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xii | |
Preface |
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xv | |
Acknowledgements |
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xix | |
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1 | (34) |
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1 | (14) |
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1 | (1) |
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2 | (4) |
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6 | (7) |
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13 | (1) |
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1.1.5 The relation of semantics and proofs |
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14 | (1) |
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15 | (11) |
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16 | (1) |
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17 | (1) |
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17 | (4) |
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21 | (5) |
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26 | (3) |
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28 | (1) |
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28 | (1) |
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28 | (1) |
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29 | (6) |
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35 | (32) |
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35 | (4) |
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2.1.1 What is a quantifier? |
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35 | (2) |
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2.1.2 Semantics of binary quantifiers |
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37 | (1) |
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2.1.3 Most: an essentially binary quantifier |
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37 | (1) |
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2.1.4 Unary quantifiers beyond and |
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38 | (1) |
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2.1.5 Generalized quantifiers |
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39 | (1) |
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2.2 Definite descriptions |
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39 | (5) |
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2.2.1 Terms or quantifiers? |
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39 | (2) |
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2.2.2 Definite descriptions and scope |
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41 | (1) |
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2.2.3 Russell's theory of descriptions |
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41 | (2) |
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43 | (1) |
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2.3 Second-order quantifiers |
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44 | (13) |
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2.3.1 Standard semantics for monadic second-order logic |
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46 | (1) |
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2.3.2 Expressive limitations of first-order logic |
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47 | (3) |
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2.3.3 Set theory in sheep's clothing? |
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50 | (2) |
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2.3.4 Boolos's plural interpretation |
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52 | (2) |
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2.3.5 Beyond monadic second-order logic |
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54 | (3) |
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2.4 Substitutional quantifiers |
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57 | (10) |
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2.4.1 Objectual and substitutional quantification |
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57 | (1) |
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2.4.2 Nonexistent objects |
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58 | (1) |
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2.4.3 Quantifying into attitude reports |
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59 | (1) |
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2.4.4 Sentence quantifiers |
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60 | (1) |
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2.4.5 Quantifying into quotes |
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61 | (1) |
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61 | (1) |
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2.4.7 Quantifying into quotes and paradox |
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62 | (2) |
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2.4.8 The circularity worry |
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64 | (3) |
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67 | (30) |
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3.1 Modal propositional logic |
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67 | (13) |
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67 | (1) |
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68 | (2) |
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3.1.3 Modal logics from K to S5 |
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70 | (4) |
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74 | (6) |
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3.2 Modal predicate logic |
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80 | (5) |
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80 | (1) |
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3.2.2 Opaque contexts and quantification |
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81 | (1) |
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3.2.3 The number of planets argument |
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82 | (1) |
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83 | (2) |
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3.3 The slingshot argument |
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85 | (5) |
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3.3.1 Applications of slingshot arguments |
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87 | (1) |
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3.3.2 The Godel slingshot |
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87 | (1) |
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3.3.3 Critique of the slingshot |
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88 | (2) |
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3.4 Kripke's defense of de re modality |
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90 | (7) |
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90 | (1) |
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3.4.2 The contingent a priori |
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91 | (2) |
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3.4.3 The necessary a posteriori |
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93 | (1) |
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3.4.4 Epistemic and alethic modals |
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94 | (3) |
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97 | (26) |
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4.1 The material conditional |
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97 | (4) |
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4.1.1 Indicative vs. counter-factual |
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97 | (2) |
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4.1.2 Entailments between indicatives and material conditionals |
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99 | (1) |
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4.1.3 Thomson against the "received opinion" |
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100 | (1) |
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101 | (8) |
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4.2.1 Arguments for the material conditional analysis |
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102 | (1) |
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4.2.2 Arguments against the material conditional analysis |
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102 | (2) |
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104 | (1) |
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4.2.4 Edgington's positive view |
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105 | (2) |
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4.2.5 Against truth conditions |
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107 | (2) |
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4.3 Stalnaker's semantics and pragmatics |
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109 | (6) |
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4.3.1 Propositions, assertion, and the common ground |
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109 | (1) |
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110 | (1) |
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4.3.3 Reasonable but invalid inferences |
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111 | (2) |
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4.3.4 Contraposition and Hypothetical Syllogism |
