Introducing Logic makes this important discipline accessible to everyone using the series' popular illustrated format. This easy-to-follow guide maps the historical development of logic, explains its symbols and methodology, traces its influence in a variety of disciplines, and shows logic in action in our digital age.
Author(s): Dan Cryan, Bill Mayblin
Publisher: Totem Books
Year: 2000
Language: English
Commentary: 49063
Pages: 178
What is Logic?......Page 5
Studying Sentences......Page 6
The Square of Oppositions......Page 7
The Syllogism......Page 8
Connective Logic......Page 10
Leibniz’s Law......Page 12
The Reductio ad Absurdum......Page 14
A “New Organon”......Page 16
Frege’s Quantifiers......Page 18
The Context Principle......Page 20
Propositional Calculus......Page 21
Cantor’s Set Theory......Page 22
The Usefulness of Connectives......Page 24
The Russell Paradox......Page 25
The Fatal Flaw......Page 26
The Problem of Surface Grammar......Page 27
Russell’s System......Page 28
Wittgenstein’s Logical Pictures......Page 30
Carnap and the Vienna Circle......Page 32
The Tolerance Principle......Page 33
Hilbert’s Proof Theory......Page 34
The Arrival of Gödel......Page 35
Gödel’s Incompleteness Theorem......Page 36
The Connections to Proof Theory......Page 37
Wittgenstein’s Table of Logical Connectives......Page 39
Wittgenstein’s Truth Tables......Page 40
Discovering Tautologies......Page 41
The Logic Gates of Digital Electronics......Page 42
A Vending Machine......Page 43
Turing and the “Enigma Code”......Page 44
Euclid’s Axiomatic Method......Page 45
Leibniz’s Proof Method......Page 47
Abuse of Contradiction......Page 48
Rules for Connectives......Page 49
Sensitivity to Grammar......Page 50
Predicate Calculus......Page 51
Model Theoretic Semantics......Page 52
Hilbert’s Recursion Model......Page 53
Finite Rules for Infinite Production......Page 56
Simple Instructions......Page 57
Proof Theory and Formal Language......Page 58
Tarski’s Truth Conditions......Page 60
Formal Semantics in Practice......Page 62
Constructing a Soap Opera......Page 63
Prolog to an AI Soap Opera......Page 64
Turing’s recipe for AI......Page 66
The Problem of Paradoxes......Page 68
Can Paradoxes be Avoided?......Page 70
Theory of Types......Page 71
Tarski’s Solution to the Liar......Page 73
The Unexorcised Paradox......Page 74
Gödel’s Incompleteness Theorem......Page 76
The Consequences of Gödel’s Theorem......Page 78
The “Halting Problem”......Page 80
The Limit of Gödel’s Proof......Page 81
Zeno’s Movement Paradox......Page 82
An Infinite Sum......Page 84
A Convergence on Limits......Page 85
How Much is a “Heap”?......Page 86
The Challenge to Sets......Page 87
Undermining Logic......Page 88
The Fiction of Vague Words......Page 89
What Do Words “Mean”?......Page 90
Fuzzy Logic......Page 91
Fuzzy Heaps......Page 92
Can Logic Escape Paradox?......Page 93
Non-Classical Logics: Intuitionism......Page 94
The Devil’s Argument......Page 95
Intuitionistic Logic......Page 96
Intuitionism versus the Reductio Method......Page 97
The Intuitionistic Fad......Page 98
Addressing Some Old Problems......Page 99
The Value of Possible......Page 100
Truth Values as Numbers......Page 101
The Possible and Non-Contradiction......Page 102
From Classical to Fuzzy Logic......Page 104
Electronic “Possible” States......Page 105
The Fuzzy Logic Search Engine......Page 106
The Fuzzy Logical Machine......Page 107
Logic in the Quantum World......Page 108
The Distributive Law of Quantum Logic......Page 109
How Quantum Logic Works......Page 110
Logic by Experiment......Page 111
Logic and Science......Page 113
The Copernican Revolution......Page 114
Galileo’s Revolution......Page 115
Methods of Deduction and Induction......Page 116
Problems with Induction......Page 118
Hume’s Fork......Page 119
Nomological Deduction......Page 120
Induction by Generalization......Page 122
Laws or Empirical Predictions......Page 126
The Raven Paradox......Page 128
A Problem of Cause and Effect......Page 130
Popper’s Answer to Hempel......Page 131
Popper’s Disconfirmation Theory......Page 132
The Probability of Viable Theory......Page 134
Quine’s “Web of Belief”......Page 136
Alterations to the “Web”......Page 138
Insufficient Evidence......Page 140
Quine’s Relativism......Page 142
Davidson’s Reply to Quine......Page 144
The Presentation of Truth......Page 145
Hard-edged Truth versus Relativism......Page 146
Cognitive Science and Logic......Page 147
Chomsky’s Universal Grammar......Page 148
Noun and Verb Categories......Page 150
Recursive Rules of Grammar......Page 153
The X-bar Theory......Page 154
A Logical Theory......Page 155
Problems of Syntax and Semantics......Page 156
Complex Grammatical Structures......Page 158
Problems with “Universal” Grammar......Page 160
The Symbolic Brain Model......Page 162
Training a Neural Net......Page 164
Pattern Recognition......Page 166
The Rational Behaviour Model......Page 168
Practical Reason......Page 169
What is Consciousness?......Page 170
The Place of Logic......Page 171
Wittgenstein’s Change of View......Page 172
Further Reading......Page 176
Index......Page 178
