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Math is falsifiable. You can derive innumerable self-contradictory mathematical systems and we discard them because they are demonstrably useless. The demonstra

• dragonwriter 10y ago
  > Math is falsifiable. Not in the sense that propositions of science are, where falsifiability refers to empirical falsification, not logical contradiction. What you are doing is called "equivocation". > You can derive innumerable self-contradictory mathematical systems and we discard them because they are demonstrably useless. No, we reject any set that includes self-contradictions; we may choose which self-consistent set to use in a particular domain because of empirical utility, but, to the extent there is falsification involved their, its not of the math or set of axioms, per se, but of its applicability to the problem domain.
• Mikhail_Edoshin 10y ago
  Non-euclidean geometries were useless for some time :)
  • Retra 10y ago
    The were very useful for modeling the structures they were used to model, and for educating on the flexibility of alternative geometries, as well as discussing the veracity of existing assumptions. So no, they were never useless. The people who discovered them and studied them knew they weren't useless, which is why they were so willing to go down that road. They just didn't make anyone any money or solve any immediate broadly applicable problems in society.
    • Mikhail_Edoshin 10y ago
      So basically a thing is not useless if you know it's not. I can accept that :)