested variety of naturalism will only appeal to a limited number of philosophers. I then suggest that if we allow for some degree of separation between different component parts of theories, IA can be formulated as an argument aimed at more than a limited number of philosophers, but in implementing this strategy the notion of indispensability needs spelling out. The best way of spelling out indispensability is in terms of theory contribution, but doing so requires adopting inference to the best explanation (IBE). IBE is however sufficient for establishing the conclusion that IA is supposed to establish. Thus, IA is a redundant argument.