EPISTEMOLOGICAL AND MATHEMATICAL CONSIDERATIONS ON THE STRUCTURE OF H-SEMIOTIC SYSTEMS

Epistemological and mathematical properties of a class of symbol-oriented systems, H-Semiotic Systems, are explored as a foundation for a form theory of environment. H-Semiotic Systems are hierarchically organized Semiotic Systems, which are Ontologic Systems that confer semantic properties (meaning) to physical interactions. Ontologic Systems are physically open systems defined by epistemologies associated with external Observers and having environments as a consequence of their openness. The Observers, too, are open in receiving physical signals (energy, matter, information) from their environments. The environments of both Ontologic Systems and Observers are dual structures, with afferent and efferent components. Observers occupy the outgoing environments of Ontologic Systems they observe, and make models (representations) of these which become epistemic elements of their (the Observers') incoming environments. Only living systems make models, which divides Ontologic Systems into two categories: objects, which make no models and respond only to ontic reality, and subjects, which make models and respond to these as elements of their total environments which are thus part ontic and part epistemic. In this paper, the symbol content of environmental interactions of H-Semiotic Ontologic Systems is formalized and analyzed from two perspectives, synchronic and diachronic. Synchronic aspects concern time-invariant compositional features. Diachronic properties pertain to succession through time. Formally, semantic content is expressed in terms of linguistic structures defined by structural functions. Time-forward and time-backward structural functions, corresponding to afferent and efferent environments, are described consistent with physical and ecological views of objects and subjects as open Ontologic Systems inseparable from their environments, which define them uniquely.