Rule-following as an Anticipatory Act: Interaction in Second Person and an Internal Measurement Model of Dialogue

We pursue anticipation in second person or normative anticipation. As the first step, we make the three concepts second person, internal measurement and asynchroneity clearer by introducing the velocity of logic vi and the velocity of communication v, in the context of social communication. After proving anticipatory nature of rule-following or language use in general via Kripke's "rule-following paradox", we present a mathematical model expressing the internality essential to second person, taking advantage of equivalences and differences in the formal language theory. As a consequence, we show some advantages of negatively considered concepts and arguments by concretizing them into an elementary and explicit formal model. The time development of the model shows a self-organizing property which never results if we adopt a third person stance.