In earlier publications, I have outlined a largely novel approach² to the semantics of certain formal languages and the semantics of certain fragments of natural languages.³ In this approach, the truth of a sentence S is defined as the existence of a winning strategy for one of the two players, called Myself, in a certain two-person game G(S) associated with S.⁴ Intuitively, G(S) may be thought of as an attempt on the part of Myself to verify S against the schemes of an actively resistant opponent who is called Nature. On the basis of this idea, most of the game rules can be anticipated. For instance, I win if the game ends with a true primitive sentence, and Nature wins if it ends with a false one. For quantifier phrases like "any Y who Z" and "every Y who Z", the game rules can also be anticipated. As special cases we have the following rules: