Faithful and Fruitful Logic :: Logic Philosophy Papers

Faithful and Fruitful Logic Appropriate for a conference relating philosophy and education, we seek ways more faithful than the truth-functional (TF) 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 ("HI logic"). It generates the negative but non-TF device "hib" (= "there is a hypothetical-inferability bar against the conjoint proposition that"), followed by a bracketed conjunction. This is an enriched negative: "hib (p . -q)" is stronger than "-(p . -q)," and "-hib" ("dash hib" = "there is no h-i bar...") offers us "-hib (p . -q)," weaker than "p . -q." Thus equipped, we can test deductive arguments by the CI ("Compatible-or-incompatible?") 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. The logic generally taught to English-speaking students is symbolic logic. How faithful is it when employed as a representation of the connectives they use and will use in their ordinary conversation and in most of their intellectual activity, at least if they are not mathematicians? How fruitful for their education? Is there a logic more faithful and likely to be more fruitful? A conference inviting us to relate philosophy and education makes those questions especially opportune. I Reviewing Strawson’s Introduction to Logical Theory in Mind (1953), Quine admits that Strawson is "good on ‘É ’ and ‘if/then’" and "rightly observes the divergence between the two". But he left unchanged his handling of "the conditional" in subsequent editions of his textbooks. In the review he writes unconcernedly (as would be impossible for Ryle, Austin or Strawson) of the "Procrustean treatment of ordinary language at the hands of logicians", defending it by offering symbolic logic as the appropriate language for science, and suggesting that philosophy of science comes close to being "philosophy enough". Ackermann, in the Preface to his Modern Deductive Logic, takes quite a different approach. He emphasises the "mathematical and scientific applications" of symbolic deductive logic, but says "one may well wonder" whether it has "enough philosophical value" to justify a major place in the philosophy curriculum.