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Explores the nature of infinity with a view toward classifying and explaining its mathematical applications. It presents not only the basics of the classical theory, but also an introduction to the many important recent results and methods. ... Read more

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The Assimilation of Biology, Logic and Set Theory presents four principles of adaptation wherein two entities occur under the same condition, or one entity occurs under two conditions, or one entity is adapted to a second, or two or more entities are adapted to two or more conditions.

These principles emerge from a wealth of empirical data, which are summarized by logically valid formulas. This account continues and presents the elements of set theory and how biological data, ensconced in logical formulas, can be integrated in sets.

This is a book of the 21st century, showing how biological data can be brought together and enhanced by logical and set theory formulation of the data. It is a primer on how to apply logic and set theory. At the same time it is interdisciplinary and so it is transformative. The Assimilation of Biology, Logic and Set Theory is a milestone to the future. ... Read more

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Willard Van Orman Quine (1908-2000) was probably the most influential American philosopher of the twentieth century. In Trading Ontology for Ideology Lieven Decock offers an insightful analysis of the development of Quine's ontological views from his first texts in the early thirties onwards. The importance of Quine's work in logic and set theory for his ontology is highlighted. Decock argues that the tenet of extensionalism is at least as important as naturalism, and assesses the relation between the two. The other focus of the work is the relation between ontology, i.e. what there is, and ideology, i.e. what can be expressed by means of words. Decock shows that the interplay between ontology and ideology is far more complicated and interesting than has generally been assumed. ... Read more

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High Quality Content by WIKIPEDIA articles! In mathematics, the symmetric difference of two sets is the set of elements which are in one of the sets, but not in both. This operation is the set-theoretic kin of the exclusive disjunction (XOR operation) in Boolean logic. The logical operation exclusive disjunction, also called exclusive or (symbolized XOR or EOR), is a type of logical disjunction on two operands that results in a value of true if exactly one of the operands has a value of true. A simple way to state this is "one or the other but not both."Put differently, exclusive disjunction is a logical operation on two logical values, typically the values of two propositions, that produces a value of true only in cases where the truth value of the operands differ. ... Read more

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This book presents the advancements and applications of neutrosophics, which are generalizations of fuzzy logic, fuzzy set, and imprecise probability. The neutrosophic logic, neutrosophic set, neutrosophic probability, and neutrosophic statistics are increasingly used in engineering applications (especially for software and information fusion), medicine, military, cybernetics, physics.In the last chapter a soft semantic Web Services agent framework is proposed to facilitate the registration and discovery of high quality semantic Web Services agent.The intelligent inference engine module of soft semantic Web Services agent is implemented using interval neutrosophic logic. ... Read more

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Chapters: Algorithm, Set Theory, Table of Mathematical Symbols, Surreal Number, Entscheidungsproblem, Recursion, Mathematical Induction, Principia Mathematica, Model Theory, Gödel's Completeness Theorem, Mathematical Proof, Vacuous Truth, Finitary Relation, Original Proof of Gödel's Completeness Theorem, Combinational Logic, Contradiction, Primitive Notion, Foundations of Mathematics, Curry's Paradox, Computability Theory, Charles Sanders Peirce Bibliography, Gödel's Incompleteness Theorems, Laws of Form, Turing's Proof, List of First-Order Theories, Kripke Semantics, Proof of Impossibility, Quantum Logic, Reverse Mathematics, Metamath, Outline of Logic, Interior Algebra, Proof Sketch for Gödel's First Incompleteness Theorem, Rewriting, Relation Algebra, Tautology, Universe, List of Mathematical Logic Topics, Residuated Lattice, Enumeration, Proof Theory, Indicator Function, on Formally Undecidable Propositions of Principia Mathematica and Related Systems, Impredicativity, Metalogic, Game Semantics, Tarski's Undefinability Theorem, Hilbert's Program, Residuated Boolean Algebra, Contraposition, Formal System, Extension by Definitions, Rational Consequence Relation, Absoluteness, Gödel Numbering, Asynchronous Logic, Leibniz Operator, Peirce's Law, Kruskal's Tree Theorem, Diagonal Lemma, Rosser's Trick, Recursive Definition, Object Language, Łukasiewicz Logic, Institution, Lf, Ground Expression, Stratification, Craig Interpolation, Laver Table, Equiconsistency, Metamathematics, Inverse Relation, And-or Tree, Bunched Logic, Epsilon Calculus, Entitative Graph, Institutional Model Theory, Double Negation, Turnstile, Continuous Predicate, Formal Calculation, Hypostatic Abstraction, Coherent Space, Complete Theory, Glivenko's Theorem, Rules of Passage, Logical Graph, Witness, Term Algebra, Substitution Instance, T-Schema, Classical Mathematics, Löb's Theorem, Gödel's Β Function, Conservativity Theorem, Ludics, Timeline of Mathemati...More: http://booksllc.net/?id=3967710 ... Read more

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Squarish 8vo. 574pp. Hardback: Laminate Boards. ... Read more