| Introduction |
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3 | (1) |
| Quodlibet Ens Est Unum |
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3 | (4) |
| Overview |
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7 | (6) |
| PART I THE UNRESTRICTED VARIABLE |
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13 | (84) |
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1 Russell's Logicist Program |
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13 | (29) |
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Two Conceptions of Logicism: Frege and Russell |
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13 | (4) |
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17 | (4) |
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Russell's Principle of Abstraction |
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21 | (9) |
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30 | (12) |
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2 The Logic of The Principles of Mathematics |
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42 | (27) |
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The Calculus for the Logic Propositions |
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42 | (6) |
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48 | (4) |
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The Theory of Implication |
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52 | (2) |
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54 | (3) |
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57 | (6) |
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The Analysis of the Variable |
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63 | (6) |
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3 The New Theory of the Variable |
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69 | (28) |
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"On Fundamentals" Against Denoting Concepts |
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72 | (8) |
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An Argument Against Frege? |
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80 | (2) |
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The Variable as Primitive |
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82 | (7) |
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89 | (8) |
| PART II TYPES AS LOGICAL GRAMMAR |
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97 | (102) |
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4 The Logic of Substitution |
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97 | (30) |
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Russell's Original Principles of Substitution |
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98 | (4) |
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The Basic Logic of Propositions |
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102 | (4) |
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Substitutional Principles |
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106 | (3) |
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109 | (3) |
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Proofs of Propositional Identities |
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112 | (15) |
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5 The "No Propositional Functions" Theory |
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127 | (19) |
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Substitution and Definite Descriptions |
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128 | (4) |
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132 | (3) |
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Comprehension and Identity |
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135 | (5) |
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140 | (6) |
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6 The "No-Classes" Theory |
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146 | (30) |
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Classes as Extensional Propositional Functions |
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147 | (2) |
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Complex Prototypes and Extensionality |
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149 | (3) |
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The General Theory of Classes |
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152 | (13) |
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Comparison with Principia Mathematica |
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165 | (11) |
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7 The "No-Relations(e)" Theory |
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176 | (23) |
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Relations-in-Extension in Principia Mathematica |
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177 | (2) |
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Relations-in-Extension in the Substitutional Theory |
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179 | (4) |
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Cantor's Paradox of the Greatest Cardinal |
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183 | (7) |
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190 | (9) |
| PART III RAMIFICATION |
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199 | (100) |
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8 Les Paradoxes de la Logique |
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199 | (35) |
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Three Paradoxes of Propositions |
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201 | (5) |
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Substitutional Manuscripts of April/May 1906 |
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206 | (7) |
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Poincare's Vicious Circle Principle |
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213 | (3) |
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Logic without General Propositions |
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216 | (4) |
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220 | (4) |
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The Konig, Dixon, Berry, Richard, and Grelling Paradoxes |
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224 | (3) |
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Russell's "Mitigating Axiom" |
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227 | (4) |
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The Demise of "Les Paradoxes" |
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231 | (3) |
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9 Mathematical Logic as Based on the Theory of Types |
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234 | (21) |
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235 | (5) |
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Substitutional Logic cum Orders of Propositions |
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240 | (6) |
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Predicativity and Reducibility |
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246 | (5) |
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Paradoxes of Propositions Avoided |
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251 | (4) |
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10 The Logic of Principia Mathematica |
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255 | (44) |
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The Formal System of Principia (cum *10) |
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255 | (3) |
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The Perils of Typical Ambiguity |
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258 | (9) |
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Orders within Types or Types within Orders? |
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267 | (5) |
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The Doctrine of the Unlimited Variable |
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272 | (3) |
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Poincare's Vicious Circle Principle |
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275 | (4) |
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The Philosophical Justification of the Type Part of an Order/Type Index |
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279 | (2) |
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The Philosophical Justification of the Order Part of an Order/Type Index |
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281 | (6) |
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The Multiple-Relation Theory of Judgment |
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287 | (4) |
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291 | (3) |
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294 | (5) |
| Appendix A: Proof of the Peano Postulates |
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299 | (15) |
| Appendix B: Axioms, Theorems, and Definitions |
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314 | (11) |
| Bibliography |
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325 | (8) |
| Index |
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333 | |
