عنوان

Diamond :

(Number (ISBN

9789814287142

(Number (ISBN

9814287148

Erroneous ISBN

9789814287135

Erroneous ISBN

981428713X

Title Proper

Diamond :

General Material Designation

[Book]

Other Title Information

a paradox logic /

First Statement of Responsibility

N.S. Hellerstein.

Edition Statement

2nd ed.

Place of Publication, Distribution, etc.

New Jersey :

Name of Publisher, Distributor, etc.

World Scientific,

Date of Publication, Distribution, etc.

©2010.

Specific Material Designation and Extent of Item

1 online resource (xiv, 294 pages) :

Other Physical Details

illustrations

Series Title

K & E series on knots and everything ;

Volume Designation

v. 23

Text of Note

Includes bibliographical references (pages 287-289) and index.

Text of Note

1. Paradox. A. The liar. B. The anti-diagonal. C. Russell's paradox. D. Santa and the grinch. E. Antistrephon. F. Parity of infinity. G. The heap. H. Finitude. I. Game paradoxes. J. Cantor's paradox. K. Paradox of the boundary -- 2. Diamond. A. The buzzer. B. Diamond values. C. Harmonic functions. D. Gluts and gaps. E. Diamond circuits. F. Brownian forms. G. Boundary logic -- 3. Diamond algebra. A. Bracket algebra. B. Laws. C. Normal forms. D. Completeness -- 4. Self-reference. A. Re-entrance and fixedpoints. B. Phase order. C. The outer fixedpoints -- 5. Fixedpoint lattices. A. Relative lattices. B. Seeds and spirals. C. Shared fixedpoints. D. Examples -- 6. Limit logic. A. Limits. B. Limit fixedpoints. C. The halting theorem -- 7. Paradox resolved. A. The liar and the anti-diagonal. B. Russell's paradox. C. Santa and the grinch. D. Antistrephon. E. Infinity, finitude and the heap. F. Game paradoxes -- 8. The continuum. A. Cantor's paradox. B. Dedekind splices. C. Null quotients. D. Cantor's number. E. The line within the diamond. F. Zeno's theorem. G. Fuzzy chaos -- 9. Clique theory. A. Cliques. B. Clique equality. C. Clique axioms. D. Graph cliques. E. Clique circuits -- 10. Orthogonal logics. A. Analytic functions. B. Function types. C. Dihedral conjugation. D. Star logic. E. Harmonic projection. F. Diamond types? -- 11. Interferometry. A. Quadrature. B. Diffraction. C. Buzzers and toggles. D. Analytic diffraction. E. Diffracting "two ducks in a box" -- 12. How to count to two. A. Brownian and Kauffman modulators. B. Diffracting the modulators. C. Rotors, pumps and tapes. D. The ganglion -- 13. Metamathematics. A. Gödelian quanta. B. Meta-logic. C. Dialectic. D. Dialectical dilemma -- 14. Dilemma. A. Milo's trick. B. Prisoner's dilemma. C. Dialemma games. D. Dilemma diamond. E. Banker's dilemma. F. The unexpected departure.

0

Text of Note

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 metamathematics and dilemma games.

Title

Diamond.

International Standard Book Number

9789814287135

Logic, Symbolic and mathematical.

Paradox.

Logic, Symbolic and mathematical.

MATHEMATICS-- Infinity.

MATHEMATICS-- Logic.

Paradox.

MAT-- 016000

MAT-- 018000

Number

Edition

Class number

Book number

Hellerstein, N. S., (Nathaniel S.)

Date of Transaction

20200823232113.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y