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...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New Jersey :
World Scientific,
©2010.
|
| Ausgabe: | 2nd ed. |
| Schriftenreihe: | K & E series on knots and everything ;
v. 23. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xiv, 294 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 287-289) and index. |
| ISBN: | 9789814287142 9814287148 |
Internformat
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| 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 | ||
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| 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. | ||
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| author | Hellerstein, N. S. (Nathaniel S.) |
| author_GND | http://id.loc.gov/authorities/names/n96065762 |
| author_facet | Hellerstein, N. S. (Nathaniel S.) |
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| contents | 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. |
| ctrlnum | (OCoLC)671654853 |
| dewey-full | 511.3 |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2nd ed. |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn671654853 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:17:34Z |
| institution | BVB |
| isbn | 9789814287142 9814287148 |
| language | English |
| oclc_num | 671654853 |
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| publisher | World Scientific, |
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| series | K & E series on knots and everything ; |
| series2 | K & E series on knots and everything ; |
| spelling | Hellerstein, N. S. (Nathaniel S.) https://id.oclc.org/worldcat/entity/E39PCjyfYtDDhVhdk66WPWkwbq http://id.loc.gov/authorities/names/n96065762 Diamond : a paradox logic / N.S. Hellerstein. 2nd ed. New Jersey : World Scientific, ©2010. 1 online resource (xiv, 294 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier K & E series on knots and everything ; v. 23 Includes bibliographical references (pages 287-289) and index. 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. 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. Print version record. Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Paradox. http://id.loc.gov/authorities/subjects/sh85097756 Logique symbolique et mathématique. Paradoxe. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Logic, Symbolic and mathematical fast Paradox fast Print version: Hellerstein, N.S. (Nathaniel S.). Diamond. 2nd ed. Singapore ; Hackensack, NJ : World Scientific, ©2010 9789814287135 (DLC) 2009023583 (OCoLC)396197045 K & E series on knots and everything ; v. 23. http://id.loc.gov/authorities/names/n91052105 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=340711 Volltext |
| spellingShingle | Hellerstein, N. S. (Nathaniel S.) Diamond : a paradox logic / K & E series on knots and everything ; 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. Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Paradox. http://id.loc.gov/authorities/subjects/sh85097756 Logique symbolique et mathématique. Paradoxe. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Logic, Symbolic and mathematical fast Paradox fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85078115 http://id.loc.gov/authorities/subjects/sh85097756 |
| title | Diamond : a paradox logic / |
| title_auth | Diamond : a paradox logic / |
| title_exact_search | Diamond : a paradox logic / |
| title_full | Diamond : a paradox logic / N.S. Hellerstein. |
| title_fullStr | Diamond : a paradox logic / N.S. Hellerstein. |
| title_full_unstemmed | Diamond : a paradox logic / N.S. Hellerstein. |
| title_short | Diamond : |
| title_sort | diamond a paradox logic |
| title_sub | a paradox logic / |
| topic | Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Paradox. http://id.loc.gov/authorities/subjects/sh85097756 Logique symbolique et mathématique. Paradoxe. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Logic, Symbolic and mathematical fast Paradox fast |
| topic_facet | Logic, Symbolic and mathematical. Paradox. Logique symbolique et mathématique. Paradoxe. MATHEMATICS Infinity. MATHEMATICS Logic. Logic, Symbolic and mathematical Paradox |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=340711 |
| work_keys_str_mv | AT hellersteinns diamondaparadoxlogic |