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jdh.hamkins.org | ||
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www.logicmatters.net
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| | | | | Logical notes and papers Some logical blog pieces Philosophy of maths: a reading list Does mathematics need a philosophy? Philosophical logic: five books from the back catalogue On Frege seeing what is in front of his nose. Begriffsschrift and absolutely unrestricted quantification What Frege didnt tell you Tarski on Truth, a thumbnail sketch Partial functions [] | |
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kpknudson.com
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carcinisation.com
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| | | | | Gödel's theorems say something important about the limits of mathematical proof. Proofs in mathematics are (among other things) arguments. A typical mathematical argument may not be "inside" the universe it's saying something about. The Pythagorean theorem is a statement about the geometry of triangles, but it's hard to make a proof of it using nothing... | |
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xorshammer.com
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| | | The Axiom of Choice is usually introduced as a non-constructive axiom that mathematicians used to care about but don't really pay much attention to anymore. It's true that mainstream mathematicians often don't pay much attention to it, but it turns out that AC isn't inherently non-constructive: it depends on what the base system it's being... | ||
