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