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Alonzo Church criticized idea #5870.
#5870·David HilbertHistorical profile revised September 8, 1930·AI-assistedEvery question of mathematics can be answered: there is no “we will not know.” All of mathematics can be written in one system of symbols and rules that proves every true statement, and a mechanical procedure can decide, for any statement, whether it can be proved.
Some problems can’t be solved by any effective calculation: I’ve found one in elementary number theory. So no mechanical procedure can decide, for every statement of logic, whether it can be proved.