DIAMOND

A PARADOX LOGIC, 2ND ED (V23)

By: HELLERSTEIN N S

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Hardcover | 27 January 2010 | Edition Number 2

At a Glance

Hardcover
314 Pages

Edition Type
Revised

Dimensions(cm)
22.86 x 15.24 x 1.91

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This book is about "diamond", a logic of paradox. In diamond, a statement can be true yet false; an "imaginary" state, midway between being and non-being. Diamond's imaginary values solve many logical paradoxes unsolvable in two-valued Boolean logic. In this volume, paradoxes by Russell, Cantor, Berry and Zeno are all resolved. This book has three sections: Paradox Logic, which covers the classic paradoxes of mathematical logic, shows how they can be resolved in this new system; The Second Paradox, which relates diamond to Boolean logic and the Spencer-Brown "modulator"; and Metamathematical Dilemma, which relates diamond to Goedelian metamathematics and dilemma games.

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Introduction	p. xi
Paradox Logic	p. 1
Paradox	p. 3
The Liar	p. 3
The Anti-Diagonal	p. 7
Russell's Paradox	p. 8
Santa and the Grinch	p. 10
Antistrephon	p. 17
Parity of Infinity	p. 18
The Heap	p. 19
Finitude	p. 21
Game Paradoxes	p. 24
Cantor's Paradox	p. 26
Paradox of the Boundary	p. 27
Diamond	p. 29
The Buzzer	p. 29
Diamond Values	p. 31
Harmonic Functions	p. 32
Gluts and Gaps	p. 35
Diamond Circuits	p. 38
Brownian Forms	p. 40
Boundary Logic	p. 46
Diamond Algebra	p. 49
Bracket Algebra	p. 49
Laws	p. 58
Normal Forms	p. 64
Completeness	p. 69
Self-Reference	p. 71
Re-Entrance and Fixedpoints	p. 71
Phase Order	p. 79
The Outer Fixedpoints	p. 79
Fixedpoint Lattices	p. 85
Relative Lattices	p. 85
Seeds and Spirals	p. 88
Shared Fixedpoints	p. 91
Examples	p. 93
Limit Logic	p. 109
Limits	p. 109
Limit Fixedpoints	p. 114
The Halting Theorem	p. 116
Paradox Resolved	p. 119
The Liar and the Anti-Diagonal	p. 119
Russell's Paradox	p. 120
Santa and the Grinch	p. 122
Antistrephon	p. 126
Infinity, Finitude and the Heap	p. 128
Game Paradoxes	p. 130
The Continuum	p. 131
Cantor's Paradox	p. 131
Dedekind Splices	p. 132
Null Quotients	p. 134
Cantor's Number	p. 136
The Line within the Diamond	p. 139
Zeno's Theorem	p. 144
Fuzzy Chaos	p. 145
Clique Theory	p. 151
Cliques	p. 151
Clique Equality	p. 156
Clique Axioms	p. 160
Graph Cliques	p. 164
Clique Circuits	p. 166
The Second Paradox	p. 169
Orthogonal Logics	p. 171
Analytic Functions	p. 171
Function Types	p. 173
Dihedral Conjugation	p. 177
Star Logic	p. 180
Harmonic Projection	p. 182
Diamond Types?	p. 183
Interferometry	p. 185
Quadrature	p. 185
Diffraction	p. 193
Buzzers and Toggles	p. 200
Analytic Diffraction	p. 204
Diffracting "Two Ducks in a Box"	p. 206
How to Count to Two	p. 209
Brownian and Kauffman Modulators	p. 209
Diffracting the Modulators	p. 212
Rotors, Pumps and Tapes	p. 218
The Ganglion	p. 222
Metamathematical Dilemma	p. 225
Metamathematics	p. 227
Gödelian Quanta	p. 227
Meta-Logic	p. 231
Dialectic	p. 236
Dialectical Dilemma	p. 238
Dilemma	p. 241
Milo's Trick	p. 241
Prisoner's Dilemma	p. 245
Dilemma Games	p. 249
Dilemma Diamond	p. 253
Banker's Dilemma	p. 257
The Unexpected Departure	p. 260
Notes	p. 265
Bibliography	p. 287
Index	p. 291
Table of Contents provided by Ingram. All Rights Reserved.

DIAMOND

A PARADOX LOGIC, 2ND ED (V23)

At a Glance

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