Screen LibraryThe diagonal infinity : problems of multiple scales /
Contains information on topics such as: Cantor Theorem/Paradox, Diagonal of Diagonalization, Hilbert's First Problem, Algebra of Scaling, Multivalued Logics, Chaos in Logic, Knife-edge and Bang-Bang Logics, Liar Paradox and many more.
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| Main Authors: | |
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| Corporate Authors: | |
| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore : |
| Publication Dates: | 1998. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/3424#t=toc |
| Summary: |
Contains information on topics such as: Cantor Theorem/Paradox, Diagonal of Diagonalization, Hilbert's First Problem, Algebra of Scaling, Multivalued Logics, Chaos in Logic, Knife-edge and Bang-Bang Logics, Liar Paradox and many more. |
| Carrier Form: | 1 online resource (xxii,522pages) : illustrations |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9789812817082 |
| Index Number: | QA9 |
| CLC: | O1 |
| Contents: |
ch. 1. Counting the integers: the very idea! 0. One, two, three, and the three-dots! 1. The original sin: ensemblum elemento a omisso. 2. Forever finite! 3. Diagonal of fiagonalization. 4. Is the set infinite and every member finite? 5. Diagonal of a single dimension: redefinition limit ordinal. 6. Axiomatic/formal systems. 7. The empty set: bug or feature? 8. Infinite numbers. 9. Enumeration and reflected spaces. 10. Another representation of the power set of the integers. 11. Fractional bases, sums of series and integers. 12. Enumeration of the continuum. 13. What is a function? 14. Infinity and sorites paradoxes -- ch. II. Mod, div, and all that. 0. Introduction. 1. Mod, div, and all that. 2. Other useful functions. 3. Simple orthogonal functions and other periodic functions. 4. Parametric equation curves and transfinites. 5. More parametric fractals and transfinites again. 6. Tag systems, integer chaos, hailstones, and primes. 7. Discrete/iterative period doubling. 8. The iteration machine -- ch. III. Chaos and scales. 0. Introduction. 1. Linear equations and periodicity. 2. Space scaling and nonlinear equations. 3. Simple strangeness. 4. Up the hierarchy of complexity. 5. Intermittency and fluctuating frequency. 6. Another limit attractor. 7. More limit attractors. 8. More on large periods and intermittency. 9. Uniqueness and completeness: partial solutions. 10. Different kind of intermittency. 11. Spatial and temporal multiple scaling. 12. More multiple scaling: space to time conversion. 13. Complexification of simple strangeness. 14. Superchaotic Functions and periodic points. 15. A versatile set of equations. 16. Some general results on the "versatile set". 17. The non-periodic tangle. 18. Products and iterates of trigonometric functions and periodicity. 19. Simple non-Lipschitzian nonlinear differential equations. 20. Chaos: discussion and questions. ch. IV. Logic, reasoning, and computation. 0. Boolean algebra: a monochromatic world. 1. Serial or parallel picture. 2. The implication: propositional logic. 3. Semantic vs. syntactic distinction. 4. An interpretation of implication, truth and falsity the diagonal infinity. 5. Syllogisms, Quantification, and Classical Mathematical Machinery. 6. Deep truth or empty statement. 7. The land of defaults: what is computation. 8. Semantics of connectives. 9. No more defaults. 10. The liar paradox. 11. Other uses of the system. 12. Time-space super liar paradox. 13. Crocodile paradox: relative truths or contradiction. 14. When can truth be told: a Godelian warm-up exercise. 15. Godel incompleteness theorems: exploration of solution space. 16. Simple ways of doing it: is provability truth? 17. A deeper look: against intuition. 18. Consistency vs. completeness. 19. Arithmetization of logic via Godel coding. 20. The Godel theorem. 21. Properties of the provability property? 22. A multivalued logic: logic of contradiction. 23. Bang-bang infinite valued logic. 24. Invariants of logic. 25. Continuous infinite valued logics. 26. Generalized idempotent and continuous max-min operators. 27. Truth valuation generator functions. 28. Oscillation, revision theory of truth, chaos, and paradox -- ch. V. Mathematics, logic and infinity. 0. What is mathematics? 1. Special role of mathematics in isms. 2. Which ism is the one? 3. Levels of indirection or veils of perception. 4. Knowledge and provability. 5. The Turing test and intelligence. 6. Attractive semigroups and semirings: is infinity a number? 7. Boolean algebra and logic again. 8. Workability/consistency and single-valuedness. 9. Life's metalogical koans. |