Abstract

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