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Nisan comments on Robust Cooperation in the Prisoner's Dilemma - Less Wrong
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On quining in arithmetic, see any exposition on Gödel's First Incompleteness Theorem and the Wikipedia article on the diagonal lemma.
I am unsure which of my questions this is supposed to answer, although perhaps that will become clear on reading the wikipedia article.
That was a response to
Let me rephrase my question, then, because the diagonal lemma seems clear enough to me. What is a good definition of quining? The term isn't used at all either in the article you linked or it the page on self-reference, which surprised me.
Oh! Ok, a quine is
If you understand how to write a quine and you understand how the diagonal lemma works, you will find that the two concepts are basically the same thing. "Quine" is more of a computer science term than a mathematical logic term, so not all expositions of Gödel's incompleteness theorem will mention "quining".