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GR and QFT are both axiomatic systems, right? If their axioms are logically independent, and a number of them are absolutely true in describing the universe, i.e. non-removable from a TOE, is there anyway to reduce the number of axioms? Is the dream of having a few axioms describing everything in the universe mathematically possible? Or am I confused about the whole nature of theories and axiomatic systems?

Edit: I guess this question has one purely mathematical aspect and one physical aspect. To focus on the physical aspect now, I concede that it's quite possible that zero of those axioms are true, which makes the question irrelevant. However, just the way that Newton's laws of motion can be derived from GR as estimations in many situations, I assume GR and QFT should be derivable as estimations from TOE. I don't know what implications this could have on the number of axioms in TOE...

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  • $\begingroup$ Are you sure that "a number of them are absolutely true in describing the universe"? How do you verify such a thing? $\endgroup$ – probably_someone Apr 26 at 14:10
  • $\begingroup$ Of course not. I'm saying that if the number of the true axioms is N and they are logically independent, is it possible for TOE to have less than N axioms? $\endgroup$ – Asmani Apr 26 at 14:11
  • $\begingroup$ Alright, let's back up a bit. What does it mean for an axiom to be "true"? $\endgroup$ – probably_someone Apr 26 at 14:14
  • $\begingroup$ I think I get it: If GR depends on A, B and C being true. And QM depends on X, Y and Z being true, can a ToE depend on < 6 things? (obvs none of A,B,C,X,Y,Z are equivalent). $\endgroup$ – Oscar Bravo Apr 26 at 14:54
  • $\begingroup$ @OscarBravo You have stated the essence of the question. Notice how you have not stated or otherwise assumed that A, B, C, X, Y, or Z are "absolutely true" and/or "non-removable from a TOE". Those are precisely the parts of the question that I take issue with, the rest is valid. $\endgroup$ – probably_someone Apr 26 at 14:59

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