4 ms·

Isn't it the other way around? Axioms are chosen because there are no observable counter examples in the real world.

• karmakaze 6y ago
  Not at all, pure math is in part about exploring axiomatic systems that may or may not have a physical counterpart. The latter is immaterial.
  • symplee 6y ago
    Can you give some examples of axioms in pure math that run completely counter to our physical world? For example: It is NOT possible to draw a straight line from any point to any other point. It is NOT possible to extend a line segment continuously in both directions. etc... or Things which are equal to the same thing are NOT equal to one another. If equals are added to equals, the wholes are NOT equal. The whole is LESS than the part. Note that the original forms of the above axioms "make sense" to us because everything in our physical experience agrees with them. So when you said that the "physical counterpart ... is immaterial", I was curious to see an example of a "physically impossible" axiom.
    • red75prime 6y ago
      Most of large cardinal axioms.