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The Transconsistent

Graham Priest

in In Contradiction

The previous chapters advocate a novel logical theory and explore its rationale and some of its applications. By implication, the applications provide a sustained attack on the dominant logical ... More

The previous chapters advocate a novel logical theory and explore its rationale and some of its applications. By implication, the applications provide a sustained attack on the dominant logical theory of our times, the logic of Frege, Russell, and their successors, or, as it has come to be known, classical logic. It is true that this logic can be seen as a special case of dialetheic logic, and is therefore subsumed by it. Nonetheless, the claims to universality of classical logic must be rejected.Less

Letters to Beall and Priest

David Lewis

in The Law of Non-Contradiction

This chapter contains two brief letters to the editors. The first states that it is impossible to engage with dialetheism, since there is not sufficient common ground. The second says that, ... More

This chapter contains two brief letters to the editors. The first states that it is impossible to engage with dialetheism, since there is not sufficient common ground. The second says that, nonetheless, it is possible to reason non-trivially about inconsistent situations in certain cases.Less

Aristotle on the Law of Non-Contradiction

Graham Priest

in Doubt Truth to be a Liar

This chapter analyzes and criticizes the argument of Aristotle in Metaphysics, Book Gamma, against those who would violate the Law of Non-Contradiction, together with what a number of later ... More

This chapter analyzes and criticizes the argument of Aristotle in Metaphysics, Book Gamma, against those who would violate the Law of Non-Contradiction, together with what a number of later commentators have made of them.Less

Theories of Truth

Graham Priest

in Doubt Truth to be a Liar

This chapter surveys standard theories of truth, and argues that they are all compatible with dialetheism.

Trivialism

Graham Priest

in Doubt Truth to be a Liar

This chapter discusses trivialism, the view that all contradictions (and so all claims) are true. It examines the grounds for rejecting the view, and how one would go about engaging an opponent who ... More

This chapter discusses trivialism, the view that all contradictions (and so all claims) are true. It examines the grounds for rejecting the view, and how one would go about engaging an opponent who holds trivialism to be true.Less

Contradiction

Graham Priest

in Doubt Truth to be a Liar

This chapter provides an account of the nature of negation which not only endorses the traditional idea of negation as a contradictory-forming operator, but also allows for the possibility of ... More

This chapter provides an account of the nature of negation which not only endorses the traditional idea of negation as a contradictory-forming operator, but also allows for the possibility of dialetheism.Less

Boolean Negation

Graham Priest

in Doubt Truth to be a Liar

This chapter argues that in the context of an account of meaning appropriate for dialetheism, Boolean (classical) negation is a meaningless notion.

Semantic Closure and the Philosophy of Language

Graham Priest

in In Contradiction

This chapter shows how to construct a semantically closed theory, that is a theory which contains the T-schema for all the sentences of its own language. The connection with the theory of meaning is ... More

This chapter shows how to construct a semantically closed theory, that is a theory which contains the T-schema for all the sentences of its own language. The connection with the theory of meaning is also discussed.Less

Autocommentary on the First Edition

Graham Priest

in In Contradiction

This chapter charts some of the developments that have taken place since the first edition of this book was published, including areas where the author's views have been revised. It does this by ... More

This chapter charts some of the developments that have taken place since the first edition of this book was published, including areas where the author's views have been revised. It does this by giving an autocommentary on the first edition, chapter by chapter.Less

Comments on Some Critics

Graham Priest

in In Contradiction

This chapter discusses and replies to a number of the more important objections that have been made to dialetheism since the publication of the first edition of the book. The topics covered include ... More

This chapter discusses and replies to a number of the more important objections that have been made to dialetheism since the publication of the first edition of the book. The topics covered include dialetheic logic, the Extended Liar Paradox, expressability, and motion.Less

Gödel's Theorem

Graham Priest

in In Contradiction

This chapter presents an argument for dialetheism which draws on Gödel's first incompleteness theorem. This is a non-constructive argument, which does not produce dialetheias explicitly, but shows ... More

