Logic

Hi I understand how to apply derivation rules like the rules of inference etc. My question is do we have a method of proving the rules themselves? Is there a way to prove that If P then Q; P; therefore Q? Or do we accept these rules out of intuition?

Comments

Rules of inference are "primitive" (i.e., basic) argument forms; all other arguments are (syntactically) proved using them. So you could either say that the rules of inference are taken as primitive and not (syntactically) provable, or you could say that they are their own (syntactic) proofs.

However, the way that they are usually justified is not syntactically, but semantically: For propositional rules of inference, this would mean that they are (semantically) proved by means of truth tables. A rule such as Modus Ponens (your example) is semantically proved (i.e., shown to be semantically valid) by showing that any assignment of truth values to the atomic propositions (P, Q in your example) that makes all of the premises true also makes the conclusion true.

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