Graham Priest
- Published in print:
- 2005
- Published Online:
- May 2006
- ISBN:
- 9780199263288
- eISBN:
- 9780191603631
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199263280.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
The Law of Non-Contradiction has been high orthodoxy in Western philosophy since Aristotle. The so-called Law has been the subject of radical challenge in recent years by dialetheism, the view that ...
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The Law of Non-Contradiction has been high orthodoxy in Western philosophy since Aristotle. The so-called Law has been the subject of radical challenge in recent years by dialetheism, the view that some contradictions are indeed true. Many philosophers have taken the Law to be central to many of our most important philosophical concepts. This book mounts the case against this view. Starting with an analysis of Aristotle on the Law, it discusses the nature of truth, rationality, negation, and logic itself, and argues that the Law is inessential to all of these things. The book develops Priest’s earlier ideas in In Contradiction.Less
The Law of Non-Contradiction has been high orthodoxy in Western philosophy since Aristotle. The so-called Law has been the subject of radical challenge in recent years by dialetheism, the view that some contradictions are indeed true. Many philosophers have taken the Law to be central to many of our most important philosophical concepts. This book mounts the case against this view. Starting with an analysis of Aristotle on the Law, it discusses the nature of truth, rationality, negation, and logic itself, and argues that the Law is inessential to all of these things. The book develops Priest’s earlier ideas in In Contradiction.
Graham Priest
- Published in print:
- 2006
- Published Online:
- May 2007
- ISBN:
- 9780199263301
- eISBN:
- 9780191718823
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263301.003.0015
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
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 ...
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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
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.
David Lewis
- Published in print:
- 2004
- Published Online:
- May 2010
- ISBN:
- 9780199265176
- eISBN:
- 9780191713989
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199265176.003.0011
- Subject:
- Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics
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, ...
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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
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.
Graham Priest
- Published in print:
- 2005
- Published Online:
- May 2006
- ISBN:
- 9780199263288
- eISBN:
- 9780191603631
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199263280.003.0002
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
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 ...
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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
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.
Graham Priest
- Published in print:
- 2005
- Published Online:
- May 2006
- ISBN:
- 9780199263288
- eISBN:
- 9780191603631
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199263280.003.0003
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
This chapter surveys standard theories of truth, and argues that they are all compatible with dialetheism.
This chapter surveys standard theories of truth, and argues that they are all compatible with dialetheism.
Graham Priest
- Published in print:
- 2005
- Published Online:
- May 2006
- ISBN:
- 9780199263288
- eISBN:
- 9780191603631
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199263280.003.0004
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
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 ...
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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
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.
Graham Priest
- Published in print:
- 2005
- Published Online:
- May 2006
- ISBN:
- 9780199263288
- eISBN:
- 9780191603631
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199263280.003.0005
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
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
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.
Graham Priest
- Published in print:
- 2005
- Published Online:
- May 2006
- ISBN:
- 9780199263288
- eISBN:
- 9780191603631
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199263280.003.0006
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
This chapter argues that in the context of an account of meaning appropriate for dialetheism, Boolean (classical) negation is a meaningless notion.
This chapter argues that in the context of an account of meaning appropriate for dialetheism, Boolean (classical) negation is a meaningless notion.
Graham Priest
- Published in print:
- 2006
- Published Online:
- May 2007
- ISBN:
- 9780199263301
- eISBN:
- 9780191718823
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263301.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
This book advocates and defends the view that there are true contradictions (dialetheism), a view that has flown in the face of orthodoxy in Western philosophy since Aristotle's time. The book has ...
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This book advocates and defends the view that there are true contradictions (dialetheism), a view that has flown in the face of orthodoxy in Western philosophy since Aristotle's time. The book has been at the centre of the controversies surrounding dialetheism ever since the first edition was published in 1987. This text contains the second edition of the book. It expands upon the original in various ways, and also contains the author's reflections on developments over the last two decades.Less
This book advocates and defends the view that there are true contradictions (dialetheism), a view that has flown in the face of orthodoxy in Western philosophy since Aristotle's time. The book has been at the centre of the controversies surrounding dialetheism ever since the first edition was published in 1987. This text contains the second edition of the book. It expands upon the original in various ways, and also contains the author's reflections on developments over the last two decades.
