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m-phi.blogspot.com | ||
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jdh.hamkins.org
I'd like to share a simple proof I've discovered recently of a surprising fact: there is a universal algorithm, capable of computing any given function! Wait, what? What on earth do I ... |
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jiggerwit.wordpress.com
What follows are the opening paragraphs of a pdf document giving an argument for controlled natural languages in mathematics. At the recent Big Proof 2 conference in Edinburgh, I realized that a case must be made for developing a controlled natural language for mathematics. There is little consensus on this issue, and mathematicians and computer... |
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xorshammer.com
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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www.lesswrong.com
Creating Friendly AI seems to require us humans to either solve most of the outstanding problems in philosophy, or to solve meta-philosophy (i.e., wh... |
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