>you are just using a different axiom system
Don't you realize the whole point of these axiom systems? Look at the history of set theory and the axiomatic approach to mathematics. The whole reason mathematicians needed it is because nobody understood what the fuck they were doing when they were spouting about the completed infinite sets, the real numbers. Rudin even has a whole video about how set theory came about in an attempt to hide the ambiguities involved in real analysis
https://www.youtube.com/watch?v=hBcWRZMP6xs
The infinitard cope is so strong that they genuinely thought basing the whole subject on a completely undefined notion of a "set" was a good idea and logically sound mathematics.
The same with different kinds of logics. Intuitionism, constructivism etc. all came about because of incredulity in each other's approach to the completed infinite.
If you ground your mathematics in reality, all of these issues completely disappear. All of the different logic systems converge to one actual logic based in reality, the questions become definite questions corresponding to states of being in actual reality, there is no longer the need to believe in some axiomatic dogma like axioms of set theory, you can pick whatever axiomatic system you want and actually PROVE using logic that the system is consistent, but why would you need to, when it's already clear what you're talking about since your math is actually GROUNDED in reality.
Do you think anyone would open Wildberger's book on trigonometry and have a question about what kind of axiomatic system he's using? There's no need to, because it's already clear what he's talking about in the book. The propositions he states doesn't ask you to do infinite amount of work or consider some sorts of unimaginable, indescribable numbers like you see in analysis. They're about rational numbers, which you can write down and calculate with.
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Don't you realize the whole point of these axiom systems? Look at the history of set theory and the axiomatic approach to mathematics. The whole reason mathematicians needed it is because nobody understood what the fuck they were doing when they were spouting about the completed infinite sets, the real numbers. Rudin even has a whole video about how set theory came about in an attempt to hide the ambiguities involved in real analysis
https://www.youtube.com/watch?v=hBcWRZMP6xs
The infinitard cope is so strong that they genuinely thought basing the whole subject on a completely undefined notion of a "set" was a good idea and logically sound mathematics.
The same with different kinds of logics. Intuitionism, constructivism etc. all came about because of incredulity in each other's approach to the completed infinite.
If you ground your mathematics in reality, all of these issues completely disappear. All of the different logic systems converge to one actual logic based in reality, the questions become definite questions corresponding to states of being in actual reality, there is no longer the need to believe in some axiomatic dogma like axioms of set theory, you can pick whatever axiomatic system you want and actually PROVE using logic that the system is consistent, but why would you need to, when it's already clear what you're talking about since your math is actually GROUNDED in reality.
Do you think anyone would open Wildberger's book on trigonometry and have a question about what kind of axiomatic system he's using? There's no need to, because it's already clear what he's talking about in the book. The propositions he states doesn't ask you to do infinite amount of work or consider some sorts of unimaginable, indescribable numbers like you see in analysis. They're about rational numbers, which you can write down and calculate with.
(1/2)