Graham Priest
- Published in print:
- 2006
- Published Online:
- May 2007
- ISBN:
- 9780199263301
- eISBN:
- 9780191718823
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263301.003.0010
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
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 ...
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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
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.
Graham Priest
- Published in print:
- 2006
- Published Online:
- May 2007
- ISBN:
- 9780199263301
- eISBN:
- 9780191718823
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263301.003.0020
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
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
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.
Graham Priest
- Published in print:
- 2006
- Published Online:
- May 2007
- ISBN:
- 9780199263301
- eISBN:
- 9780191718823
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263301.003.0021
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
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
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.
Graham Priest
- Published in print:
- 2006
- Published Online:
- May 2007
- ISBN:
- 9780199263301
- eISBN:
- 9780191718823
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263301.003.0004
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
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 ...
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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
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.
Graham Priest
- Published in print:
- 2006
- Published Online:
- May 2007
- ISBN:
- 9780199263301
- eISBN:
- 9780191718823
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263301.003.0005
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
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 ...
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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
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.
Graham Priest
- Published in print:
- 2006
- Published Online:
- May 2007
- ISBN:
- 9780199263301
- eISBN:
- 9780191718823
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263301.003.0008
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
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 ...
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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
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.
Graham Priest
- Published in print:
- 2006
- Published Online:
- May 2007
- ISBN:
- 9780199263301
- eISBN:
- 9780191718823
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263301.003.0009
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
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, ...
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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
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.
Hartry Field
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199230747
- eISBN:
- 9780191710933
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230747.003.0025
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
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 ...
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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
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.
Hartry Field
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199230747
- eISBN:
- 9780191710933
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230747.003.0027
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
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 ...
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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
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.
Hartry Field
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199230747
- eISBN:
- 9780191710933
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230747.003.0009
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
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 ...
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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
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.
Graham Priest, JC Beall, and Bradley Armour-Garb (eds)
- Published in print:
- 2004
- Published Online:
- May 2010
- ISBN:
- 9780199265176
- eISBN:
- 9780191713989
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199265176.001.0001
- Subject:
- Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics
The aim of this book is to present a comprehensive debate about the Law of Non-Contradiction (LNC), from discussions as to how the law is to be understood, to reasons for accepting or re-thinking the ...
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The aim of this book is to present a comprehensive debate about the Law of Non-Contradiction (LNC), from discussions as to how the law is to be understood, to reasons for accepting or re-thinking the law, and to issues that raise challenges to the law, such as the Liar Paradox, and a ‘dialetheic’ resolution of that paradox. The essays in this collection address the ‘Law of Non-Contradiction’ (LNC), and the challenges posed to it by contemporary dialetheism (the view that some contradictions are true). After an introduction that puts the individual essays in the collection into perspective, and an essay setting up the debate, the discussion is structured around four topics: (i) what exactly is the LNC? (ii) methodological issues surrounding challenges to the LNC and similar apparently fundamental logical laws; (iii) arguments against the LNC; and (iv) arguments for the LNC.Less
The aim of this book is to present a comprehensive debate about the Law of Non-Contradiction (LNC), from discussions as to how the law is to be understood, to reasons for accepting or re-thinking the law, and to issues that raise challenges to the law, such as the Liar Paradox, and a ‘dialetheic’ resolution of that paradox. The essays in this collection address the ‘Law of Non-Contradiction’ (LNC), and the challenges posed to it by contemporary dialetheism (the view that some contradictions are true). After an introduction that puts the individual essays in the collection into perspective, and an essay setting up the debate, the discussion is structured around four topics: (i) what exactly is the LNC? (ii) methodological issues surrounding challenges to the LNC and similar apparently fundamental logical laws; (iii) arguments against the LNC; and (iv) arguments for the LNC.