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ix | |
Preface |
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xi | |
Acknowledgments |
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xvii | |
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1 The Quandary on the Characterization of Scientific Theories |
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1 | (20) |
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1.1 The Received View and Syntactical Approaches |
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3 | (7) |
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1.2 The Semantic Approach |
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10 | (8) |
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1.3 Scientific Theories and Philosophical Tools |
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18 | (3) |
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21 | (21) |
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25 | (5) |
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30 | (4) |
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34 | (8) |
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2.3.1 First-Order Classical Logic With Identity |
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34 | (4) |
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38 | (4) |
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3 A Mathematical Background |
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42 | (20) |
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3.1 The Principle of Constructivity |
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42 | (3) |
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3.2 The ZF(C) Set Theories |
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45 | (8) |
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3.2.1 The Postulates of ZF(C) |
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48 | (3) |
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3.2.2 A Matter of Terminology |
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51 | (1) |
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3.2.3 Inaccessible Cardinals |
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52 | (1) |
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3.2.4 Informal Semantics of 6 |
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52 | (1) |
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3.3 `Models' of ZF(C), Again |
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53 | (3) |
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56 | (2) |
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58 | (1) |
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3.5 More on the `Models' of ZF(C) |
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58 | (4) |
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4 Criticism of the Axiomatic Method and Its Defense |
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62 | (14) |
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4.1 Does the AM Encompass Heuristics? |
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62 | (2) |
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4.1.1 The Axiomatic Method and Heuristics |
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63 | (1) |
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4.2 Truesdell Against the `Suppesians' |
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64 | (4) |
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4.3 Arnol'd and the Bourbaki Program |
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68 | (1) |
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68 | (3) |
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4.5 Does Axiomatization Really Axiomatize? |
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71 | (5) |
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5 Axiomatization and Scientific Theories |
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76 | (36) |
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5.1 External Axiomatizations |
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77 | (2) |
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79 | (4) |
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5.3 Languages and Algebras |
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83 | (3) |
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5.4 Languages for Speaking of Structures |
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86 | (3) |
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5.4.1 The Language of a Structure |
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88 | (1) |
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5.5 Definability and Expressive Elements |
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89 | (3) |
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92 | (2) |
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5.7 Da Costa and Chuaqui--Suppes Predicates |
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94 | (5) |
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5.7.1 A Suppes Predicate for Group Theory |
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95 | (1) |
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5.7.2 A Suppes Predicate for Classical Particle Mechanics |
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96 | (3) |
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5.8 The Approach of Suppes |
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99 | (13) |
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5.8.1 An Axiomatization of Non-relativistic Quantum Mechanics |
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104 | (8) |
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6 Models and Scientific Theories |
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112 | (15) |
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6.1 Again on the Order of Languages and Structures |
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112 | (2) |
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6.2 Further Remarks on the Suppes Approach |
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114 | (3) |
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6.3 Da Costa and Chuaqui, Further Remarks |
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117 | (2) |
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6.4 The Metamathematical Framework |
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119 | (8) |
Bibliography |
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127 | (8) |
Index |
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135 | |