by N S Hellerstein (City College of San Francisco, USA)

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 Gödelian meta-mathematics and dilemma games.

• 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:
  • Gödelian Quanta
  • Meta-Logic
  • Dialectical Dilemma
• Dilemma:
  • Milo's Trick
  • Prisoner's Dilemma
  • Dilemma Diamond
  • Banker's Dilemma
  • The Unexpected Departure