Logic, Meaning and Computation
Essays in Memory of Alonzo Church
Published on 31. January 2002
Book
Hardback
XIII, 627 pages
978-1-4020-0141-3 (ISBN)
Description
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 .
More details
Series
Edition
2001 ed.
Language
English
Place of publication
Dordrecht
Netherlands
Target group
Professional and scholarly
Research
Product notice
sewn/stitched
Cloth over boards
Illustrations
XIII, 627 p.
Dimensions
Height: 241 mm
Width: 162 mm
Thickness: 43 mm
Weight
1136 gr
ISBN-13
978-1-4020-0141-3 (9781402001413)
DOI
10.1007/978-94-010-0526-5
Schweitzer Classification
Other editions
Additional editions
C. Anthony Anderson | Michael Zelëny
Logic, Meaning and Computation
Essays in Memory of Alonzo Church
Book
10/2012
Springer
€160.49
Shipment within 15-20 days
Content
Logic, truth and number: The elementary genesis of arithmetic.- Second-order logic.- A representation of relation algebras using Routley-Meyer frames.- Church's set theory with a universal set.- Axioms of infinity in Church's type theory.- Logical objects.- The lambda calculus and adjoint functors.- Atomic Boolean algebras and classical propositional logic.- Improved decision procedures for pure relevant logic.- The "triumph" of first-order languages.- Equivalence relations and groups.- Discriminating coded lambda terms.- ?-calculus as a foundation for mathematics.- Peano's lambda calculus: The functional abstraction implicit in arithmetic.- The undecidability of ?-definability.- A construction of the provable wellorderings of the theory of species.- Semantics for first and higher order realizability.- Language and equality theory in logic programming.- Alternative (1*): A criterion of identity for intensional entities.- Nominalist paraphrase and ontological commitment.- Peace, justice and computation: Leibniz' program and the moral and political significance of Church's theorem.- Tarski's theorem and NFU.- Church's theorem and randomness.- Russellian type theory and semantical paradoxes.- The logic of sense and denotation: Extensions and applications.- Analysis, synonymy and sense.- The very possibility of language.