Formal and Material Implication

Modern Logic distinguishes between 'Formal' Implication and 'Material' Implication. Formal Implication, a key component of the Modern interpretation of Aristotelian Categorical statements, asserts a relation of inclusion to obtain between predicates, e. g. (x)(If x is F, then x is G). On the other hand, Material Implication, asserts the existence of a propositional connection between actual states-of-affairs, e. g. If P is True, then Q is True. Now, this Formal-Material contrast has little to do with the meaning of those terms in Formaterialism. Rather, the Logical connective that is closest to the Formal Principle is Conjunction, while that closest to the Material Principle is Disjunction, specifically the Exclusive variety. But the more the general problem is accepting Material Implication as a species of Implication. For both Aristotle and Modern Logicians, the medium of Implication is Universals, whereas the propositions connected by Material Implication are Singular states-of-affairs. The associated peculiarities of the Truth-Computation of this connective are well-known. When P is True and Q is False, 'If P, then Q' is plainly False. But a lacuna arises when P is False, one which Logicians have opted to fill with the blanket computation that 'If P, then Q' is True whenever P is False. Because Material Implication, and this method of its Truth-Computation, is a foundation of much of contemporary Logic, and is a staple of academic Introductory Logic courses, students are, therefore, expected to puzzle out how 'If Earth is Mars, then Belgium is a tree' is a True statement, one that is part of what is meant to teach them how to recognize rhetorical double-talk.