In Contradiction A Study of the Transconsistent

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ISBN: 9780199263301 | 0199263302
Cover: Paperback
Copyright: 4/27/2006

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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 center 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.

Acknowledgements of First Edition	p. xii
Preface of First Edition	p. xiii
Preface of Second Edition	p. xvii
Introduction
Dialetheism	p. 3
The Logical Paradoxes
Semantic Paradoxes	p. 9
Logical Paradoxes	p. 9
Semantical Paradoxes: The Tarski Conditions	p. 10
Truth Value Gaps	p. 12
In Defence of the T-scheme	p. 17
The Demise of a Hierarchy	p. 18
...or Two	p. 20
Extended Semantic Paradoxes and Semantic Ascent	p. 23
Appendix: Berry's Paradox	p. 25
Set Theoretic Paradoxes	p. 28
Set Theoretic Paradoxes	p. 28
The Cumulative Hierarchy: Its Lack of Rationale	p. 30
...and its Inadequacy in Category Theory	p. 32
...and Logic	p. 36
Semantics and Set Theory	p. 37
Godel's Theorem	p. 39
Godel's Theorem	p. 39
Naive Proof	p. 40
...and Dialetheism	p. 44
Inconsistency v. Incompleteness	p. 46
Appendix: Proof of Godel's Theorem	p. 48
Dialetheic Logical Theory
Truth and Falsity	p. 53
Preliminary Issues	p. 53
The T-scheme	p. 55
...and Meaning	p. 56
But Truth is More than This	p. 59
The Teleological Account of Truth	p. 61
Assertion	p. 62
Truth or Falsity: Truth Value Gaps	p. 64
Truth and Falsity: Dialetheism	p. 67
Untruth	p. 69
Dialetheic Semantics for Extensional Connectives	p. 73
Formal Languages: Abstraction	p. 73
Extensional Sentential Connectives	p. 74
Quantifiers and Identity	p. 76
The Truth Predicate	p. 78
Appendix: Proofs of Theorems	p. 80
Entailment	p. 82
Preliminary Issues	p. 82
Curry Paradoxes	p. 83
Entailment	p. 84
The Omniscience of G	p. 86
Non-Contraposible Implications	p. 88
Relevant Logic	p. 89
Quantification and Identity	p. 92
Pragmatics	p. 94
Pragmatics	p. 94
Assertion: Content	p. 94
Belief: Acceptance and Rejection	p. 96
Rational Belief	p. 99
Rational Change of Belief	p. 103
Appendix: Probability Theory	p. 107
The Disjunctive Syllogism and Quasi-Validity	p. 110
The Disjunctive Syllogism	p. 110
What it is Not	p. 111
...and What it is	p. 113
The Improbability of Inconsistency	p. 115
The Classical Recapture	p. 117
Appendix: Consequence	p. 119
Applications
Semantic Closure and the Philosophy of Language	p. 125
Applications of Dialetheism	p. 125
A Semantically Closed Theory	p. 125
Comments on the Construction	p. 130
Truth and Meaning	p. 132
Appendix: Proofs of Theorems	p. 136
Set Theory and the Philosophy of Mathematics	p. 141
Naive Set Theory	p. 141
Substitutional Semantics	p. 143
Analyticity and Paradoxicality	p. 146
Mathematical Realism	p. 148
...and Anti-Realism	p. 152
Cardinality and Syntax	p. 154
The Metaphysics of Change I: The Instant of Change	p. 159
Contradictions in the World	p. 159
The Instant of Change	p. 160
Dialectical Tense Logic	p. 162
The Leibniz Continuity Condition	p. 165
The LCC and Contradiction	p. 169
The Metaphysics of Change II: Motion	p. 172
Change and Motion	p. 172
The Orthodox Account of Motion	p. 172
The Hegelean Account of Motion	p. 175
...and its Consequences	p. 179
Norms and the Philosophy of Law	p. 182
Inconsistent Obligations	p. 182
Legal Dialetheias	p. 184
Deontic Semantics	p. 188
Some Semantic Invalidities	p. 195
Other Norms, Rules and Games	p. 197
The Resolution of Dialetheias	p. 200
Language Games	p. 203
Conclusion
The Transconsistent	p. 207
Material New to the Second Edition
The Metaphysics of Change III: Time	p. 213
The Spread Hypothesis and the Hegelean Definition of Change	p. 213
The Flow of Time	p. 215
The Direction and Duration of Time	p. 216
Some Variations and Extensions	p. 217
Minimally Inconsistent LP	p. 221
The Classical Recapture	p. 221
Limiting the Models	p. 222
Semantics for LP	p. 223
Semantics for LPm	p. 224
Properties of LPm	p. 224
Reassurance: the Propositional Case	p. 226
Reassurance: the First Order Case	p. 226
Appendix Proofs of Lemmas	p. 228
Inconsistent Arithmetic	p. 231
Some History	p. 231
Collapsed Models of Arithmetic	p. 232
Consistent v. Inconsistent Arithmetics	p. 234
Godel's Theorems	p. 236
The Naive Notion of Proof	p. 237
Shapiro's Criticisms	p. 239
The Inconsistency of Peano Arithmetic	p. 240
The Incredulous Stare	p. 241
Appendix: The Structure of Inconsistent Models of Arithmetic	p. 244
Paraconsistent Set Theory	p. 247
Paraconsistent Set Theory: Background	p. 247
The Material Strategy	p. 249
The Relevant Strategy	p. 251
The Model-Theoretic Strategy	p. 256
Metatheory of Paraconsistent Logic	p. 258
Technical Appendix	p. 260
Autocommentary on the First Edition	p. 262
Twenty Years On	p. 262
Chapter 0	p. 263
Chapter 1	p. 263
Chapter 2	p. 265
Chapter 3	p. 266
Chapter 4	p. 266
Chapter 5	p. 269
Chapter 6	p. 269
Chapter 7	p. 273
Chapter 8	p. 275
Chapter 9	p. 276
Chapter 10	p. 277
Chapter 11	p. 281
Chapter 12	p. 281
Chapter 13	p. 282
Chapter 14	p. 283
Comments on Some Critics	p. 284
The Empire Strikes Back	p. 284
Dialetheic Logic	p. 284
The Extended Liar Paradox	p. 287
Expressability	p. 290
Motion	p. 295
Contradictions in the World	p. 299
Bibliography	p. 303
Index	p. 317
Table of Contents provided by Ingram. All Rights Reserved.

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In Contradiction A Study of the Transconsistent

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In Contradiction A Study of the Transconsistent

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