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Kurt Gödel kind of proved that it doesn't make much sense to build math based on axioms. This is what I consider the most important result of his work.
by DeathArrow 2y ago
Kurt Gödel kind of proved that it doesn't make much sense to build math based on axioms. This is what I consider the most important result of his work.
- ndr 2y agoIt doesn't make much sense... except for the fact that it works unreasonably well. https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...
- croes 2y agoHe didn't prove it doesn't make sense, he proved it's impossible to prove everything.
- hucker 2y agoThis is not.. really the right takeaway from his work. That not every true statement within a system is provable from its axioms, or that the consistency of a system is not provable within that system, does not mean that axioms are not useful. Indeed, what math is not grounded in the end by axioms?
- a-dub 2y agoin my mind, i compressed it to: there are always root assumption(s), that are just that, assumptions.