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www.logicmatters.net | ||
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jdh.hamkins.org
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| | | | | Philosophy of Mathematics, Exam Paper 122, Oxford University Wednesdays 12-1 during term, Radcliffe Humanities Lecture Room Joel David Hamkins, Professor of Logic Lucy, Charles - Personifications o... | |
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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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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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analog-antiquarian.net
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| | | [AI summary] This chapter explores the legacy of ancient knowledge, focusing on figures like Claudius Ptolemy and the transmission of their works through history. It discusses the decline of classical learning after the fall of Rome, the role of Islamic scholars in preserving and expanding ancient texts, and the eventual rediscovery of these works in medieval Europe. The chapter also touches on the controversies surrounding Pythagoras and the broader philosophical debates about the limits of ancient wisdom versus modern scientific inquiry. | ||
