A Logical Approach to Philosophy: Essays in Honour of Graham Solomon (The Western Ontario Series in Philosophy of Science)

Cover......Page 1
Half Title......Page 3
Title Page......Page 5
Contents......Page 7
Preface......Page 9
Introduction......Page 13
1 Epistemology and Epistemic Logic......Page 14
2 Choice Principles and Logic......Page 16
3 Epistemology and Anti-Realism......Page 19
4.1 An Episode in the History of Modal Logic......Page 21
4.2 Logic and the Sweep of History......Page 22
4.3 Why History didn’t take a Different Turn......Page 25
5 Non-Classical Logics and Pluralism......Page 26
5.1 Expressive Power, Paradox and Negations......Page 27
5.2 More than One Logic?......Page 31
6 A Logical Approach......Page 33
1 The KK-thesis......Page 34
2 Internalism......Page 37
3 Externalism......Page 40
2 Choice Principles in Intuitionistic Set Theory......Page 48
3 Assertion, Proof, and the Axiom of Choice......Page 57
1 Introduction......Page 58
2 Luminosity......Page 60
2.1 Anti-Anti-Realism......Page 63
3 Two Flavours of Type Theory......Page 65
3.1 Propositions as Types......Page 68
4 The Problems with PAT: Luminosity?......Page 70
5 Problems with PAT: Is Choice Constructive?......Page 75
5.1 AC and The Axiom of Choice......Page 79
5.2 Problems with PAT: Choice is not Constructive......Page 82
5.3 Some Philosophical Lessons......Page 85
6 Conclusion......Page 87
4 Montague's Modal Completeness Theorem of 1955......Page 89
1 Introduction......Page 96
2 Russell’s Theory of Propositional Understanding......Page 98
3 Ramsey’s Primary and Secondary Systems......Page 106
4 Carnap’s Reconstruction of the Language of Science and an Observation of Newman......Page 114
5 Extension to Constructive Empiricism......Page 121
6 Putnam’s Model-Theoretic Argument and the Semantic View of Theories......Page 124
7 The Problem Clarified and Resolved......Page 127
8 Acknowledgements......Page 139
1 History......Page 140
1.1 Notion of Set Problematic......Page 142
1.2 First Order Axiomatizations......Page 143
1.3 Löwenheim–Skolem......Page 144
1.4 Goal of Deductive Completeness......Page 146
2 Tennant......Page 149
3.1 Answer the First......Page 152
3.2 Answer the Second......Page 153
4 Counterexample......Page 155
5 Comments......Page 159
1 Prologue......Page 163
2 The Proposal......Page 168
2.1 Basic Semantics......Page 169
2.2 Why Stop with Negation?......Page 171
2.3 Further Conditions on A?......Page 173
2.4 Another Negation, Briefly......Page 174
3 Understanding A and ≤......Page 175
4 Concluding remarks: Why isn’t this More Complicated?......Page 178
8 Negation's Holiday: Aspectival Dialetheism......Page 181
1 Falsity and the Liar......Page 182
2.2 Valuations......Page 183
2.3 Admissible Valuations and Classical Consequence......Page 184
3 The Dialetheic Response to Paradox......Page 185
4 Dropping Exclusion: The Logic P......Page 186
4.1 P-theory of Negation......Page 188
5.1 The Law of Non-Contradiction......Page 189
5.2 Mere Sub-Contraries......Page 190
5.3 Traditional Properties of ‘Real Negation’......Page 191
5.4 The Double-Aspect Hypothesis......Page 192
6 Double-Aspect Negation: The Logic AP......Page 193
6.1 Non-monotonicity......Page 194
6.2 The Philosophical Import......Page 195
7.1 Field’s Criticism......Page 197
7.2 Shapiro’s Challenge......Page 199
8 Closing Remarks and Further Directions......Page 202
1 Logical Pluralism......Page 205
2 Priest’s Challenge......Page 206
3 Truth-Preservation......Page 210
4 Classical Semantics......Page 214
5 Conclusion......Page 221
Bibliography......Page 222
Index......Page 231