This chapter presents an argument for dialetheism which draws on Gödel's first incompleteness theorem. This is a non-constructive argument, which does not produce dialetheias explicitly, but shows that that there must be some. Although the argument starts at some distance from the ground traversed in the preceding chapters, it leads to the same terrain: the logical paradoxes and the trade-off between consistency and completeness. Proof of Gödel's theorem is presented.Less

Truth and Falsity

Graham Priest

in In Contradiction

This chapter discusses truth and related notions: the T-schema, meaning, assertion, falsity. It defends the T-schema, and argues for a teleological account of truth. It concludes with a discussion ... More

This chapter discusses truth and related notions: the T-schema, meaning, assertion, falsity. It defends the T-schema, and argues for a teleological account of truth. It concludes with a discussion of whether negation commutes with truth.Less

Pragmatics

Graham Priest

in In Contradiction

This chapter shows that dialetheism poses no particular problems for pragmatics; that is, a dialetheic pragmatics faces no problems other than those faced by a non-dialetheic one. A number of ... More

This chapter shows that dialetheism poses no particular problems for pragmatics; that is, a dialetheic pragmatics faces no problems other than those faced by a non-dialetheic one. A number of objections to dialetheism drawn from pragmatics are formulated and answered. The areas of assertion, belief, rational belief, and rational change of belief are also considered.Less

The Disjunctive Syllogism and Quasi-Validity

Graham Priest

in In Contradiction

In this chapter the disjunctive syllogism is discussed. This is not valid in the semantics of the previous chapters. It is argued that the form of inference may be used in consistent situations, ... More

In this chapter the disjunctive syllogism is discussed. This is not valid in the semantics of the previous chapters. It is argued that the form of inference may be used in consistent situations, though the understanding of this claim has to be handled with care. A notion of quasi-validity is developed, and the paraconsistent recapture of classical reasoning is discussed.Less

An Introduction to Paraconsistent Dialetheism

Hartry Field

in Saving Truth From Paradox

This chapter introduces ‘dialetheic’ approaches, according to which Liar sentences are both true and false, indeed both true and not true. (Some contradictions are accepted.) Dialetheism provides ... More

This chapter introduces ‘dialetheic’ approaches, according to which Liar sentences are both true and false, indeed both true and not true. (Some contradictions are accepted.) Dialetheism provides another way (in addition to restricting excluded middle) to retain the Intersubstitutivity Principle, but some who believe in dialetheism (such as Priest) prefer to give up the Intersubstitutivity Principle. The rationales for going one way or the other on this, the topic of gluts and gaps, and the relation to the classical glut theories of Chapter 8 are discussed.Less

Paraconsistent Dialetheism and Soundness

Hartry Field

in Saving Truth From Paradox

Priest has argued that his dialetheic theories declare themselves sound and in this regard are better than non-dialetheic theories. This chapter shows this to be unfounded. Indeed, dialetheic ... More

Priest has argued that his dialetheic theories declare themselves sound and in this regard are better than non-dialetheic theories. This chapter shows this to be unfounded. Indeed, dialetheic theories cannot on pain of triviality declare modus ponens to be truth-preserving, and those that accept excluded middle declare it not to be. Moreover, Priest's favored dialetheic theories say that modus ponens doesn't preserve truth even when applied to premises we accept. In this respect, they do worse than glut theories in classical logic and weakly classical theories. This however is not a problem for all dialetheic theories.Less

Truth‐Value Gluts in Classical Theories

Hartry Field

in Saving Truth From Paradox

This chapter deals with classical theories that postulate truth value gluts, especially theories that accept the right-to-left half of the Tarski biconditionals. The duality with gap theories is ... More

This chapter deals with classical theories that postulate truth value gluts, especially theories that accept the right-to-left half of the Tarski biconditionals. The duality with gap theories is explored, and with it the question of whether the theories are notational variants. It is shown that these theories take modus ponens not to be truth-preserving. Reasons are given why this is not as debilitating as declaring one's axioms untrue. Still, glut theories like gap theories preclude truth from having its usual role in expressing agreement and disagreement.Less