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.
I see philosophy as a place to make nonrigorous arguments.
It’s the other way around: math is where you just ignore questions about what makes sense, what knowledge is, what truth is, what a proof is, how scientific consensus is reached, what the scientific method should be, and so on. Instead, you just handwave and assume it will all work out somehow.
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.
It’s the other way around: math is where you just ignore questions about what makes sense, what knowledge is, what truth is, what a proof is, how scientific consensus is reached, what the scientific method should be, and so on. Instead, you just handwave and assume it will all work out somehow.
Philosophy of mathematics is were these questions are treated rigorously.
Of course, serious mathematicians are often philosophers at the same time.
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.
They all debated the question what being mathematical means there whole lives.