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jdh.hamkins.org | ||
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math.andrej.com
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| | | | | [AI summary] The discussion revolves around the nuances of proof methods in constructive mathematics, particularly the distinction between proof by contradiction and proof by negation. Key points include the definition of irrational numbers without relying on the law of excluded middle, the use of contrapositive in proofs, and the limitations of certain classical theorems like the intermediate value theorem in constructive settings. The conversation also touches on the philosophical and practical implications of these proof methods in both classical and intuitionistic logic, as well as the role of type theory and univalent foundations in modern mathematical proofs. | |
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mycqstate.wordpress.com
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| | | | | This post is a follow-up on some somewhat off-hand comments that I made earlier regarding the notion of truth in a "proof-based" discipline such as pure mathematics or theoretical computer science. Since the former is easier to circumscribe and also has a larger literature available on it, for the purposes of the post I will... | |
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ncatlab.org
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| | | | | [AI summary] The nLab entry explores philosophical aspects of mathematics, including metaphysics, foundational issues, and historical paradigms, with references to key thinkers and texts. | |
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backreaction.blogspot.com
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| | | Science News, Physics, Science, Philosophy, Philosophy of Science | ||
