A Survey of Symbolic Logic

Preface ......Page 6
Section I. The Scope of symbolic logic. Symbolic logic and logistic. Summary account of their development ......Page 8
Section II. Leibniz ......Page 12
Section III. From Leibniz to De Morgan and Boole ......Page 25
Section IV. De Morgan ......Page 44
Section V. Boole ......Page 58
Section VI. Jevons ......Page 79
Section VII. Peirce ......Page 86
Section VIII. Developments since Peirce ......Page 114
Section I. General character of the algebra. The postulates and their interpretation ......Page 125
Section II. Elementary theorems ......Page 129
Section III. General properties of functions ......Page 139
Section IV. Fundamental laws of the theory of equations ......Page 151
Section V. Fundamental laws of the theory of inequations ......Page 173
Section VI. Note on the inverse operations, “subtraction” and “division” ......Page 180
Section I. Diagrams for the logical relations of classes ......Page 182
Section II. The application to classes ......Page 191
Section III. The application to propositions ......Page 220
Section IV. The application to relations ......Page 226
Section I. The two-valued algebra ......Page 229
Section II. The calculus of propositional functions. Functions of one variable ......Page 239
Section III. Propositional functions of two or more variables ......Page 253
Section IV. Derivation of the logic of classes from the calculus of propositional functions ......Page 267
Section V. The logic of relations ......Page 276
Section VI. The logic of Principia Mathematica ......Page 286
V. The system of strict implication ......Page 298
Section I. Primitive ideas, primitive propositions, and immediate consequences ......Page 299
Section II. Strict relations and material relations ......Page 306
Section III. The transformation {-/~} ......Page 307
Section IV. Extensions of strict implication. The calculus of consistencies and the calculus of ordinary inference ......Page 317
Section V. The meaning of “implies” ......Page 331
Section I. General character of the logistic method. The “orthodox” view ......Page 347
Section II. Two varieties of logistic method: Peano’s Formulaire and Principia Mathematica. The nature of logistic proof ......Page 350
Section III. A “heterodox” view of the nature of mathematics and of logistic ......Page 361
Section IV. The logistic method of Kempe and Royce ......Page 369
Section V. Summary and conclusion ......Page 374
Appendix. Two fragments from Leibniz ......Page 380
Bibliography ......Page 396