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Logic, Meaning and Computation

C. Anthony Anderson

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ISBN 10: 140200141X / ISBN 13: 9781402001413
Editore: Springer-Verlag Gmbh Jan 2002, 2002
Nuovi Condizione: Neu
Da Rhein-Team Lörrach Ivano Narducci e.K. (Lörrach, Germania)

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Neuware - Alonzo Church was undeniably one ofthe intellectual giants of theTwenti eth Century . These articles are dedicated to his memory and illustrate the tremendous importance his ideas have had in logic , mathematics, comput er science and philosophy . Discussions of some of thesevarious contributions have appeared in The Bulletin of Symbolic Logic, and th e interested reader is invited to seek details there . Here we justtry to give somegener al sense of the scope, depth,and value of his work. Church is perhaps best known for the theorem , appropriately called ' C h u r c h ' s Theorem ', that there is no decision procedure forthelogical valid ity of formulas first-order of logic . A d ecision proce dure forthat part of logic would have come near to fulfilling Leibniz's dream of a calculus that could be mechanically used tosettle logical disputes . It was not to . be It could not be . What Church proved precisely is that there is no lambda-definable function that can i n every case providethe right answer , ' y e s ' or ' n o', tothe question of whether or not any arbitrarily given formula is valid . 627 pp. Englisch. Codice inventario libreria 9781402001413

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Titolo: Logic, Meaning and Computation

Casa editrice: Springer-Verlag Gmbh Jan 2002

Data di pubblicazione: 2002

Legatura: Buch

Condizione libro:Neu

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This volume began as a remembrance of Alonzo Church while he was still with us and is now finally complete. It contains papers by many well-known scholars, most of whom have been directly influenced by Church's own work. Often the emphasis is on foundational issues in logic, mathematics, computation, and philosophy - as was the case with Church's contributions, now universally recognized as having been of profound fundamental significance in those areas. The volume will be of interest to logicians, computer scientists, philosophers, and linguists. The contributions concern classical first-order logic, higher-order logic, non-classical theories of implication, set theories with universal sets, the logical and semantical paradoxes, the lambda-calculus, especially as it is used in computation, philosophical issues about meaning and ontology in the abstract sciences and in natural language, and much else. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields.


Preface; C.A. Anderson, M. Zelëny. Remembering Alonzo Church; D. Kaplan, T. Burge. Part I: Logic. Logic, truth and number: The elementary genesis of arithmetic; P. Apostoli. Second-order logic; J. Corcoran. A representation of relation algebras using Routley-Meyer frames; J.M. Dunn. Church's set theory with a universal set; Th. Forster. Axioms of infinity in Church's type theory; R.O. Gandy. Logical objects; E.L. Keenan. The lambda calculus and adjoint functors; S.M. Lane. Atomic Boolean algebras and classical propositional logic; G.J. Massey. Improved decision procedures for pure relevant logic; R.K. Meyer. The `triumph' of first-order languages; S. Shapiro. Equivalence relations and groups; R. Smullyan. Part II: Computation. Discriminating coded lambda terms; H. Barendregt. lambda-calculus as a foundation for mathematics; K. Grue. Peano's lambda calculus: The functional abstraction implicit in arithmetic; D. Leivant. The undecidability of lambda-definability; R. Loader. A construction of the provable wellorderings of the theory of species; P. Martin-Löf. Semantics for first and higher order realizability; C. Mclarty. Language and equality theory in logic programming; J.C. Shepherdson. Part III: Philosophy, Meaning, and Intensional Logic. Alternative (1*): A criterion of identity for intensional entities; C.A. Anderson. Nominalist paraphrase and ontological commitment; J.P. Burgess. Peace, justice and computation: Leibniz' program and the moral and political significance of Church's theorem; M. Detlefsen. Tarski's theorem and NFU; M.R. Holmes. Church's theorem and randomness; G. Mar. Russellian type theory andsemantical paradoxes; E. Martino. The logic of sense and denotation: Extensions and applications; T. Parsons. Analysis, synonymy and sense; M. Richard. The very possibility of language; N. Salmon. Index.

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