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The argument from Church's theorem

According to Church's theorem there's no decision procedure for predicate calculus. This means that there is no computable procedure by which a machine can decide whether a given sentence in predicate calculus is true or false.

Human mathematicians, on the other hand, often decide the truth or falsity of sentences of predicate calculus.

Moreover, human mathematicians decide such questions by constructing proofs in a reasonable amount of time and not just a random.

Argument anticipated by J. J. C. Smart (1961).
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