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.
Reihe
Auflage
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Mathematicians and computer scientists
Editions-Typ
Produkt-Hinweis
Maße
Höhe: 235 mm
Breite: 157 mm
Dicke: 21 mm
Gewicht
ISBN-13
978-981-4287-13-5 (9789814287135)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
City College Of San Francisco, Usa
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.
