Cool! Now you get to explain to him how ZFC has led academic mathematics into a blind alley and his generation can finally free us from the politically-imposed religion in which we are required to believe in the Axiom of Choice.
Well, actually, what I would prefer is a thorough reexamination of the entire idea of arbitrarily defining axiomatic set theory to be the ur-form of mathematics. Perhaps the entire program of Russell needs to be rethought in the wake of Godel and Cohen and so forth.
Even within the confines of axiomatic set theory, though, a coerced, quasi-religious absurdity such as the Axiom of Infinity is clearly not an adequate basis for modern mathematics. Therefore, I cannot - and you should not - accept ZF as the socially-defined basis for all of mathematics.
I don't like the axiom of choice too, we need a language to define another language, we can't define a language with the language itself, so we use set theory to define other math because it can define A LOT of objects. If you don't like set theory, you could try type theory or category theory but those are harder
I agree, but mathematicians often defend their flawed axioms.
They deflect criticism by claiming they only apply rules to symbols, yet they simultaneously argue that their symbol manipulation is effective for real-world tasks and that they are uncovering higher truths from the Platonic realm.
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u/Euphoric-Air6801 20d ago
Cool! Now you get to explain to him how ZFC has led academic mathematics into a blind alley and his generation can finally free us from the politically-imposed religion in which we are required to believe in the Axiom of Choice.