ABSTRACT
I.e. for y and b E Ao, WE V( <::::>, y, b») iff W rf: V(y) or WE V(b). This is in fact the normal rule for material implication. Whether the rule for material implication really does reflect the English 'if then' is a question we need not go into. Let us suppose it does in this case. It is easy to see that <::::>, p, p) will be true and furthermore true no matter what value is assigned to p. Or to put the matter more correctly <::::> ,p, p) will be true in all models which satisfy [V::::> ] whatever values they may assign to IX and p. (2') then will be a truth of logic because it is not only true in the model which represents its ordinary language meaning but also in the class of models which agree only on [V::::> J.
