Logic, Meaning and Computation.pdf

Logic, Meaning and Computation PDF

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 Leibnizs 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 .

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

7.23 MB DATEIGRÖSSE
9401038910 ISBN
Englisch SPRACHE
Logic, Meaning and Computation.pdf

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