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