Axioms necessarily must be consensual, i.e. shared by 2 or more interlocutors. If everyone invents their own personal axioms, they cease to be axioms and are just personal opinions.
What are the axioms that you believe are commonly shared, that lead to this conclusion?
‘Established’ by whom?
(If ‘established’ by yourself, haven’t you just replaced an infinite regress with circularity?)
Kind of, and it’s unavoidable—by definition, you cannot justify your own axioms, and you cannon reason without some axioms. See https://www.lesswrong.com/posts/TynBiYt6zg42StRbb/my-kind-of-reflection and https://www.lesswrong.com/posts/C8nEXTcjZb9oauTCW/where-recursive-justification-hits-bottom for some meta-justification of why it is an OK thing to do.
Axioms necessarily must be consensual, i.e. shared by 2 or more interlocutors. If everyone invents their own personal axioms, they cease to be axioms and are just personal opinions.
What are the axioms that you believe are commonly shared, that lead to this conclusion?
Rarely happens in practice, at least not without a lot of work for people to sync up their intuitions and agree on a common subset.
Not sure it exists. But see the links I shared to Eliezer’s post expressing the axioms he is /hoping/ would be commonly shared.