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Not encountering this for the first time, I've given much thought to your position over the years. But according to many mathematicians, mathematics is within
by dwringer 8y ago
Not encountering this for the first time, I've given much thought to your position over the years. But according to many mathematicians, mathematics is within the purview of natural language[1][2]. And wasn't it Feynman himself alleged to have said if we can't explain something in a lecture intended for undergraduate freshmen, we don't really understand it? [3, p19].
[1] https://en.wikipedia.org/wiki/Language_of_mathematics https://en.wikipedia.org/wiki/Language_of_mathematics
[2] http://www.cut-the-knot.org/language/MathIsLanguage.shtml http://www.cut-the-knot.org/language/MathIsLanguage.shtml
[3] http://calteches.library.caltech.edu/563/2/Goodstein.pdf http://calteches.library.caltech.edu/563/2/Goodstein.pdf
EDIT: This is not to challenge your specific assertions on this topic - on which I cannot speak with any particular authority.
- ahelwer 8y agoUndergraduate freshmen are perfectly capable of understanding basic linear algebra, and thus quantum entanglement. Regarding the nature of language and how it relates to mathematics, I don't think it's correct to say math is a "subset" of language; there is no satisfactory definition of language that encompasses all the way humans communicate with one another, and it makes more sense to restrict the definition of language to its use in specific interactions (the language of interacting with a cashier to buy an item from a store, and the different language of telling your team what you worked on during standup, for example). In this sense the use of mathematics to describe quantum mechanics is a language in itself.
- dwringer 8y agoSorry, my earlier use of the word subset was a mistake and I have edited the sentence in question to say "within the purview" which is more what I had in mind. I appreciate your reply and do agree with your final statement, though I'm not really sure on the idea of restricting the definition of language as you've described and personally have trouble finding such delineations.
- ahelwer 8y agoYou can read more on Wittgenstein's idea of "language games" here: https://plato.stanford.edu/entries/wittgenstein/#LangGameFamiRese https://plato.stanford.edu/entries/wittgenstein/#LangGameFam...