Diamond: A Paradox Logic
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-02-2850-7 (ISBN)
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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. Diamond is a new way to solve the dilemmas of higher mathematics. In this volume, paradoxes by Russell, Cantor, Berry and Zeno are all resolved. This book consists of two sections: Elementary; which covers the classic paradoxes of mathematical logic and shows how they can be resolved in this new system; and Advanced, which relates diamond to Boolean logic, three-valued logic, Gödelian meta-mathematics and dilemma games.
Part 1 Paradoxes: Russell's paradox; Heap paradoxes; game paradoxes. Part 2 Diamond: diamond values; harmonic functions; diamond circuits; Brownian forms. Part 3 Diamond laws. Part 4 Self-reference: re-entrance and fixed points; phase order; the outer fixed points. Part 5 Fixed point lattices: relative lattices; shared fixed points. Part 6 Limit logic: limit fixed points; diamond computation. Part 7 Paradox resolved: Russell's paradox; Santa sentences; antistrephon; Heap paradoxes; game paradoxes. Part 8 The continuum: Cantor's paradox; Dedekind splices; Zeno's theorem. Part 9 Analytic functions - harmonic analysis - 3-logic metamathematics - dilemma: prisoner's dilemma; dilemma as diamond metric; banker's dilemma. Part 10 Speculations: diamond types?; null quotients?; general lattices?; general waves?.
| Reihe/Serie | Series on Knots & Everything ; 14 |
|---|---|
| Verlagsort | Singapore |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 981-02-2850-3 / 9810228503 |
| ISBN-13 | 978-981-02-2850-7 / 9789810228507 |
| Zustand | Neuware |
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