 An oddity pointed out early by MacColl (1908) is the observation that of any two sentences of the form “not A or B” and “not B or A”, at least one must be true. Assuming the equivalence with the material conditional, this implies that either “if John is a physician, then he is red-haired” or “if John is red-haired, then he is a physician” must be true. Intuitively, however, one may be inclined to reject both conditionals. Similar complications, known as the paradoxes of material implication, concern the fact that for any sentences A and B, “if A then B” follows from “not A”, but also from “B”, thereby allowing true and false sentences to create true conditionals irrespective of their content (C. I. Lewis 1912). Another peculiarity looms large: the negation of “if A then B” is predicted to be “A and not B”, but intuitively one may deny that “if God exists, all criminals will go to heaven” without committing oneself to the existence of God (cited in Lycan 2001).