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- Hartry Field (2003). A Revenge-Immune Solution to the Semantic Paradoxes. Journal of Philosophical Logic 32 (2).The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema True(A)A, and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in ordinary contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True(A) with A within the language.The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are defective. We can in fact define a hierarchy of defectiveness predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes (revenge problems) involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various levels of defectiveness can all be made coherent together within a single object language.In my reading list | Discuss this article | Edit | Categorize |My bibliography
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I express my dissatisfaction with the common ways to treat the semantic paradoxes. Not only do they give rise to revenge paradoxes, they ignore the wisdom contained in the ordinary reaction to paradoxes. I instead propose an account that vindicates the ordinary reaction to paradox by putting the blame on us philosophers. It is the wrong conception of what a valid inference is, one that is central to “the ideal of deductive logic” that gives rise to the problem. The solution (...)
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It is “the received wisdom” that any intuitively natural and consistent resolution of a class of semantic paradoxes immediately leads to other paradoxes just as bad as the first. This is often called the “revenge problem”. Some proponents of the received wisdom draw the conclusion that there is no hope of any natural treatment that puts all the paradoxes to rest: we must either live with the existence of paradoxes that we are unable to treat, or adopt artificial and ad (...)
The paradoxes of self-reference are genuinely paradoxical. The liar paradox, Russell’s paradox and their cousins pose enormous difficulties to anyone who seeks to give a comprehensive theory of semantics, or of sets, or of any other domain which allows a modicum of self-reference and a modest number of logical principles. One approach to the paradoxes of self-reference takes these paradoxes as motivating a non-classical theory of logical consequence. Similar logical principles are used in each of the paradoxical inferences. If one (...)
Both in dealing with the semantic paradoxes and in dealing with vagueness and indeterminacy, there is some temptation to weaken classical logic: in particular, to restrict the law of excluded middle. The reasons for doing this are somewhat different in the two cases. In the case of the semantic paradoxes, a weakening of classical logic (presumably involving a restriction of excluded middle) is required if we are to preserve the naive theory of truth without inconsistency. In the case of vagueness (...)
The aim of this paper is to show that Graham Priest's dialetheic account of semantic paradoxes and the paraconsistent logics employed cannot achieve semantic universality. Dialetheism therefore fails as a solution to semantic paradoxes for the same reason that consistent approaches did. It will be demonstrated that if dialetheism can express its own semantic principles, a strengthened liar paradox will result, which renders dialetheism trivial. In particular, the argument is not invalidated by relational valuations, which were brought into paraconsistent logic (...)
Consideration of a paradox originally discovered by John Buridan provides a springboard for a general solution to paradoxes within the Liar family. The solution rests on a philosophical defence of truth-value-gaps and is consistent (non-dialetheist), avoids ‘revenge’ problems, imports no ad hoc assumptions, is not applicable to only a proper subset of the semantic paradoxes and implies no restriction of the expressive capacities of language.
that all the paradoxes of set theory and logic fall under one schema; and (2) hence they should be solved by one kind of solution. This reply addresses both claims, and counters that (1) in fact at least one paradox escapes the schema, and also some apparently 'safe' theorems fall within it; and (2) even for the (considerable) range of paradoxes so captured by the schema, the assumption of a common solution is not obvious; each paradox surely depends upon the (...)
Truth values are, properly understood, merely proxies for the various relations that can hold between language and the world. Once truth values are understood in this way, consideration of the Liar paradox and the revenge problem shows that our language is indefinitely extensible, as is the class of truth values that statements of our language can take – in short, there is a proper class of such truth values. As a result, important and unexpected connections emerge between the semantic paradoxes (...)
In Beyond the Limits of Thought [2002], Graham Priest argues that logical and semantic paradoxes have the same underlying structure (which he calls the Inclosure Schema ). He also argues that, in conjunction with the Principle of Uniform Solution (same kind of paradox, same kind of solution), this is sufficient to 'sink virtually all orthodox solutions to the paradoxes', because the orthodox solutions to the paradoxes are not uniform. I argue that Priest fails to provide a non-question-begging method to 'sink (...)
In Rabern and Rabern (2008) we presented a two question solution to 'the hardest logic puzzle ever' (as presented in Boolos (1996)), which relied on self-referential questions. In this note we respond to several worries related to this solution. We clarify our claim that some yes-no questions cannot be answered by the gods and thus that asking such questions of the gods will result in head explosion. We argue that the inclusion of exploding head possibilities is neither cheating nor ad (...)
