Elements of the cognitive universe

Based on philosophical considerations, interpretations which connect concepts from the cognitive universe are presented. The resulting abstract theory is downward compatible with basic elements of Shannon Theory. Though philosophically based, the theory is quantitative and besides pragmatic with a multitude of possible applications, some of which are indicated. Major attention is payed to the concept of inference. Technically, this is based on two-person zero-sum games and notions of equilibrium play a central role. This will lead us to abstract versions of the Pythagorean theorems, thereby uniting classical geometric results rooted in antiquity and probabilistic results on information projections which are well known to the information theory community. Concepts of equilibrium also lead to a notion of core which is closely related to that of exponential families as known from the the theory of statistical inference.