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You can do a lot of math (almost all of it?) without ever touching logic. It's only important when you ask yourself things like "hmm, okay, the reals are closed
by H8crilA 6y ago
You can do a lot of math (almost all of it?) without ever touching logic. It's only important when you ask yourself things like "hmm, okay, the reals are closed under taking supremum of bounded sets, isn't that too much to ask for? how do I know reals are possible?". And of course the great logicians showed us that you can find "significant problems" already in natural numbers.
- andi999 6y agoThats not what i meant. I mean certainly you are using some logic for doing math, do you agree with this? And if you agree, is the logic we use 1st or 1st and 1nd order?
- Kranar 6y agoThe overwhelming majority of math is done using informal logic, similar to using pseudocode to describe an algorithm. Almost no one proves mathematical theorems using formal logic, whether it's first order logic or otherwise.