Operational Pointer Semantics: Solution to Self-Referential Puzzles I

In the t rad i t iona l approach to semant ics t r u t h values are assigned to sentence types. Moreover, the mean i ng of l inguistic expressions is given th rough a m a p which associates with t h e m extra l inguis t ic enti t ies, in such a way tha t the mean ing of a complex expression is derivable f rom tha t of its components . By t rea t ing equal ly all tokens of the same expression such an approach makes for an enormous reduc t ion in complextiy. Sometimes modif icat ions are needed: The in te rp re ta t ion of indexicals, expressions such as 'I ' , 'now' etc., is de t e rmined not only by type but by context dependen t parameters : a token of 'I ' denotes the person u t t e r ing it. But these addi t ional pa ramete r s can be specified and made explicit , resul t ing in a p ic ture which is still wi th in the scope of the original conception. Yet some language games convey mean ing in much more compl ica ted ways. They necessi tate a radical depa r tu re f rom the deno ta t iona l style of semantics . These are discourses which involve self-referential applicat ions of semant ic predicates , ' t rue ' , 'false', as well as moda l predicates like 'know' or 'necessary ' .