by N S Hellerstein (Lincoln University)

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.

• Paradox:
  • Russell's Paradox
  • Santa Paradoxes
  • Game Paradoxes
• Diamond:
  • Diamond Values
  • Harmonic Functions
  • Diamond Circuits
  • Brownian Forms
• Diamond Algebra
  • Laws
  • Normal Forms Completeness and Categoricity
• Self-Reference:
  • Re-entrance and Fixedpoints
  • Phase Order
  • The Outer Fixedpoints
• Fixedpoint Lattices:
  • Relative Lattices
  • Shared Fixedpoints
• Limit Logic:
  • Limit Fixedpoints
  • Diamond Computation
• Paradox Resolved:
  • Russell's Paradox
  • Santa Sentences
  • Antistrephon
  • Game Paradoxes
• The Continuum:
  • Cantor's Paradox
  • Dedekind Splices
  • Zeno's Theorem
• Analytic Functions:
  • Analytic Functions
  • Dihedral Conjugation
• Harmonic Analysis:
  • Harmonic Projection
  • Differentials
  • Quadrature
  • Diffraction
• Three-logic:
  • Ternary Logic Embeds; Voter's Paradox
• Metamathematics:
  • Gödelian Quanta
  • Meta-Logic
• Dilemma:
  • Prisoner's Dilemma
  • Dilemma As Diamond Metric
  • Banker's Dilemma
• Speculations:
  • Diamond Types?
  • Null Quotients?
  • General Lattices?
  • General Waves?
  • and other papers