Although the notion of decidability has been used somewhat uncritically in the preceding chapter, it is by no means an uncontroversial notion. Dummett's use of it is clearly heavily influenced by an idea which applies most naturally to mathematical sentences but it is quite different to the usual notion found in mathematical logic. There one speaks of a set of sentences as being decidable just when there is an effective procedure for determining whether any particular sentence is a member of that set or one talks of a sentence as being decidable in a given formal system just when there is a proof or disproof of the sentence in that system. Dummett's use of the notion is similar in some respects to the latter notion but is importantly different in others. First, and most obviously, Dummett is not concerned about decidability in a particular formal system. But secondly, Dummett's notion concerns a subject's epistemic position (it isn't simply a relational property holding between a sentence and a formal system). For Dummett a sentence is decidable just in case we can guarantee to be able to furnish a proof or a disproof of it. So any sentence which can be proved or disproved by instituting a mechanical procedure or algorithm – one which is certain to terminate after a finite number of steps – is decidable. But also any sentence for which we possess a proof (even if that proof wasn't the result of implementing a mechanical procedure: it took ingenuity to find) is decidable.