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rjlipton.com | ||
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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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www.logicmatters.net
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| | | | | I have at last returned to finish reading Jeremy Avigad's Mathematical Logic and Computation, which was published last year by CUP. Here, now put together into one post, are some thoughts about the book (increasingly less per chapter, as I came to realise that - despite Avigad's intentions and despite the many virtues of the [...] | |
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billwadge.com
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| | | | | The famous mathematician Kurt Gödel proved two "incompleteness" theorems. This is their story. By the 1930s logicians, especially Tarski, had figured out the semantics of predicate logic. Tarski described what exactly was an 'interpretation' and what it meant for a formula to be true in an interpretation. Briefly, an interpretation is a nonempty set (the... | |
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cromwell-intl.com
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| | | Hypercomputation is a wished-for magic that simply can't exist given the way that logic and mathematics work. Its purported imminence serves as an excuse for AI promoters. | ||
