3 ms·
Actually, I'd say that in mathematics, things are provably true given that the initial assumptions are true. However, mathematics does not so far as I know deal
by sea6ear 14y ago
Actually, I'd say that in mathematics, things are provably true given that the initial assumptions are true. However, mathematics does not so far as I know deal with the truth of those initial assumptions (axioms), it simply accepts them as true.
Where this gets interesting is that you can say, what if this axiom was not true? Let's assume it's not. And then possibly come up with a whole new system of mathematics (like non-euclidean geometry) which may turn out to have actual use in previously unsolvable problems.
- lotharbot 14y agoI think it's better to conceive of mathematical axioms as being part of mathematical system X or not, rather than as true or false. That is, they're not self-evident or universal or true according to some external standard, they're merely postulated as properties of a given mathematical structure. See http://en.wikipedia.org/wiki/Axiom#Non-logical_axioms http://en.wikipedia.org/wiki/Axiom#Non-logical_axioms
- sea6ear 14y agoThat's seems like a useful understanding.