Modal models

There are many different approaches to the logic of truth. We could agree with Tarski, that the appropriate way to formalise a truth predicate is in a hierarchy, in which the truth predicate in one language can apply only to sentences from another language. Or, we could attempt to do without type restrictions on the truth predicate. Bradwardine’s theory of truth takes the second of these options: it is type-free, and admits sentences which say of themselves that they are not true to be well-formed. We could take the behaviour of the paradoxes such as the liar to motivate a revision of the basic logic of propositional inference, to allow for truth-value gaps or gluts [9, 11, 15]. On the other hand, we could take it that the paradoxes are no reason to revise our account of the basic laws of logic: a novel account of the behaviour of the truth predicate is what is required. Bradwardine’s account, as elaborated by Read, takes this second option.1 Finally.
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