Preface to the First Edition |
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xvii | |
Preface to the Second Edition |
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xxi | |
Mathematical Prolegomenon |
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xxvii | |
Set-theoretic Notation |
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xxvii | |
Proof by Induction |
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xxix | |
Equivalence Relations and Equivalence Classes |
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xxx | |
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Part I Propositional Logic |
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1 | (240) |
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Classical Logic and the Material Conditional |
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3 | (17) |
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3 | (1) |
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The Syntax of the Object Language |
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4 | (1) |
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5 | (1) |
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6 | (4) |
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10 | (1) |
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11 | (1) |
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12 | (1) |
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Subjunctive and Counterfactual Conditionals |
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13 | (1) |
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14 | (1) |
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15 | (1) |
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16 | (2) |
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18 | (1) |
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18 | (1) |
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18 | (2) |
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20 | (16) |
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20 | (1) |
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Necessity and Possibility |
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20 | (1) |
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21 | (3) |
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24 | (4) |
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Possible Worlds: Representation |
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28 | (1) |
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28 | (1) |
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29 | (1) |
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30 | (1) |
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31 | (2) |
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33 | (1) |
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34 | (1) |
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34 | (2) |
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36 | (28) |
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36 | (1) |
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Semantics for Normal Modal Logics |
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36 | (2) |
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Tableaux for Normal Modal Logics |
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38 | (4) |
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42 | (3) |
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45 | (1) |
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Which System Represents Necessity? |
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46 | (3) |
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49 | (2) |
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51 | (5) |
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56 | (4) |
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60 | (1) |
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60 | (1) |
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60 | (4) |
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Non-normal Modal Logics; Strict Conditionals |
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64 | (18) |
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64 | (1) |
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64 | (1) |
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Tableaux for Non-normal Modal Logics |
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65 | (2) |
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The Properties of Non-normal Logics |
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67 | (2) |
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69 | (3) |
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72 | (1) |
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The Paradoxes of Strict Implication |
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72 | (1) |
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73 | (1) |
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The Explosion of Contradictions |
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74 | (2) |
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Lewis' Argument for Explosion |
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76 | (1) |
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77 | (2) |
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79 | (1) |
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80 | (1) |
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80 | (2) |
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82 | (21) |
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82 | (1) |
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Some More Problematic Inferences |
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82 | (2) |
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84 | (2) |
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86 | (1) |
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87 | (3) |
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90 | (4) |
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94 | (3) |
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Further Philosophical Reflections |
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97 | (1) |
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98 | (2) |
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100 | (1) |
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101 | (1) |
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101 | (2) |
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103 | (17) |
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103 | (1) |
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Intuitionism: The Rationale |
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103 | (2) |
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Possible-world Semantics for Intuitionism |
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105 | (2) |
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Tableaux for Intuitionist Logic |
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107 | (5) |
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The Foundations of Intuitionism |
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112 | (1) |
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The Intuitionist Conditional |
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113 | (1) |
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114 | (2) |
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116 | (1) |
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117 | (1) |
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117 | (3) |
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120 | (22) |
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120 | (1) |
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Many-valued Logic: The General Structure |
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120 | (2) |
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The 3-valued Logics of Kleene and Lukasiewicz |
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122 | (2) |
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124 | (1) |
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Many-valued Logics and Conditionals |
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125 | (2) |
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Truth-value Gluts: Inconsistent Laws |
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127 | (2) |
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Truth-value Gluts: Paradoxes of Self-reference |
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129 | (1) |
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Truth-value Gaps: Denotation Failure |
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130 | (2) |
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Truth-value Gaps: Future Contingents |
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132 | (1) |
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Supervaluations, Modality and Many-valued Logic |
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133 | (4) |
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137 | (2) |
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139 | (1) |
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140 | (1) |
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140 | (2) |
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142 | (21) |
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142 | (1) |
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142 | (2) |
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144 | (2) |
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FDE and Many-valued Logics |
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146 | (3) |
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Relational Semantics and Tableaux for L3 and RM3 |
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149 | (2) |
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151 | (3) |
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Paraconsistency and the Disjunctive Syllogism |
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154 | (1) |
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155 | (6) |
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161 | (1) |
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161 | (1) |
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161 | (2) |
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Logics with Gaps, Gluts and Worlds |
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163 | (25) |
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163 | (1) |
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163 | (1) |
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164 | (2) |
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166 | (2) |
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168 | (1) |
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169 | (2) |
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Impossible Worlds and Relevant Logic |
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171 | (4) |
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Logics of Constructible Negation |
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175 | (4) |
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179 | (5) |
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184 | (1) |
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185 | (1) |
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185 | (3) |
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188 | (33) |
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188 | (1) |
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188 | (2) |
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190 | (4) |
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194 | (3) |
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197 | (6) |
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203 | (3) |
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206 | (2) |
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Ceteris Paribus Enthymemes |
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208 | (3) |
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211 | (5) |
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216 | (1) |
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217 | (1) |
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218 | (3) |
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221 | (20) |
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221 | (1) |
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221 | (1) |
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222 | (2) |
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The Continuum-valued Logic L |
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224 | (3) |
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227 | (3) |
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230 | (1) |
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231 | (3) |
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234 | (3) |
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237 | (1) |
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238 | (1) |
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239 | (2) |
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Appendix: Many-valued Modal Logics |
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241 | (18) |
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241 | (1) |
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241 | (2) |
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Illustration: Modal Lukasiewicz Logic |
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243 | (1) |
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244 | (3) |
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247 | (3) |
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250 | (1) |
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Future Contingents Revisited |
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251 | (3) |
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254 | (1) |
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255 | (4) |
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Postscript: An Historical Perspective on Conditionals |
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259 | (2) |
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Part II Quantification and Identity |
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261 | (323) |
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Classical First-order Logic |
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263 | (27) |
