The Pinocchio paradox, devised by Veronique Eldridge-Smith in February 2001, is a counter-example to solutions to the Liar that restrict the use or definition of semantic predicates. Pinocchio’s nose grows if and only if what he is stating is false, and Pinocchio says ‘My nose is growing’. In this statement, ‘is growing’ has its normal meaning and is not a semantic predicate. If Pinocchio’s nose is growing it is because he is saying something false; otherwise, it is not growing. ‘Because’ (...) stands here for a non-semantic relation; it might be supposed to be causal or of some other nature, but it is not semantic. The paradox is discussed in relation to Tarski’s and Kripke’s theories of truth. Although the paradox is not necessarily a counter-example to a theory of a truth predicate, it is a problem for a theory of truth of the kind preserved by validity. (shrink)

Semantic dialetheists astutely dodge Explosion, the logical contagion of everything being true if a single contradiction is true. A dialetheia is contained in their semantics, and sustained by a paraconsistent logic. Graham Priest has shown that this is a solution to the Liar paradox. I use the Pinocchio paradox, devised by Veronique Eldridge-Smith, as a counter-example. The Pinocchio paradox turns on the truth of Pinocchio, whose nose grows if and only if what he is saying is not true, saying ‘My (...) nose is growing’. It is not just a matter of interpretation whether Pinocchio’s nose is and is not growing. (shrink)

The doctrine of semantic dialetheism is set out and contrasted with metaphysical dialetheism. We find that there is a lot to be said in favour of semantic dialetheism. Semantic dlaietheism is given credence by the doctrine of partially defined predicates. To make sense of a partially defined predicate, Tappenden and Soames suggest that the seman tics of predicates should be given in terms of a set of conditions under which the predicate can be applied to things and a set of (...) conditions under which its negation can be applied. If Tappenden and Soames are correct that many predicates are partially defined then it is also plausible that some are 'overdefined'. We say that a predicate is overdefined if and only if it is possible that its negative and positive conditions pick out some of the same objects at the same time. Some examples of overdefined predicates are discussed and it is suggested that a semantic dialetheist treatment of some folk theories (such as the folk theory of identity and the folk theory of belief) is appropriate. (shrink)

Approaches to paraconsistency can be arranged on a spectrum similar to the way in which approaches to vagueness are often understood. On the left are the metaphysical realists; those who think that there are real contradictory facts, that are mind and language independent. On the right are those who think that although we can have inconsistent beliefs and inconsistent theories — and we need a paraconsistent logic to deal with them — the world itself is perfectly consistent. In the middle (...) are the semantic dialetheists, who claim that there are true contradictions, but that these come about because of particular features of our use of language. This chapter outlines a particular version of semantic dialetheism based on a four-valued logic. It contends that although we need such a logic to deal with our current language, we could regiment our uses of predicates (and other expressions) to eliminate all true contradictions. (shrink)