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113 | (1) |
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4.3.5 The argument for fatalism |
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114 | (1) |
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4.4 Is Modus Ponens valid? |
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115 | (8) |
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4.4.1 The intuitive counterexamples |
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116 | (1) |
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4.4.2 McGee's counterexamples as seen by Edgington |
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117 | (2) |
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4.4.3 McGee's counterexamples as seen by Stalnaker |
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119 | (1) |
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4.4.4 Modus Ponens vs. Exportation |
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120 | (3) |
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5 Logical Consequence via Models |
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123 | (22) |
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5.1 Informal characterizations of consequence |
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123 | (9) |
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5.1.1 In terms of necessity |
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123 | (3) |
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126 | (2) |
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5.1.3 In terms of counterexamples |
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128 | (4) |
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5.2 Tarski's account of logical consequence |
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132 | (8) |
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132 | (1) |
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5.2.2 Why proof-based approaches won't work |
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132 | (3) |
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5.2.3 Criteria of adequacy |
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135 | (1) |
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5.2.4 The insufficiency of (F) |
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136 | (1) |
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5.2.5 The semantic definition |
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137 | (1) |
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5.2.6 Satisfying the criteria of adequacy |
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138 | (1) |
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139 | (1) |
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5.3 Interpretational and representational semantics |
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140 | (5) |
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6 Logical Consequence via Proofs |
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145 | (24) |
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6.1 Introduction rules as self-justifying |
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145 | (6) |
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6.1.1 Carnap's Copernican turn |
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146 | (1) |
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146 | (1) |
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6.1.3 Stevenson's response |
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147 | (1) |
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148 | (2) |
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150 | (1) |
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6.2 Prawitz's proof-theoretic account of consequence |
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151 | (5) |
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152 | (1) |
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152 | (1) |
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153 | (1) |
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154 | (1) |
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6.2.5 Philosophical reflections |
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155 | (1) |
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156 | (3) |
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6.4 Kripke semantics for intuitionistic logic |
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159 | (3) |
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6.5 Fundamental logical disagreement |
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162 | (7) |
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6.5.1 Changing the subject? |
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163 | (1) |
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6.5.2 Interpreting classical logic in intuitionistic logic |
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164 | (2) |
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6.5.3 Interpreting intuitionistic logic in classical logic |
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166 | (1) |
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167 | (2) |
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7 Relevance, Logic, and Reasoning |
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169 | (22) |
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7.1 Motivations for relevance logic |
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170 | (1) |
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171 | (5) |
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7.2.1 Rejecting Disjunctive Weakening |
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172 | (1) |
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7.2.2 Rejecting transitivity |
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173 | (2) |
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7.2.3 Rejecting Disjunctive Syllogism |
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175 | (1) |
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7.3 First-degree entailment |
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176 | (5) |
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7.3.1 A syntactic procedure |
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176 | (4) |
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7.3.2 The four-valued truth tables |
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180 | (1) |
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181 | (4) |
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7.5 Uses for relevance logic |
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185 | (6) |
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186 | (1) |
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7.5.2 The moderate approach |
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187 | (1) |
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188 | (3) |
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8 Vagueness and the Sorites Paradox |
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191 | (24) |
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191 | (3) |
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194 | (4) |
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8.2.1 Semantics for connectives |
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194 | (2) |
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8.2.2 Defining validity in multivalued logics |
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196 | (1) |
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8.2.3 Application to the sorites |
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196 | (2) |
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198 | (5) |
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199 | (1) |
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8.3.2 Application to the sorites |
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199 | (1) |
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8.3.3 Can we make sense of degrees of truth? |
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200 | (2) |
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8.3.4 Troubles with degree-functionality |
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202 | (1) |
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203 | (6) |
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8.4.1 Application to sorites |
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206 | (1) |
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8.4.2 Higher-order vagueness |
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207 | (1) |
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8.4.3 The logic of definiteness |
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208 | (1) |
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8.5 Vagueness in the world? |
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209 | (6) |
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8.5.1 Evans on vague identity |
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210 | (2) |
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212 | (3) |
Appendix A Greek Letters |
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215 | (2) |
Appendix B Set-Theoretic Notation |
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217 | (2) |
Appendix C Proving Unrepresentability |
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219 | (4) |
References |
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223 | (8) |
Index |
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231 | |