Logic and Truth Value Gaps

A salient feature of contemporary philosophical logic is the great interest in so-called ‘free logics’, logics admitting non-denoting terms without paraphrase. Proponents of such logics have generally followed one of two approaches, each of which was considered and rejected by Russell in ‘On Denoting’. The first, suggested by Meinong, requires the introduction of possible but non-existent objects as ‘references’ for non-denoting terms. This approach has been by far the more popular among contemporary free logicians, perhaps because many of them came to free logic by way of modal logic.1 The second approach was first suggested by Frege2 and later developed at length by Strawson.3 Roughly put, it characterizes sentences containing non-denoting terms as truth-valueless, i.e. as neither true nor false, while at the same time insisting that such sentences are meaningful and express (truth-valueless) propositions.