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Diamond : a paradox logic /
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, paradoxe...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New Jersey :
World Scientific,
©2010.
|
| Edición: | 2nd ed. |
| Colección: | K & E series on knots and everything ;
v. 23. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Hellerstein, N. S. |q (Nathaniel S.) |1 https://id.oclc.org/worldcat/entity/E39PCjyfYtDDhVhdk66WPWkwbq | |
| 245 | 1 | 0 | |a Diamond : |b a paradox logic / |c N.S. Hellerstein. |
| 250 | |a 2nd ed. | ||
| 260 | |a New Jersey : |b World Scientific, |c ©2010. | ||
| 300 | |a 1 online resource (xiv, 294 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a K & E series on knots and everything ; |v v. 23 | |
| 504 | |a Includes bibliographical references (pages 287-289) and index. | ||
| 505 | 0 | |a 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. | |
| 520 | |a 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. | ||
| 588 | 0 | |a Print version record. | |
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| 650 | 0 | |a Logic, Symbolic and mathematical. | |
| 650 | 0 | |a Paradox. | |
| 650 | 6 | |a Logique symbolique et mathématique. | |
| 650 | 6 | |a Paradoxe. | |
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| 776 | 0 | 8 | |i Print version: |a Hellerstein, N.S. (Nathaniel S.). |t Diamond. |b 2nd ed. |d Singapore ; Hackensack, NJ : World Scientific, ©2010 |z 9789814287135 |w (DLC) 2009023583 |w (OCoLC)396197045 |
| 830 | 0 | |a K & E series on knots and everything ; |v v. 23. | |
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