Why Does Aristotle Defend the Principle of Non‐Contradiction Against its Contrary?

The argument above is unsound. But according to modern propositional logic, the argument is valid. There is not a semantic interpretation in which the argument’s premises are both true and its conclusion is false. More specifically, if P1 is true then P2 is false, and vice versa. As a result of the fact that P1 and P2 cannot both be true, any well-formed formula—or combination of well-formed formulas—could take the place of the sentence currently in use as the conclusion without making the argument invalid. “Socrates is a chess master” could be used as the conclusion, and still validity would be preserved, as could, “The square root of forty-nine is eighteen” and/or, “You’re both alive and not alive.” For a more general illustration of the point, consider a proof of the claim that from the