Logic, Meaning and Computation

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 .

Includes supplementary material: sn.pub/extras

Klappentext
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 .

Zusammenfassung
Contains papers by well-known scholars, most of whom have been directly influenced by Alonzo Church's own work. This work emphasises on foundational issues in logic, mathematics, computation, and philosophy. It is of interest to logicians, computer scientists, philosophers, and linguists.

Inhalt
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.

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