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I think that mathematical proofs, as they are actually written, rely on natural language and on a large amount of implicit shared knowledge. They are not formal
by JacobiX 10mo ago
I think that mathematical proofs, as they are actually written, rely on natural language and on a large amount of implicit shared knowledge. They are not formalized in the Principia Mathematica sense, and they are even further from the syntax required by modern theorem provers. Even the most rigorous proofs such as those in Bourbaki are not directly translatable into a fully formal system.
- drawnwren 10mo agoIf you don't mind stretching your brain a bit, Wittgenstein was obsessed with this notion. https://www.bu.edu/wcp/Papers/Educ/EducMaru.htm#:~:text=Wittgenstein%20uses%20this%20fictional%20situation,or%20has%20learned%20different%20activities. https://www.bu.edu/wcp/Papers/Educ/EducMaru.htm#:~:text=Witt...