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www.logicmatters.net | ||
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neilmadden.blog
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| | | | | I saw another article on Gödel's incompleteness theorems linked from Reddit today. It's a topic I've wanted to write about for some time. Although many articles do a decent job in giving an idea of what the big deal is (and this one is pretty good), they can sometimes give a misleading impression of what... | |
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xorshammer.com
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| | | | | Let $latex \mathrm{PA}$ be Peano Arithmetic. Gödel's Second Incompleteness Theorem says that no consistent theory $latex T$ extending $latex \mathrm{PA}$ can prove its own consistency. (I'll write $latex \mathrm{Con}(T)$ for the statement asserting $latex T$'s consistency; more on this later.) In particular, $latex \mathrm{PA} + \mathrm{Con}(\mathrm{PA})$ is stronger than $latex \mathrm{PA}$. But certainly, given that... | |
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unstableontology.com
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| | | | | (note: some readers may find the LaTeX more readable on LessWrong.) In this post I prove a variant of Gödel's completeness theorem. My intention has been to really understand the theorem, so that I am not simply shuffling symbols around, but am actually understanding why it is true. I hope it is helpful for at... | |
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blog.paulhankin.net
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