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Comment by paganel | Hacker News Reader

> Why not Math as a religion

Math is indeed a religion deep down, at least according to people like Hume, you have to "believe" in things like induction, you have to "believe" that natural numbers "don't end at some point" (for lack of a better word) or that two parallel lines don't finally meet, because who's there to watch them till the end of the world to say that they don't in fact meet? (Hume writes it down way better than I could ever do).

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That's not how it works, though. We can study any set of axioms we want. Mathematics often study "multiple incompatible worlds". For example, euclidean space where parallel lines never meet, and projective space, where parallel lines do meet at infinity. This is a general theme of math; we can study different sets of "beliefs" when we don't know which one is the "correct belief".

Thus, we come out on top, since we know what happens in all possible worlds.

> what happens in all possible worlds.

Talking about "all possible worlds" is religious-talk (at least that's what Hume would say), afaik we only know of one world, talking about the "possibility" of other worlds is what established/institutional religions do.

Not literal worlds, mathematical possibilities. Analysis like "If XYZ is true, then [conclusion 1], but if XYZ is false, then [conclusion 2]". It's not religion, it's logic and mathematics, and we absolutely can look at all possibilities in many circumstances.

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