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263 | (1) |
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263 | (1) |
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264 | (2) |
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266 | (6) |
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272 | (3) |
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Some Philosophical Issues |
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275 | (2) |
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Some Final Technical Comments |
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277 | (1) |
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278 | (5) |
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283 | (2) |
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285 | (2) |
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287 | (1) |
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287 | (1) |
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288 | (2) |
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290 | (18) |
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290 | (1) |
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290 | (1) |
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291 | (2) |
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Free Logics: Positive, Negative and Neutral |
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293 | (2) |
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Quantification and Existence |
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295 | (2) |
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297 | (3) |
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300 | (4) |
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304 | (1) |
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305 | (1) |
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305 | (3) |
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Constant Domain Modal Logics |
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308 | (21) |
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308 | (1) |
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308 | (1) |
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309 | (5) |
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Other Normal Modal Logics |
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314 | (1) |
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Modality De Re and De Dicto |
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315 | (3) |
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318 | (2) |
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320 | (5) |
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325 | (1) |
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326 | (1) |
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327 | (2) |
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Variable Domain Modal Logics |
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329 | (20) |
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329 | (1) |
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329 | (1) |
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Variable Domain K and its Normal Extensions |
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330 | (1) |
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Tableaux for VK and its Normal Extensions |
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331 | (4) |
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Variable Domain Tense Logic |
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335 | (1) |
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336 | (3) |
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339 | (2) |
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Existence and Wide-Scope Quantifiers |
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341 | (1) |
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342 | (4) |
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346 | (1) |
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346 | (1) |
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347 | (2) |
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Necessary Identity in Modal Logic |
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349 | (18) |
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349 | (1) |
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350 | (2) |
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The Negativity Constraint |
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352 | (2) |
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Rigid and Non-rigid Designators |
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354 | (3) |
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357 | (1) |
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358 | (4) |
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362 | (2) |
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364 | (1) |
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364 | (1) |
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365 | (2) |
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Contingent Identity in Modal Logic |
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367 | (17) |
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367 | (1) |
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367 | (6) |
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SI Again, and the Nature of Avatars |
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373 | (3) |
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376 | (6) |
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382 | (1) |
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382 | (1) |
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382 | (2) |
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384 | (15) |
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384 | (1) |
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Non-normal Modal Logics and Matrices |
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384 | (1) |
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Constant Domain Quantified L |
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385 | (1) |
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Tableaux for Constant Domain L |
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386 | (1) |
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387 | (4) |
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391 | (2) |
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393 | (4) |
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397 | (1) |
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397 | (1) |
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397 | (2) |
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399 | (22) |
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399 | (1) |
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Constant and Variable Domain C |
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399 | (4) |
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403 | (5) |
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408 | (5) |
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Some Philosophical Issues |
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413 | (2) |
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415 | (4) |
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419 | (1) |
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419 | (1) |
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419 | (2) |
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421 | (35) |
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421 | (1) |
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Existence and Construction |
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421 | (1) |
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Quantified Intuitionist Logic |
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422 | (2) |
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Tableaux for Intuitionist Logic 1 |
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424 | (3) |
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Tableaux for Intuitionist Logic 2 |
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427 | (4) |
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431 | (1) |
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432 | (2) |
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434 | (3) |
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437 | (11) |
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448 | (5) |
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453 | (1) |
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453 | (1) |
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453 | (3) |
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456 | (20) |
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456 | (1) |
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Quantified Many-valued Logics |
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456 | (1) |
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457 | (2) |
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459 | (2) |
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461 | (1) |
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Existence and Quantification |
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462 | (3) |
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465 | (2) |
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467 | (1) |
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468 | (1) |
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Supervaluations and Subvaluations |
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469 | (2) |
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471 | (2) |
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473 | (1) |
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474 | (1) |
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474 | (2) |
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476 | (28) |
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476 | (1) |
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Relational and Many-valued Semantics |
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476 | (3) |
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479 | (2) |
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Free Logics with Relational Semantics |
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481 | (2) |
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Semantics with the Routley* |
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483 | (3) |
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486 | (3) |
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489 | (4) |
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493 | (6) |
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499 | (3) |
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502 | (1) |
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502 | (1) |
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502 | (2) |
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Logics with Gaps, Gluts and Worlds |
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504 | (31) |
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504 | (1) |
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505 | (1) |
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505 | (3) |
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508 | (2) |
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510 | (2) |
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512 | (3) |
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515 | (2) |
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Logics with Constructible Negation |
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517 | (4) |
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Identity for Logics with Constructible Negation |
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521 | (2) |
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523 | (4) |
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527 | (3) |
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530 | (2) |
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532 | (1) |
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532 | (1) |
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533 | (2) |
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535 | (29) |
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535 | (1) |
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535 | (2) |
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537 | (4) |
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Restricted Quantification |
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541 | (2) |
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Semantics vs Proof Theory |
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543 | (5) |
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548 | (5) |
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553 | (2) |
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555 | (4) |
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559 | (2) |
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561 | (1) |
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561 | (1) |
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562 | (2) |
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564 | (20) |
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564 | (1) |
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Quantified Lukasiewicz Logic |
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564 | (1) |
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565 | (5) |
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570 | (2) |
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572 | (1) |
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573 | (3) |
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576 | (2) |
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*Appendix: Quantification and Identity in t-norm Logics |
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578 | (3) |
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581 | (1) |
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582 | (1) |
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582 | (2) |
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Postscript: A Methodological Coda |
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584 | (3) |
References |
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587 | (16) |
Index of Names |
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603 | (4) |
Index of Subjects |
|
607 | |