The papers in this collection are united by an approach to philosophy. They illustrate the manifold contributions that logic makes to philosophical progress, both by the application of formal methods to traditional philosophical problems and by opening up new avenues of inquiry as philosophers sort out the implications of new and often surprising technical results. Contributions include new technical results rich with philosophical significance for contemporary metaphysics, attempts to diagnose the philosophical significance of some recent technical results, philosophically motivated proposals for new approaches to negation, investigations in the history and philosophy of logic, and contributions to epistemology and philosophy of science that make essential use of logical techniques and results. Where the work is formal, the motives are obviously philosophical, not merely mathematical. Where the work is less formal, it is deeply informed by the relevant formal material. The volume includes contributions from some of the most interesting philosophers now working in philosophical logic, philosophy of logic, epistemology and metaphysics.
Author(s): David DeVidi, Tim Kenyon (Editors)
Series: The Western Ontario Series in Philosophy of Science
Edition: 1
Publisher: Springer
Year: 2006
Language: English
Pages: 239
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
