Diamond : a paradox logic
著者
書誌事項
Diamond : a paradox logic
（Series on knots and everything, v. 23）
World Scientific, c2010
2nd ed
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注記
Includes bibliographical references (p. 287-289) and index
内容説明・目次
内容説明
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.
目次
- Paradox: Russell's Paradox
- Santa Sentences
- Antistrephon
- Game Paradoxes
- Paradox of the Boundary
- Diamond: Diamond Values
- Harmonic Functions
- Diamond Circuits
- Brownian Forms
- Diamond Algebra: Bracket Algebra
- Laws
- Normal Forms
- Completeness
- Self-Reference: Re-entrance and Fixedpoints
- Phase Order
- The Outer Fixedpoints
- Fixedpoint Lattices: Relative Lattices
- Seeds and Spirals
- Shared Fixed-Points
- Limit Logic: Limit Fixedpoints
- the Halting Theorem
- Paradox Resolved: Russell's Paradox
- Santa Sentences
- Antistrephon
- Game Paradoxes
- The Continuum: Cantor's Paradox
- Dedekind Splices
- Zeno's Theorem
- Fuzzy Chaos
- Clique Theory: Cliques Defined
- Clique Axioms
- Graph Cliques
- Clique Circuits
- Orthogonal Logics: Analytic Functions
- Star Logic
- Harmonic Projection
- Interferometry: Quadrature
- Diffraction
- Buzzers and Toggles
- How to Count to Two: Brownian and Kauffman Modulators
- Diffracting the Modulators
- Rotors, Pumps and Tapes
- the Ganglion
- Metamathematics: Godelian Quanta
- Meta-Logic
- Dialectical Dilemma
- Dilemma: Milo's Trick
- Prisoner's Dilemma
- Dilemma Diamond
- Banker's Dilemma
- The Unexpected Departure.
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