Revenge of the Liar : New Essays on the Paradox

The Liar paradox raises foundational questions about logic, language, and truth (and semantic notions in general). A simple Liar sentence like 'This sentence is false' appears to be both true and false if it is either true or false. For if the sentence is true, then what it says is the case; but what it says is that it is false, hence it must be false. On the other hand, if the statement is false, then it is true, since it says (only) that it is false. How, then, should we classify Liar sentences? Are they true or false? A natural suggestion would be that Liars are neither true nor false; that is, they fall into a category beyond truth and falsity. This solution might resolve the initial problem, but it beckons the Liar's revenge. A sentence that says of itself only that it is false or beyond truth and falsity will, in effect, bring back the initial problem. The Liar's revenge is a witness to the hydra-like nature of Liars: in dealing with one Liar you often bring about another. JC Beall presents fourteen new essays and an extensive introduction, which examine the nature of the Liar paradox and its resistance to any attempt to solve it. Written by some of the world's leading experts in the field, the papers in this volume will be an important resource for those working in truth studies, philosophical logic, and philosophy of language, as well as those with an interest in formal semantics and metaphysics. Annotation The Liar paradox raises foundational questions about logic, language, and truth (and semantic notions in general). A simple Liar sentence like 'This sentence is false' appears to be both true and false if it is either true or false. For if the sentence is true, then what it says is the case; but what it says is that it is false, hence it must be false. On the other hand, if the statement is false, then it is true, since it says (only) that it is false. How, then, should we classify Liar sentences? Are they true or false? A natural suggestion would be that Liars are neither true nor false; that is, they fall into a category beyond truth and falsity. This solution might resolve the initial problem, but it beckons the Liar's revenge. A sentence that says of itself only that it is false or beyond truth and falsity will, in effect, bring back the initial problem. The Liar's revenge is a witness to the hydra-like nature of Liars: in dealing with one Liar you often bring about another. JC Beall presents fourteen new essays and an extensive introduction, which examine the nature of the Liar paradox and its resistance to any attempt to solve it. Written by some of the world's leading experts in the field, the papers in this volume will be an important resource for those working in truth studies, philosophical logic, and philosophy of language, as well as those with an interest in formal semantics and metaphysics "The Liar paradox raises foundational questions about logic, language, and truth (and semantic notions in general). A simple Liar sentence like 'This sentence is false' appears to be both true and false if it is either true or false, For if the sentence is true, then what it says is the case; but what it says is that it is false, hence it must be false. On the other hand, if the statement is false, then it is true, since it says (only) that it is false." "How, then, should we classify Liar sentences? Are they true or false? A natural suggestion would be that Liars are neither true not false: that is, they fall into a category beyond truth and falsity. This solution might resolve the initial problem, but it beckons the Liar's revenge. A sentence that says of itself only that it is false or beyond truth and falsity will, in effect, bring back the initial problem. The Liar's revenge is a witness to the hydra-like nature of Liars: in dealing with one Liar you often bring about another."--Jacket Contents......Page 6 Notes on Contributors......Page 8 1 Prolegomenon to Future Revenge......Page 12 2 Embracing Revenge: On the Indefinite Extendibility of Language......Page 42 3 The Liar Paradox, Expressibility, Possible Languages......Page 64 4 Solving the Paradoxes, Escaping Revenge......Page 89 5 Validity, Paradox, and the Ideal of Deductive Logic......Page 156 6 On the Metatheory of Field’s ‘Solving the Paradoxes, Escaping Revenge’......Page 170 7 Reducing Revenge to Discomfort......Page 195 8 Understanding the Liar......Page 208 9 Revenge, Field, and ZF......Page 236 10 Field on Revenge......Page 245 11 Bradwardine’s Revenge......Page 261 12 Curry’s Revenge: The Costs of Non-classical Solutions to the Paradoxes of Self-reference......Page 273 13 Aletheic Vengeance......Page 283 14 Burali–Forti’s Revenge......Page 331 15 Revenge and Context......Page 356 D......Page 380 H......Page 381 M......Page 382 S......Page 383 Y......Page 384 Z......Page 385 Contents 6 Notes on Contributors 8 1 Prolegomenon to Future Revenge 12 2 Embracing Revenge: On the Indefinite Extendibility of Language 42 3 The Liar Paradox, Expressibility, Possible Languages 64 4 Solving the Paradoxes, Escaping Revenge 89 5 Validity, Paradox, and the Ideal of Deductive Logic 156 6 On the Metatheory of Field’s ‘Solving the Paradoxes, Escaping Revenge’ 170 7 Reducing Revenge to Discomfort 195 8 Understanding the Liar 208 9 Revenge, Field, and ZF 236 10 Field on Revenge 245 11 Bradwardine’s Revenge 261 12 Curry’s Revenge: The Costs of Non-classical Solutions to the Paradoxes of Self-reference 273 13 Aletheic Vengeance 283 14 Burali–Forti’s Revenge 331 15 Revenge and Context 356 Index 380 A 380 B 380 C 380 D 380 E 381 F 381 G 381 H 381 I 382 K 382 L 382 M 382 N 383 O 383 P 383 Q 383 R 383 S 383 T 384 U 384 V 384 W 384 Y 384 Z 385 Prolegomenon to future revenge / J.C. Beall Embracing revenge: on the indefinite extendibility of language / Roy T. Cook The liar paradox, expressibility, possible languages / Matti Eklund Solving the paradoxes, escaping revenge / Hartry Field Validity, paradox, and the ideal of deductive logic / Thomas Hofweber On the metatheory of Field's 'Solving the paradoxes, escaping revenge' / Hannes Leitgeb Reducing revenge to discomfort / Tim Maudlin Understanding the liar / Douglas Patterson Revenge, Field, and ZF / Graham Priest Field on revenge / Agustín Rayo and P.D. Welch Bradwardine's revenge / Stephen Read Curry's revenge: the costs of non-classical solutions to the paradoxes of self-reference / Greg Restall Alethic vengeance / Kevin Scharp Burali-Forti's revenge / Stewart Shapiro Revenge and context / Keith Simmons. Fourteen new essays by some of the world's leading experts, together with an extensive introduction, examine the nature of the Liar paradox and its resistance to any attempt to solve it. - ;The Liar paradox raises foundational questions about logic, language, and truth (and semantic notions in general). A simple Liar sentence like 'This sentence is false' appears to be both true and false if it is either true or false. For if the sentence is true, then what it says is the case; but what it says is that it is false, hence it must be false. On the other hand, if the statement is false, then it i