Precision, Language and Logic (eBook)

Front Cover 1
Precision, Language and Logic 4
Copyright Page 5
Table of Contents 8
Dedication 6
FOREWORD 10
PART I: SOME BASIC LOGIC 12
CHAPTER 1. A BACKGROUND TO LOGIC 14
SUMMARY 20
EXERCISES 20
REFERENCES 21
CHAPTER 2. PROPOSITIONS AND THE SYLLOGISM 22
THE ANTILQGISM 29
THE SORITES 31
SUMMARY 32
EXERCISES 32
REFERENCES 32
CHAPTER 3. FIRST STEPS IN SYMBOLIC LOGIC 33
SYMBOLIC LOGIC 33
BOOLEAN ALGEBRA 36
LAWS OF BOOLEAN ALGEBRA 40
BASIC ISSUES INVOLVED 44
THE SYLLOGISM 45
SUMMARY 46
EXERCISES 47
REFERENCES 47
CHAPTER 4. THE PROPOSITIONAL CALCULUS 48
THE DOT CONVENTION 52
FORMAL PROOFS 54
BACKGROUND OF THE PROPOSITIONAL CALCULUS 58
SUMMARY 59
EXERCISES 59
REFERENCES 60
CHAPTER 5. PROPERTIES OF THE PROPOSITIONAL CALCULUS 61
SYNTACTIC THEOREMS 62
AN INTERPRETATION OF PART OF P 64
MANY-VALUED LOGIC 66
SUMMARY 69
EXERCISES 69
REFERENCES 70
CHAPTER 6. THE FUNCTIONAL AND PREDICATE CALCULUS 71
PREDICATE CALCULUS 77
SUMMARY 80
EXERCISES 80
REFERENCES 81
PART II: LOGIC, PROBABILITY AND PHILOSOPHY 82
CHAPTER 7. SCIENTIFIC METHOD 84
INDUCTION 86
SCIENCE IN ACTION 88
IN GENERAL 90
SUMMARY 91
EXERCISES 91
REFERENCES 92
CHAPTER 8. INDUCTION AND HYPOTHESIS FORMATION 93
INTRODUCTION 93
EXAMPLES OF INDUCTIONS 94
HYPOTHESIS FORMATION AND INDUCTION 95
NON-SEQUENTIAL ANALYSIS AND HEURISTIC METHODS 99
INDUCTION AND BEHAVIOUR 100
BELIEF FORMATION 100
SUMMARY 103
EXERCISES 104
REFERENCES 104
CHAPTER 9. PROBABILITY AND STATISTICS 105
THE CALCULUS OF PROBABILITY 106
DECISION PROCESSING 111
GAMES AGAINST NATURE 113
RISK ANALYSIS 114
THEORY OF GAMES 117
STOCHASTIC PROCESSES 118
STATISTICS 120
SUMMARY 121
EXERCISES 122
REFERENCES 122
CHAPTER 10. LANGUAGE AND PHILOSOPHY 123
INTRODUCTION 123
WITTGENSTEIN'S PHILOSOPHY OF LANGUAGE 124
RUSSELL'S LINGUISTIC ANALYSIS 128
THE PHILOSOPHY OF ORDINARY LANGUAGE 131
IN SUMMARY 133
SUMMARY 135
EXERCISES 136
REFERENCES 136
CHAPTER 11. EPISTEMOLOGY 138
THE PHILOSOPHICAL PROBLEM OF PERCEPTION 138
SUMMARY 150
EXERCISES 150
REFERENCES 150
CHAPTER 12. A PRAGMATIC THEORY OF BEHAVIOUR 151
A THEORY OF SIGNS 154
IN SUMMARY 161
EXERCISES 162
REFERENCES 162
PART III: FORMALISATION 164
CHAPTER 13. APPLIED LOGIC 166
THE CALCULUS OF RELATIONS 166
EMPIRICAL LOGIC 171
GOAL ORIENTATED APPLIED LOGIC (GOAL) 172
EXERCISES 177
REFERENCES 177
CHAPTER 14. FORMALISATION 178
A FIRST STAGE FORMALISATION OF THE PRAGMATIC THEORY 180
A FIRST FORMALISATION OF THE THEORY 183
EXERCISES 187
REFERENCES 187
CHAPTER 15. AUTOMATA THEORY 188
AUTOMATA IN GENERAL 188
INTRODUCTION TO NEURAL NETS 195
EXERCISES 199
REFERENCES 199
CHAPTER 16. A NEURAL NET APPROACH TO A PRAGMATIC THEORY 200
1 A BELIEF NET 200
2 CLASSIFICATION AND CONTROL MACHINES 203
3 PROPERTIES OF NEURAL NETS 206
EXERCISES 211
REFERENCES 211
CHAPTER 17. HIERARCHICAL NETS 212
NEURAL NETS IN ACTION 212
MANY LEVELLED NETS 215
ARTIFICIAL INTELLIGENCE AND NEURAL NETS 218
EXERCISES 224
REFERENCES 225
ADDITIONAL REFERENCES 227
AUTHOR INDEX 230
SUBJECT INDEX 232