Description
Book SynopsisThis 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 Gödelian metamathematics and dilemma games.
Table of ContentsParadox: 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.
