Does Gödel's incompleteness theorem refute Leibniz's dream about the machine that solves all mathematical problems, as Smullyan suggests?
The argument is that the machine couldn't correctly answer the question "will you answer false to this question"?
Yes, supposing the Church-Turing thesis
No, the Church-Turing thesis does not apply to this machine
No, Leibniz dreamed of something different
No, Leibniz didn't know what he actually wanted
No, you won't actually ask such a question from it
No, for some other reason
Update: changed "Do you suppose " to "Does " in the question.
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