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SEMANTICAL GAMES AND THE BACH-PETERS PARADOX

In this paper the game-theoretical semantics of Hintikka is extended so as to cover some typical uses of the English definite article. It is shown that in this approach the semantical problems involved in the so-called Bach-Peters paradox admit a straightforward solution. The game-theoretical approach is compared with certain other approaches to the paradox. A "logicians' Bach-Peters paradox" is formulated and a solution to it proposed. Finally it is argued that the game-theoretical semantics might even suggest an approach to syntax that discriminates between the different Bach-Peters sentences in a way the transformational syntax does not.