But the axiom schema of induction does not completely exclude
Eliezer isn’t using an axiom schema, he’s using an axiom of second order logic.
I don’t see what the difference is… They look very similar to me.
At some point you have to translate it into a (possibly infinite) set of first-order axioms or you wont be able to perform first-order resolution anyway.
What’s wrong with second order resolution?
There’s no complete deductive system for second-order logic.
Eliezer isn’t using an axiom schema, he’s using an axiom of second order logic.
I don’t see what the difference is… They look very similar to me.
At some point you have to translate it into a (possibly infinite) set of first-order axioms or you wont be able to perform first-order resolution anyway.
What’s wrong with second order resolution?
There’s no complete deductive system for second-order logic.