  In the twentieth century there were many creative uses of logical tools and techniques in reassessing past doctrines. One might naturally wonder if there is some ingenious interpretation of the square that attributes existential import to the O form and makes sense of it all without forbidding empty or universal terms, thus reconciling traditional doctrine with modern views. Peter Geach, 1970, 62–64, shows that this can be done using an unnatural interpretation. Peter Strawson, 1952, 176–78, had a more ambitious goal. Strawson’s idea was to justify the square by adopting a nonclassical view of truth of statements, and by redefining the logical relation of validity. First, he suggested, we need to suppose that a proposition whose subject term is empty is neither true nor false, but lacks truth value altogether.  Then we say that Q entails R just in case there are no instances of Q and R such that the instance of Q is true and the instance of R is false. For example, the A form ‘Every S is P’ entails the I form ‘Some S is P’ because there is no instance of the A form that is true when the corresponding instance of the I form is false. The troublesome cases involving empty terms turn out to be instances in which one or both forms lack truth value, and these are irrelevant so far as entailment is concerned. With this revised account of entailment, all of the “traditional” logical relations result, if they are worded as follows: