in reply to poll ideas quest 2009
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.