In earlier papers, I have sketched an approach to logical and linguistic semantics that embodies some of the same ideas on which Wittgenstein's notion of language game is based.¹ One of these ideas is that in order to appreciate the semantics of a word (or any other primitive expression of a language) we should study its function in the rule-governed human activities that serve to connect the language (or the fragment of a language) with the world. What Wittgenstein called "language games' can typically be considered such linking activities. In the languages (or parts of languages) that I will study in this chapter, certain activities of this kind are construed as games in the strict sense of the mathematical theory of games. They are called 'semantical games", and the semantics based on them is called game-theoretical semantics. Its basic ideas are explained most easily by reference to formal but interpreted first-order languages. Such a language, say L, can be assumed to have a finite number of primitive predicates that are interpreted on some given fixed domain D.