In this final chapter we look at the application of anti-realist ideas in two particular cases, that of the past and that of mathematics. Both provide potentially favourable ground for a Dummettian approach since the anti-realist in either case is unlikely to adopt a reductionist view. The anti-realist about the past doesn't think that there's a class of statements which is both distinct from past-tense statements and such that the truth of any past-tense statement consists in the truth of some statement or statements of this class. For an anti-realist understanding of past-tense statements will consist in an appropriate sensitivity to evidence. But at least some evidence will consist in the deliverances of memory, that is, remembering that such and such occurred. There won't be any characterizing the content of the memory independently of the past tense itself. Also an attempt to construe realism or anti-realism about the past as views about a range of entities is completely counter-intuitive.

In the mathematical case it seems far more natural to think of the realism debate as a debate about a range of entities. But Dummett argues (in “The Philosophical Basis of Intuitionistic Logic”, T&OE: essay 14) that the clearest, most plausible form of anti-realism here too relates primarily not to matters ontological but to the manner in which the meanings of mathematical statements are given. The antirealist once again will characterize those meanings in terms of what counts as establishing the truth of a sentence, namely, proof.