Laws of Form

Description

Book on logic in pictorial notation with new appendices on Four Color Theorem and Riemann Hypothesis Contents Preface to the fifth English Edition ........................................... vii Preface to the first American edition .......................................... x Preface ............................................................... xiii Introduction .............................................................. xiv A note on the mathematical approach ....................................... xxii 1 Theform ........................................................ . 1 2 Forms taken out of the form ........................................ 3 3 The conception of ca!,culation ....................................... 7 4 The primary arithmetic .......................................... 10 5 A calculus taken out of the calculus ................................ 21 6 The primary algebra ............................................. 23 7 Theorems of the second order ...................................... 31 8 Re-uniting the two orders ......................................... 35 9 Completeness .................................................... 41 10 Independence ................................................... 44 11 Equations of the second degree ..................................... 45 12 Re-entry into the form ............................................ 57 Notes ................................................................ 64 Appendix 1. Proofs of Sheffer's postulates ...................................... 87 Appendix 2. The calculus interpreted/or logic ................................. 90 Index of references ....................................................... 108 Index of forms ............................................................ 109 Appendix 3. Bertrand Russell and the Laws of Form ........................... 113 Introduction to Appendices 4 & 5 ........................................... 117 Appendix 4. An algebra for the natural numbers ............................... 120 Appendix 5. 'l\vo proofs of the four-colour map theorem ......................... 129 Appendix 6. My simplest proof of the four-colour map theorem .................. 177 Appendix 7. The prime limit theorem ........................................ 181 Appendix 8. Primes between squares ........................................ 189 Appendix 9. A proof of Riemann's hypothesis via Dertjoy's equivalent theorem ...... 203 Closing remarks ..........................................................