Abstract

Appropriate for a conference relating philosophy and education, we seek ways more faithful than the truth-functional hook to understand and represent that ordinary-language conditional which we use in, e.g., modus ponens, and that conditional’s remote and counterfactual counterparts, and also the proper negations of all three. Such a logic might obviate the paradoxes caused by T-F representation, and be educationally fruitful. William and Martha Kneale and Gilbert Ryle assist us: "In the hypothetical case in which p, it is inferable, on the basis that p and at least in the given context, that q." "Inferable" is explained. This paraphrase is the foundation of the logic of hypothetical inferability. It generates the negative but non-TF device "hib", followed by a bracketed conjunction. This is an enriched negative: "hib " is stronger than "-," and "-hib" offers us "-hib," weaker than "p. -q." Thus equipped, we can test deductive arguments by the CI method explained, and explode paradoxes. The paraphrase, "hib," and the CI method are fruitful in training students to understand this conditional, and to demonstrate genuine validity or invalidity.