In Contradiction
In Contradiction advocates and defends the view that there are true contradictions (dialetheism), a view that flies in the face of orthodoxy in Western philosophy since Aristotle. The book has been at the centre of the controversies surrounding dialetheism ever since its first publication in 1987. This second edition of the book substantially expands upon the original in various ways, and also contains the author's reflections on developments over the last two decades. Further aspects of dialetheism are discussed in the companion volume, Doubt Truth to be a Liar, also published by Oxford University Press in 2006
1 online resource (351 pages)
9780191532481, 9780199263295, 0191532487, 0199263299
1030899022
Table of Contents
Acknowledgements of First Edition
Preface of First Edition
Preface of Second Edition
INTRODUCTION
0 Dialetheism
PART I: THE LOGICAL PARADOXES
1 Semantic Paradoxes
1.1 Logical Paradoxes
1.2 Semantical Paradoxes: The Tarski Conditions
1.3 Truth Value Gaps
1.4 In Defence of the T-scheme
1.5 The Demise of a Hierarchy
1.6 ... or Two
1.7 Extended Semantic Paradoxes and Semantic Ascent
1.8 Appendix: Berry's Paradox
2 Set Theoretic Paradoxes
2.1 Set Theoretic Paradoxes
2.2 The Cumulative Hierarchy: Its Lack of Rationale
2.3 ... and its Inadequacy in Category Theory
2.4 ... and Logic
2.5 Semantics and Set Theory
3 Gödel's Theorem
3.1 Gödel's Theorem
3.2 Naive Proof
3.3 ... and Dialetheism
3.4 Inconsistency volume Incompleteness
3.5 Appendix: Proof of Gödel's Theorem
PART II: DIALETHEIC LOGICAL THEORY
4 Truth and Falsity
4.1 Preliminary Issues
4.2 The T-scheme
4.3 ... and Meaning
4.4 But Truth is More than This
4.5 The Teleological Account of Truth
4.6 Assertion
4.7 Truth or Falsity: Truth Value Gaps
4.8 Truth and Falsity: Dialetheism
4.9 Untruth
5 Dialetheic Semantics for Extensional Connectives
5.1 Formal Languages: Abstraction
5.2 Extensional Sentential Connectives
5.3 Quantifiers and Identity
5.4 The Truth Predicate
5.5 Appendix: Proofs of Theorems
6 Entailment
6.1 Preliminary Issues
6.2 Curry Paradoxes
6.3 Entailment
6.4 The Omniscience of G
6.5 Non-Contraposible Implications
6.6 Relevant Logic
6.7 Quantification and Identity
7 Pragmatics
7.1 Pragmatics
7.2 Assertion: Content
7.3 Belief: Acceptance and Rejection
7.4 Rational Belief
7.5 Rational Change of Belief
7.6 Appendix: Probability Theory
8 The Disjunctive Syllogism and Quasi-Validity. 8.1 The Disjunctive Syllogism
8.2 What it is Not
8.3 ... and What it is
8.4 The Improbability of Inconsistency
8.5 The Classical Recapture
8.6 Appendix: *Consequence
PART III: APPLICATIONS
9 Semantic Closure and the Philosophy of Language
9.1 Applications of Dialetheism
9.2 A Semantically Closed Theory
9.3 Comments on the Construction
9.4 Truth and Meaning
9.5 Appendix: Proofs of Theorems
10 Set Theory and the Philosophy of Mathematics
10.1 Naive Set Theory
10.2 Substitutional Semantics
10.3 Analyticity and Paradoxicality
10.4 Mathematical Realism
10.5 ... and Anti-Realism
10.6 Cardinality and Syntax
11 The Metaphysics of Change I: The Instant of Change
11.1 Contradictions in the World
11.2 The Instant of Change
11.3 Dialectical Tense Logic
11.4 The Leibniz Continuity Condition
11.5 The LCC and Contradiction
12 The Metaphysics of Change II: Motion
12.1 Change and Motion
12.2 The Orthodox Account of Motion
12.3 The Hegelean Account of Motion
12.4 ... and its Consequences
13 Norms and the Philosophy of Law
13.1 Inconsistent Obligations
13.2 Legal Dialetheias
13.3 Deontic Semantics
13.4 Some Semantic Invalidities
13.5 Other Norms, Rules and Games
13.6 The Resolution of Dialetheias
13.7 Language Games
CONCLUSION
14 The Transconsistent
PART IV: MATERIAL NEW TO THE SECOND EDITION
15 The Metaphysics of Change III: Time
15.1 The Spread Hypothesis and the Hegelean Definition of Change
15.2 The Flow of Time
15.3 The Direction and Duration of Time
15.4 Some Variations and Extensions
16 Minimally Inconsistent LP
16.1 The Classical Recapture
16.2 Limiting the Models
16.3 Semantics for LP
16.4 Semantics for LPm
16.5 Properties of LPm
16.6 Reassurance: the Propositional Case. 16.7 Reassurance: the First Order Case
16.8 Appendix Proofs of Lemmas
17 Inconsistent Arithmetic
17.1 Some History
17.2 Collapsed Models of Arithmetic
17.3 Consistent volume Inconsistent Arithmetics
17.4 Gödel's Theorems
17.5 The Naive Notion of Proof
17.6 Shapiro's Criticisms
17.7 The Inconsistency of Peano Arithmetic
17.8 The Incredulous Stare
17.9 Appendix: The Structure of Inconsistent Models of Arithmetic
18 Paraconsistent Set Theory
18.1 Paraconsistent Set Theory: Background
18.2 The Material Strategy
18.3 The Relevant Strategy
18.4 The Model-Theoretic Strategy
18.5 Metatheory of Paraconsistent Logic
18.6 Technical Appendix
19 Autocommentary on the First Edition
19.1 Twenty Years On
19.2 Chapter 0
19.3 Chapter 1
19.4 Chapter 2
19.5 Chapter 3
19.6 Chapter 4
19.7 Chapter 5
19.8 Chapter 6
19.9 Chapter 7
19.10 Chapter 8
19.11 Chapter 9
19.12 Chapter 10
19.13 Chapter 11
19.14 Chapter 12
19.15 Chapter 13
19.16 Chapter 14
20 Comments on Some Critics
20.1 The Empire Strikes Back
20.2 Dialetheic Logic
20.3 The Extended Liar Paradox
20.4 Expressability
20.5 Motion
20.6 Contradictions in the World
Bibliography
Index
A
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D
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K
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N
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Z
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