4 ms·
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 wh
by bollu 6y ago
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.
- paganel 6y ago> 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.
- mkl 6y agoNot 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.