Meanwhile the mathematicians who got a bit too close Philosophy are still arguing about which logic to use and if a proof by contradiction is even a proof at all.
But that’s math. And its proof is math. And that proof is true everywhere forever.
I see philosophy as a place to make nonrigorous arguments. Eventually, other fields advance enough to do away with many philosophical arguments, like whether matter is infinitely divisible or whether the physical brain or some metaphysical spirit determines our actions.
Since this is a question that math hasn’t advanced enough to answer, we can have a philosophical argument about whether other fields will eventually advance enough to get rid of all philosophical arguments.
Meanwhile the mathematicians who got a bit too close Philosophy are still arguing about which logic to use and if a proof by contradiction is even a proof at all.
Exactly.
But at the same time, even if it’s true everywhere forever, it might still not be provable, because Gödel.
Worse: If the chosen axioms are contradictory, then the theorem is effectively worthless.
And it is impossible to know whether axioms are consistent. You can only prove that they are not.
But that’s math. And its proof is math. And that proof is true everywhere forever.
I see philosophy as a place to make nonrigorous arguments. Eventually, other fields advance enough to do away with many philosophical arguments, like whether matter is infinitely divisible or whether the physical brain or some metaphysical spirit determines our actions.
Since this is a question that math hasn’t advanced enough to answer, we can have a philosophical argument about whether other fields will eventually advance enough to get rid of all philosophical arguments.
Wait do you think Bertrand Russell and Alan Turing and Kurt Gödel weren’t making philosophical arguments?
They are clearly mathematical. Starting with definitions and axioms and deriving from there using mathematical statements.