This paper is a development and extension of the semantical theory for natural languages proposed and developed by the senior author under the name of game-theoretical semantics (GTS).¹ The topics discussed include the general explanatory strategies for natural-language semantics employed by GTS, the treatment of negation in GTS, and the thesis that the English quantifier-word "any" is always to be considered a universal quantifier. We shall start with no-problems and then consider any-problems, all the while keeping an eye on methodological considerations.