“natural languages are extremely impractical, which is why mathematicians don’t write any real proofs in them.”
I have never seen such a blatant disqualifaction of one’s self. Why do you think you are able to talk to these subjects if you are not versed in Proof theory?
Just type it into chat gpt:
Which one is true:
”natural languages are extremely impractical, which is why mathematicians don’t write any real proofs in them.”
OR
”They do. AND APPART FROM THAT Language is not impractical, language too expressive (as in logical expressivity of second-order-logic)”
Research proof theory, type theory, and Zermelo–Fraenkel set theory with the axiom of choice (ZFC) before making statements here.
At the very least, try not to be miserable. Someone who mistakes prose for an argument should not have the privilege of indulging in misery.
“natural languages are extremely impractical, which is why mathematicians don’t write any real proofs in them.”
I have never seen such a blatant disqualifaction of one’s self.
Why do you think you are able to talk to these subjects if you are not versed in Proof theory?
Just type it into chat gpt:
Research proof theory, type theory, and Zermelo–Fraenkel set theory with the axiom of choice (ZFC) before making statements here.
At the very least, try not to be miserable. Someone who mistakes prose for an argument should not have the privilege of indulging in misery.
The sentence you quoted is a typo, it’s is meant to say that formal languages are extremely impractical.
well this is also not true. because “practical” as a predicate… is incomplete.… meaning its practical depending on who you ask.
Talking over “Formal” or “Natural” languages in a general way is very hard...
The rule is this: Any reasoning or method is acceptable in mathematics as long as it leads to sound results.