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www.logicmatters.net | ||
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xorshammer.com
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| | | | | There are a number of applications of logic to ordinary mathematics, with the most coming from (I believe) model theory. One of the easiest and most striking that I know is called Ax's Theorem. Ax's Theorem: For all polynomial functions $latex f\colon \mathbb{C}^n\to \mathbb{C}^n$, if $latex f$ is injective, then $latex f$ is surjective. Very... | |
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dvt.name
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| | | | | Gödel's incompleteness theorems have been hailed as "the greatest mathematical discoveries of the 20th century" - indeed, the theorems apply not only to mathematics, but all formal systems and have deep implications for science, logic, computer science, philosophy, and so on. In this post, I'll give a simple but rigorous sketch of Gödel's First Incompleteness ... | |
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www.umsu.de
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| | | | | [AI summary] A blog post explores the philosophical conflict between mathematical pluralism and logical consistency using Peano Arithmetic, followed by a comment section debating the implications for semantic meaning and privileged models. | |
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blog.computationalcomplexity.org
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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... | ||
