Er, sorry. Meant propositional calculus not first order logic. I think my statement works in that context.
What’s specifically going on here is that (P=>Q) ⇒ (Q=> P) is false whenever P is false and Q is true.
Adding it as an axiom schema to propositional calculus results in a contradiction. It cannot be added as a single axiom to first-order logic.
Yes, you are correct. I was confused in a very stupid way.
Er, sorry. Meant propositional calculus not first order logic. I think my statement works in that context.
What’s specifically going on here is that (P=>Q) ⇒ (Q=> P) is false whenever P is false and Q is true.
Adding it as an axiom schema to propositional calculus results in a contradiction. It cannot be added as a single axiom to first-order logic.
Yes, you are correct. I was confused in a very stupid way.