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Books > Science & Mathematics > Mathematics > Mathematical foundations
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Logic, Meaning and Computation - Essays in Memory of Alonzo Church (Paperback, Softcover reprint of the original 1st ed. 2001)
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Logic, Meaning and Computation - Essays in Memory of Alonzo Church (Paperback, Softcover reprint of the original 1st ed. 2001)
Series: Synthese Library, 305
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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 .
General
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