3 ms·

Where can I find this standard set of axioms?

• cmrx64 10y ago
  One widely-used system is Higher Order Logic (with various extensions sometimes), one core of which you can find here: http://sourceforge.net/projects/hol/files/hol/kananaskis-10/kananaskis-10-logic.pdf/download http://sourceforge.net/projects/hol/files/hol/kananaskis-10/... This is based on type theory (and has a model in set theory), but isn't as powerful as the logics used in Coq and similar theorem provers (the Calculus of (Inductive) Constructions). You might be interested in metamath: http://us.metamath.org/ http://us.metamath.org/, which lists the axioms used in its largest body of work: http://us.metamath.org/mpegif/mmset.html#axioms http://us.metamath.org/mpegif/mmset.html#axioms
• baddox 10y ago
  I'm not sure what the parent commenter means by "reason and science" giving us axioms, but for mathematics the most common axiomatic system is ZFC set theory. Some of the axioms are easy to understand even with a mathematics background: https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory#Axioms https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_t...
  • lgas 10y ago
    I would consider these to be mathematical axioms. I was looking for what pitaj was describing as coming from outside of math. Maybe I'm just misunderstanding what pitaj was saying.
• pitaj 10y ago
  By axioms, maybe I used the wrong word, but what I was referring to is things like the concept of "burden of proof" in reason.