This book, provides a critical approach to all major logical paradoxes: from ancient to contemporary ones. There are four key aims of the book: 1. Providing systematic and historical survey of different approaches – solutions of the most prominent paradoxes discussed in the logical and philosophical literature. 2. Introducing original solutions of major paradoxes like: Liar paradox, Protagoras paradox, an unexpected examination paradox, stone paradox, crocodile, Newcomb paradox. 3. Explaining the far-reaching significance of paradoxes of vagueness and change for philosophy and ontology. 4. Proposing a novel, well justified and, as it seems, natural classification of paradoxes.
Author(s): Piotr Łukowski
Series: Trends in Logic 31
Publisher: Springer
Year: 2011
Language: English
Pages: 202
Paradoxes......Page 3
1 Introduction......Page 8
References......Page 10
2.1…Bottle Imp Paradox (Stevenson’s Bottle), or the Unintuitive Character of a Conclusion Following a Sufficient Multiplication of a Simple Reasoning......Page 11
2.2…Newcomb’s Paradox, or the Unintuitive Character of a Conclusion Drawn from Premises with Non-intuitive Assumption......Page 13
2.3…Paradox of Common Birthday, or the Unintuitive Character of Some Results in Probability Calculus......Page 17
2.4…Paradox of Approximation and Paradox of the Equator, or the Unintuitive Character of Some Results in Euclidean geometry......Page 19
2.5…Horses’ Paradox, or the Intuitive Character of an Erroneous Application of Mathematical Induction......Page 21
2.6…Hempel’s Paradox (Raven, Confirmation), or the Unintuitive Character of Some Inductive Reasoning Results......Page 22
2.7.1 Aristotelian Circles Paradox, or the Definition of an Infinite Set......Page 25
2.7.2 Holy Trinity Paradox, or Application of the Definition of Infinite Set in Theology......Page 33
2.8…Fitch’s Paradox, or the Conflict of Two Intuitions......Page 38
References......Page 41
3.1…Protagoras’ (Law Teacher’s) Paradox......Page 42
3.2…Electra’s (the Veiled One’s) Paradox and Other Equivocations......Page 53
3.3…The Horny One’s Paradox......Page 56
3.4…Nameless Club Paradox......Page 57
3.5…Paradox of a Stone, or an Attempt at Disproving God’s Omnipotence......Page 59
References......Page 78
4.1…Möbius Ribbon and Klein Bottle, or Self-Reference in Mathematics......Page 80
4.2.1 Liar Antinomy......Page 85
4.2.1.1 Tarski’s Proposal......Page 90
4.2.1.2 Parsons’ Proposal......Page 91
4.2.1.3 Burge’s Proposal......Page 93
4.2.1.4 Martin’s and Woodruff’s Proposal......Page 94
4.2.1.5 Kripke’s Proposal......Page 95
4.2.1.6 Gupta’s Proposal......Page 96
4.2.1.7 Feferman’s Proposal......Page 98
4.2.1.8 Priest’s Proposal......Page 100
4.2.1.9 Barwise’s and Etchemendy’s Proposal......Page 101
4.2.1.10 The Author’s Own Proposal......Page 104
4.2.1.11 Summing up of the Proposed Solution......Page 110
4.2.2 Buridan’s Paradox......Page 111
4.2.2.1 Proposed Solution of Buridan’s Paradox......Page 112
4.2.3 Generalized Form of Liar Antinomy......Page 113
4.2.4 Curry’s Paradox......Page 114
4.3…Other Semantic Paradoxes......Page 115
4.3.1 Barber’s Antinomy......Page 116
4.3.2 Richard’s and Berry’s Antinomies......Page 118
4.3.3 Grelling’s Antinomy (Vox Non Appellans Se)......Page 123
4.4…Unexpected Examination (Hangman’s) Paradox, or Self-Reflexive Reasoning......Page 124
4.5…Crocodile’s Paradox, or Baron Münchhausen Fallacy......Page 129
References......Page 133
5.1…Paradoxes of Difference: Paradox of a Heap......Page 135
5.1.1 What is Vagueness?......Page 145
5.1.2 Proposals Substituting Preciseness for Vagueness......Page 155
5.1.3 Vagueness Respecting Proposals......Page 170
5.2.1 Paradox of the Moment of Death (Change of State Paradox)......Page 175
5.2.2 Paradoxes of Identity......Page 176
5.2.3 The Paradoxes of Motion......Page 179
5.3…Diagnosis of Paradoxes of Vagueness and Change......Page 185
References......Page 189
Names Index......Page 193
Subject Index......Page 196
Contents......Page 6
