Grant the following premises.

1. • Premise 1: We understand sentences for which we lack a decision procedure – that is, undecidable sentences.

2. • Premise 2: If an expression has a semantic value its possession of that value must be justified by the character of speakers' understanding of it. (Sense determines reference.)

3. • Premise 3: A speaker's understanding of an expression must be capable of being fully manifested in the use she is able to make of it.

Now, if realism holds, truth applies bivalently to all sentences (or, perhaps better, statements). In view of premise 2 this supposed fact must be justified by the character of speakers' understanding of those sentences. Moreover, premise 3 ensures that this understanding must be capable of full manifestation. So the question is: what manifestable feature of speakers' understanding shows that the sentences they grasp are subject to bivalence? Where the sentences concerned are those we can recognize (in suitable circumstances) as being either true or false, the question is easy to answer. The ability to recognize the sentence as true or as false is itself the manifestable feature of speakers' understanding of them which shows that truth applies bivalently. But premise 1 informs us that this fails to exhaust the range of sentences that speakers understand. So our question now becomes: what manifestable feature of speakers' understanding shows that truth applies bivalently to undecidable sentences? And this question is rather more difficult to answer.