4 ms·

Exactly. What are axioms and what are rules of inference ends up being a distinction without a difference.

• mafribe 11y ago
  I'm not sure I would go that far. There is a difference, but it's not clear quite what it is. For example, it becomes progressively harder to get nice (with cut elimination and finite rule schemata) sequent calculi for richer axiomatic systems. For example I have not come across a nice (in the above sense) sequent style formalisation of ZFC set theory. Have you?
  • plutooo 11y ago
    No, but why is that a problem?
    • mafribe 11y ago
      It's an indication, a hint, that rules and axioms are not always completely exchangable.