This book is a collection of studies applying game-theoretical concepts and ideas to analysing the semantics of natural language and some formal languages. The bulk of the book consists of several papers by Hintikka, Carlson and Saarinen and discusses several of the central problems of the semantics of natural language.
The topics covered are the semantics of natural language quantifiers, conditionals, pronouns and anaphora more generally. Hintikkäs famous essay presenting examples of "branching quantifier structures" in English, as well as one formulating his "any-every thesis", are included. The book also includes Hintikkäs closely argued philosophical discussion of the relationships between the new semantical games with the language games of Wittgenstein. Other papers apply the game-theoretical approach to formal languages including tense logics and tense anaphora (Saarinen), deontic logic and Ross¿ paradox (Hintikka), and usual predicate logic (Rantala). The latter amounts to an explication of the "impossible possible" worlds as is shown in Hintikkäs concluding paper.

Language-Games.- Quantifiers in Logic and Quantifiers in Natural Languages.- Quantifiers vs. Quantification Theory.- Quantifiers in Natural Languages: Some Logical Problems.- Game-Theoretic Semantics, Quantifiers and Truth: Comments on Professor Hintikka's Paper.- Rejoinder to Peacocke.- Semantical Games and the Bach-Peters Paradox.- Conditionals, Generic Quantifiers, and Other Applications of Subgames.- Backwards-Looking Operators in Tense Logic and in Natural Language.- Intentional Identity Interpreted: A Case Study of the Relations among Quantifiers, Pronouns, and Propositional Attitudes.- The Ross Paradox as Evidence for the Reality of Semantical Games.- Urn Models: A New Kind of Non-Standard Model for First-Order Logic.- Impossible Possible Worlds Vindicated.