Pragmatics, Mental Models and One Paradox of the Material Conditional

Most instantiations of the inference ‘y; so if x, y’ seem intuitively odd, a phenomenon known as one of the paradoxes of the material conditional. A common explanation of the oddity, endorsed by Mental Model theory, is based on the intuition that the conclusion of the inference throws away semantic information. We build on this explanation to identify two joint conditions under which the inference becomes acceptable: (a) the truth of x has bearings on the relevance of asserting y; and (b) the speaker can reasonably be expected not to be in a position to assume that x is false. We show that this dual pragmatic criterion makes accurate predictions, and contrast it with the criterion defined by the mental model theory of conditionals, which we show to be inadequate.