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" Diamond : "
N.S. Hellerstein.
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BL
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| Record Number
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890676
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| Main Entry
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Hellerstein, N. S., (Nathaniel S.)
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| Title & Author
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Diamond : : a paradox logic /\ N.S. Hellerstein.
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| Edition Statement
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2nd ed.
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| Publication Statement
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New Jersey :: World Scientific,, ©2010.
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| Series Statement
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K & E series on knots and everything ;; v. 23
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| Page. NO
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1 online resource (xiv, 294 pages) :: illustrations
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| ISBN
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9789814287142
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: 9814287148
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9789814287135
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981428713X
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| Bibliographies/Indexes
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Includes bibliographical references (pages 287-289) and index.
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| Contents
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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.
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| Abstract
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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.
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| Subject
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Logic, Symbolic and mathematical.
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Paradox.
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Logic, Symbolic and mathematical.
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MATHEMATICS-- Infinity.
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| Subject
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MATHEMATICS-- Logic.
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| Subject
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Paradox.
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| Dewey Classification
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511.3
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| LC Classification
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QA9.H396 2010eb
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