I am from India. Here, in all the sects of religion descended from Hinduism, we had a concept of 'Shaastraarth'.
This was basically a debate between learned men of different religions or learned men of different schools of thought from the same religion. There would be an impartial judge, and the judge, the audience, or they themselves would ask each other questions. Both of them had to reply on the basis of their 'Shaastras' or their holy and/or philosophical texts.
It was perfectly logical. Whoever lost would have to change their and their disciples' school of thought or religion to that of the winner. Search 'Adi Shankaracharya' for an example. My question is, is there a set of axioms that can answer every question we throw at it?
This is when we assume Godel's Incompleteness theorems to be false, as it was proved true in conditions which forced it to be. I find it sketchy. Even if it is logically sound, let us not talk about it. I don't like thinking about how mathematics is not absolute.
P.S. I have no background in philosophy, I just had this question and I thought this site was the best place for it.
Edit: I now have another question. How did they get these done?
If an atheist has a debate with a theist, the scriptures of the theist will obviously say that there is a god, and the beliefs of the atheist will lead him to say that there is no god. We have a conflicting set of axioms.
Edit2: I solved my own doubt in the comments.