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Mathematical logic --- Constructive mathematics --- Recursive functions --- Unsolvability (Mathematical logic) --- Degrees of unsolvability --- Turing degrees of unsolvability --- Functions, Recursive --- Algorithms --- Arithmetic --- Logic, Symbolic and mathematical --- Number theory --- Recursion theory --- Decidability (Mathematical logic) --- Mathematics, Constructive --- Foundations --- Recursive functions. --- Constructive mathematics. --- Mathématiques constructives. --- Fonctions récursives. --- Non-résolubilité (logique mathématique)

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Recursion theory --- Logic, Symbolic and mathematical --- Mathematical logic

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The forms and scope of logic rest on assumptions of how language and reasoning connect to experience. In this volume an analysis of meaning and truth provides a foundation for studying modern propositional and predicate logics. Chapters on propositional logic, parsing propositions, and meaning, truth and reference give a basis for criteria that can be used to judge formalizations of ordinary language arguments. Over 120 worked examples of formalizations of propositions and arguments illustrate the scope and limitations of modern logic, as analyzed in chapters on identity, quantifiers, descriptive names, functions, and second-order logic. The chapter on second-order logic illustrates how different conceptions of predicates and propositions do not lead to a common basis for quantification over predicates, as they do for quantification over things. Notable for its clarity of presentation, and supplemented by many exercises, this volume is suitable for philosophers, linguists, mathematicians, and computer scientists who wish to better understand the tools they use in formalizing reasoning.

Logic --- Predicate (Logic) --- Logic, symbolic and mathematical --- Semantics

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Science

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Logic --- Logic, Symbolic and mathematical --- Semantics --- Formal semantics --- Semasiology --- Semiology (Semantics) --- Comparative linguistics --- Information theory --- Language and languages --- Lexicology --- Meaning (Psychology) --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Psychology --- Science --- Reasoning --- Thought and thinking --- Methodology --- Logic, Symbolic and mathematical. --- Logic. --- Semantics.