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The 3-level paradigm is not simply a description of inter-level relationships, though it is very useful simple as such. It is also a dynamical interpretation of the emergence of new levels of organization in complex self-organizing systems. It says, first of all, that new levels do not appear, or should not be analyzed as appearing, at the top or bottom of a existing hierarchy of organizational levels, but always as emerging in between pre-existing levels of organization. Salthe's original characterization of the inter-level relationships (constituency and contraint, or in his terms, initial and boundary conditions) already implies a set of informational relations as well: the new intermediate level of organization filters out information from [N-1] for [N+1], and informationally buffers the dynamics of [N+1] against (normal scale) fluctuations at level [N-1]. What I do here is to more formally assimilate this to the semiotic paradigm (which leads to the principle of alternation).
It is worth noting that Peirce's view of the sign as essentially triadic (i.e. X, R, SI), in comparison to Saussurean more dyadic views (signifier and signified), introduces the essential notion of the context-dependence of meaning which is somewhat backgrounded in other models of semiotics (though never absent). The SI here is not simply a formal system of correspondences or interpreting rules; it is a material system that does semiosis, that reacts to R's in ways that are adaptive to the underlying X's. (In Bickard and Terveen's terms, this is an interactive, not an encoding view of semiosis.) Two features of the mapping of organizational levels in complex systems onto the triadic view of semiosis are highly non-trivial (one can always map any triple onto another triple). First is the claim that the SI, in order to do semiosis, must be at a higher scale (either in spatial extension, or in temporal duration and reactivity, or both) than the scale of R's and of X's. To do semiosis you have to be able to assess difference in context, difference across space and/or across time. The scale relation of R-to-SI must be order-of-magnitude greater than the scale relation of R-to-X. The second non-trivial element is the principle of alternation itself: that the emergence of new levels of organization correspond to the re-organization of continuum variation from below as discrete typological equivalence classes with respect to the reactivity of the SI supersystem, and/or to the reorganization of discrete types at lower levels as continuously variable meaningful input to the SI.
What do we see in real complex hierarchically organized infodynamical systems?
I believe we can discern a pattern that may be highly significant for any model of the evolution, development, and emergence of semiosis in such systems: this pattern of alternation across levels of the re-organization of typological information as topological meaning, and of topological information as typological meaning ---