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DanArmak comments on Rationality Quotes September 2012 - Less Wrong
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I hadn't considered that irony. I was thinking about the explicit irony of the text itself in its proof of sqrt(2) being irrational. The reader is expected to know the punchline, that sqrt(2) is irrational but that irrational numbers are important and useful. So the text that (ironically) appears to dismiss the concept of irrational numbers is in fact wrong in its dismissal, and that is a meta-irony.
...I feel confused by the meta levels of irony. Which strengthens my belief that mathematical proofs should not be ironical if undertaken seriously.
Yes, I feel similarly about this modus stuff; it seems simple and trivial, but the applications become increasingly subtle and challenging, especially when people aren't being explicit about the exact reasoning.