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Church's fundamental paradox: "Is there such a thing as logic?"[Church 1934] stated the fundamental paradox as follows: "in the case of any system of symbolic logic, the set of all provable theorems is [computationally] enumerable... any system of symbolic logic not hopelessly inadequate ... would contain the formal theorem that this same system ... was either insufficient [theorems are not computationally enumerable] or oversufficient [that theorems are computationally enumerable means that the system is inconsistent]... By Hewitt at 20150428 16:44  LtU Forum  previous forum topic  next forum topic  other blogs  2637 reads

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