Truth is one of the oldest and most central topics in philosophy. Formal theories explore the connections between truth and logic, and they address truth-theoretic paradoxes such as the Liar. Three leading philosopher-logicians now present a concise overview of the main issues and ideas in formal theories of truth. Beall, Glanzberg, and Ripley explain key logical techniques on which such formal theories rely, providing the formal and logical background needed to develop formal theories of truth. They examine the most important truth-theoretic paradoxes, including the Liar paradoxes. They explore approaches that keep principles of truth simple while relying on nonclassical logic; approaches that preserve classical logic but do so by complicating the principles of truth; and approaches based on substructural logics that change the shape of the target consequence relation itself. Finally, inconsistency and revision theories are reviewed, and contrasted with the approaches previously discussed. For any reader who has a basic grounding in logic, this book offers an ideal guide to formal theories of truth.
Author(s): Jc Beall, Michael Glanzberg, David Ripley
Publisher: Oxford University Press
Year: 2018
Language: English
Pages: 151
Cover......Page 1
FORMAL THEORIES OF TRUTH......Page 4
Copyright......Page 5
Dedication......Page 6
CONTENTS......Page 8
PREFACE......Page 10
ACKNOWLEDGMENTS......Page 12
CHAPTER ONE: Introduction......Page 14
1.1 Our goals in the book......Page 16
1.2 Basic structure of discussion......Page 17
2.1 Introducing the Liar......Page 19
2.2 Simple-falsity Liar......Page 22
2.3 Simple-untruth Liar......Page 23
2.5 Boolean compounds......Page 24
2.6 Infinite sequences......Page 26
2.7 On paradoxes beyond the Liar......Page 27
3.1 Basic ingredients......Page 29
3.1.2 Principles of truth......Page 30
3.1.3.1 existence of liar-like sentences......Page 32
3.1.3.2 other logical “laws”......Page 33
3.1.3.3 the liar in abs tract......Page 34
3.2 Guiding questions......Page 36
4.1 Truth and satisfaction......Page 37
4.2.1 Terms from formulas......Page 39
4.2.2 Auxiliary function......Page 41
4.2.3 Arithmetic......Page 43
4.3 Compositional principles......Page 47
4.4 Consequence relations......Page 48
CHAPTER FIVE: Nonclassical Logic: Unrestricted Capture–Release......Page 51
5.1 Kleene–Kripke models......Page 53
5.1.1 Strong Kleene models......Page 54
5.1.2 Fixed points......Page 56
5.2 Consequence......Page 58
5.2.1 A paracomplete logic: K3TT......Page 59
5.2.2 A paraconsistent logic: LPTT......Page 60
5.2.3 Neither and both......Page 62
5.2.4 Some alternatives......Page 63
5.3.1 Why an extra conditional?......Page 65
5.3.2 Some constraints......Page 67
5.4 Common objections......Page 69
5.4.1 Nonclassical logic!......Page 70
5.4.2 Disagreement, claims of paradoxicality, and expressive power......Page 71
5.4.3 Value 1 and revenge......Page 74
6.1 Classical logic......Page 76
6.2.1 Basic motivation......Page 77
6.2.2 A formal picture......Page 78
6.2.3 Common objections......Page 82
6.3.1 Basic motivation......Page 83
6.3.2 A formal picture......Page 84
6.3.2.1 common objections......Page 86
6.3.3 Another formal picture......Page 87
6.4.1 A formal picture......Page 89
6.4.2 Common objections......Page 92
6.5.1 Basic motivation......Page 93
6.5.2 A formal picture......Page 97
6.5.3 Other Approaches......Page 102
6.5.5 Common objections......Page 103
6.6 Determinacy revisited......Page 105
7.1 Deep structure......Page 107
7.2 A formal framework......Page 108
7.3 Going substructural......Page 113
7.4 Advantages......Page 114
7.5 Common objections......Page 117
8.1 Inconsistency views......Page 122
8.1.1 Now what?......Page 124
8.1.2 Relations to other views......Page 126
8.1.3 Objections......Page 127
8.2.1 formal picture......Page 128
8.2.2 common objections......Page 130
CHAPTER NINE: Closing Remarks......Page 132
BIBLIOGRAPHY......Page 134
NAME INDEX......Page 146
GENERAL INDEX......Page 149
