|
|
|
Series on Knots and Everything - Vol. 14
DIAMOND
A Paradox Logic
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.
Contents:
- 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
Readership: Mathematicians and computer scientists.
"This book should be interesting for everyone, and especially for logicians."
| Mathematical Reviews, 1999 |
| 272pp |
Pub. date: Jan 1997 |
|
|
