The logical properties of the 'if-then' connective of ordinary English differ markedly from the logical properties of the material conditional of classical, two-valued logic. This becomes apparent upon examination of arguments in conversational English which involve (noncounterfactual) usages of if-then'. A nonclassical system of propositional logic is presented, whose conditional connective has logical properties approximating those of 'if-then'. This proposed system reduces, in a sense, to the classical logic. Moreover, because it is equivalent to a certain nonstandard three-valued logic, its (...) decision procedure is almost as efficient as that of the classical logic. It therefore provides a rational and convenient system in which to formalize English arguments. (shrink)

THE INDICATIVE CONDITIONAL. A PROBABILISTIC CRITERION OF SOUNDNESS FOR DEDUCTIVE INFERENCES Our objective in this section is to establish a prima facie case ...

The standard use of the propositional calculus ('P.C.?) in analyzing the validity of inferences involving conditionals leads to fallacies, and the problem is to determine where P.C. may be ?safely? used. An alternative analysis of criteria of reasonableness of inferences in terms of conditions of justification rather than truth of statements is proposed. It is argued, under certain restrictions, that P. C. may be safely used, except in inferences whose conclusions are conditionals whose antecedents are incompatible with the premises in (...) the sense that if the antecedent became known, some of the previously asserted premises would have to be withdrawn. (shrink)

The discrepancy between English if's and the horseshoe is far from being negligible. That is not a reason for distrusting the horseshoe, which is useful so long as it is taken to mean just what it is defined to mean; and it is not a reason for distrusting our English if's, which in spite of their ambiguities are indispensable to our daily discourse. But it is a reason for distrusting the current logical pedagogy that leads students to take the two (...) as being intertranslatable. So if symbolic logic is to help us in our English arguments (and that should surely be one of its functions) it needs to be supplemented: it needs to be provided with additional symbols (presumably with the introduction of one or more primitive concepts) that will preserve the meaning of our various if's with greater accuracy. In the present paper I shall point in the direction of such a logic. I cannot undertake to develop it in a complete postulational form; but I can at least call attention to certain English locutions by which the required postulates should be guided. And I can venture to state some of the postulates using appropriate symbols. (shrink)