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 ianwrightsite.wordpress.com
Materialism and Cantor's higher infinities (transcript of talk) -
| | existentialtype.wordpress.com
Proofs by contradiction, versus contradiction proofs | Existential Type
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| | It is well-known that constructivists renounce "proof by contradiction", and that classicists scoff at the critique. "Those constructivists," the criticismgoes, "want to rule out proofs by contradiction. How absurd! Look, Pythagoras showed that the square root of two is irrational by deriving a contradiction from the assumption that it is rational. There is nothing wrong...
| | njwildberger.com
Finite versus "infinite" | njwildberger: tangential thoughts
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| | There are several approaches to the modern theory of "real numbers". Unfortunately, none of them makes complete sense. One hundred years ago, there was vigorous discussion about the ambiguities with them and Cantor's theory of "infinite sets". As time went by, the debate subsided but the difficulties didn't really go away. A largely unquestioning uniformity...
| | blog.computationalcomplexity.org
Computational Complexity: Why did 1+1=2 take Russell and Whitehead 300 pages?
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| | In my post about the myth that Logicians are crazy I mentioned in passing that Whitehead and Russell spend 300 pages proving 1+1=2 (but we...
| | xorshammer.com
But Why Is Proof by Contradiction Non-Constructive? - XOR's Hammer
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| We think of a proof as being non-constructive if it proves "There exists an $latex x$ such that $latex P(x)$ without ever actually exhibiting such an $latex x$. If you want to form a system of mathematics where all proofs are constructive, one thing you can do is remove the principle of proof by contradiction:...