Validity is defined in a couple of ways. I like to define it like this: An argument is valid iff the superconjunction1 of all the premises and the negation of the conclusion is impossible. It sounds a bit unusual at first but it is worded that way to prevent confusion about modalities. A more common definition is: An argument is valid iff it is impossible for all the premises to be true and the conclusion false. I contend that mine is clearer when understood. Consider this argument: n Proposition Explanation 1 P Premise 2 P→Q Premise 3 Q From 1, 2, MP Anyone trained in logic will immediately recognize that this argument is valid (and the form valid too) for it has the form of MP and all arguments of that form are valid. To see this using my definition of valid above we can simply make the superconjunction of the argument and put it into a truth table: P Q ¬Q P→Q P∧(P→Q)∧¬Q T T F T F T F T F F F T F T F F F T T F Note that I skipped a conjunction step.
Validity and necessary truths
Validity and necessary truths
Validity and necessary truths
Validity is defined in a couple of ways. I like to define it like this: An argument is valid iff the superconjunction1 of all the premises and the negation of the conclusion is impossible. It sounds a bit unusual at first but it is worded that way to prevent confusion about modalities. A more common definition is: An argument is valid iff it is impossible for all the premises to be true and the conclusion false. I contend that mine is clearer when understood. Consider this argument: n Proposition Explanation 1 P Premise 2 P→Q Premise 3 Q From 1, 2, MP Anyone trained in logic will immediately recognize that this argument is valid (and the form valid too) for it has the form of MP and all arguments of that form are valid. To see this using my definition of valid above we can simply make the superconjunction of the argument and put it into a truth table: P Q ¬Q P→Q P∧(P→Q)∧¬Q T T F T F T F T F F F T F T F F F T T F Note that I skipped a conjunction step.