Entitlement in mathematics

Crispin Wright has recently introduced a non-evidential notion of warrant – entitlement of cognitive project – as a promising response to certain sceptical arguments, which have been subject to extensive discussion within mainstream epistemology. The central idea is that, for a given class of cognitive projects, there are certain basic propositions – entitlements – which one is warranted in trusting provided there is no sufficient reason to think them false. (See Wrigh [2].) The aim of this paper is to provide an account of the notion of entitlement of cognitive project and briefly discuss the question whether there is any work for the notion of entitlement to do within the philosophy of mathematics. Bearing in mind its applications in mainstream epistemology, it will be suggested that the notion can be used to formulate a response to certain kinds of scepticism which call into question the warrantability of (acceptances of) propositions that appear integral to mathematical theorizing in a given mathematical theory T – in particular, that T is consistent and that T ’s background logic is sound.