Philosophy of Logic: Classical, Modal, and Non-Classical Systems

Classical logic, formalized in its modern quantificational form by Gottlob Frege's Begriffsschrift (1879) and given a widely adopted textbook shape in David Hilbert and Wilhelm Ackermann's Grundzüge der theoretischen Logik (1928), rests on principles such as bivalence, the claim that every statement is either true or false, the law of excluded middle, and a truth-functional account of the logical connectives, including the much-debated "material conditional," whose classical truth-table renders any conditional with a false antecedent automatically true — the so-called paradoxes of material implication that motivated much subsequent research into alternative logics.