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by ryugarden
2394 days ago
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Yes, there are objective mathematical truths, but you cannot be sure there exists a physical reality or anything that corresponds to our experiences. You just know that there are subjective experiences right now. That's the only thing you can be absolutely certain about. So I see no sense in talking about "reality". |
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Of course, the debate remains of the "validity" of pure mathematics for its own sake. Many mathematicians, while not being religious in the common sense, have longed for a Platonic reality. Why do you think Hardy was so derided for his Mathematician's Apology?
Mathematics is simply another formal game of language, based on a number of axioms which can be either held to be true or not. Look at the differences between Euclidean and projective geometry. No one is asking which one is "true". Projective geometry helps for some lines of thought, Euclidean works for others.