 It is possible that we may come across a proof, or a counterexample, but the key point is that we do not know a method, or methods, the application of which is guaranteed to yield one or the other. A semantic realist, in Dummett’s sense, is one who holds that our understanding of a sentence like (G) consists in knowledge of its truth-condition, where the notion of truth involved is potentially recognition-transcendent or bivalent. To say that the notion of truth involved is potentially recognition-transcendent is to say that (G) may be true (or false) even though there is no guarantee that we will be able, in principle, to recognise that that is so. To say that the notion of truth involved is bivalent is to accept the unrestricted applicability of the law of bivalence, that every meaningful sentence is determinately either true or false. Thus the semantic realist is prepared to assert that (G) is determinately either true or false, regardless of the fact that we have no guaranteed method of ascertaining which. (Note that the precise relationship between the characterisation in terms of bivalence and that in terms of potentially recognition-transcendent truth is a delicate matter that will not concern us here. See the Introduction to Wright 1993 for some excellent discussion. It is also important to note that in introducing the idea that a speaker’s understanding of a sentence consists in her knowledge of its truth-condition, Dummett is packing more into the notion of truth than the disquotational properties made use of in §1 above. See Dummett’s essay ‘Truth’, in his 1978).