Hier(an)archical synplexity

This is one of my favorite topics as viewed through Lakoff and Johnson's cogsci. E.g., from Philosophy in the Flesh:

"The science and the social sciences all use causal theories, but the metaphors for causation can vary widely and thus so can the kinds of causal inferences you can draw. Again, there is nothing wrong with this. You just have to realize that causation is not just one thing. There are many kinds of modes of causation, each with different logical inferences, that physical, social, and cognitive scientists attribute to reality using different metaphors for causation. Again, it is important to know which metaphor for causation you are using. Science cannot be done without metaphors of all sorts, starting with a choice of metaphors for causation. Most interestingly, if you look at the history of philosophy, you will find a considerable number of "theories of causation." When we looked closely at the philosophical theories of causation over the centuries, they all turned out to be one or another of our commonplace metaphors for causation. What philosophers have done is to pick their favorite metaphor for causation and put it forth as an eternal truth."

I was just re-reading some of Lakoff & Nunez, Where Mathematics Comes From. Even in math there is no one correct or universal math. There are equally valid but mutually inconsistent maths depending on one's premised axioms (354-55). This is because math is also founded on embodied, basic categories and metaphors, from which particular axioms are unconsciously based (and biased), and can go in a multitude of valid inferential directions depending on which metaphor (or blend) is used in a particular contextual preference. Hence they dispel the myth of a transcendent, Platonic math while validating a plurality of useful and accurate maths. However Lakoff & Nunez do not see the above as relativistic postmodernism (pomo) because of empirically demonstrated, convergent scientific evidence of universal, embodied grounding of knowledge via image schema, basic categories and extended in metaphor. They see both transcendent math and pomo as a priori investments.

Specifically as to categorization, more from PITF:

“For the sake of imposing sharp distinctions, we develop what might be called essence prototypes, which conceptualize categories as if they were sharply defined and minimally distinguished from one another. When we conceptualize categories in this way, we often envision them using a spatial metaphor, as if they were containers, with an interior, an exterior, and a boundary. When we conceptualize categories as containers, we also impose complex hierarchical systems on them, with some category-containers inside other category-containers. Conceptualizing categories as containers hides a great deal of category structure. It hides conceptual prototypes, the graded structures of categories, and the fuzziness of category boundaries.”

This is the crux of the developmental holarchy lens/metaphor, itself only one of a multitude of lenses/metaphors (Edwards, 2008). Its inference structure indeed hides a great deal of other categorical structures discussed in the book. While this lens is useful and consistent within its own limited inferential structure, it is inconsistent with other equally valuable metaphorical inference structures. L&J make clear there is no one structure that is the foundation for the others. Hence the problem is that we take the holarchy lens to be the defining context within which all others must be contextualized, often based on some metaphysical premise that it's the way reality itself is organized.

We can also conceptualize container schema differently, i.e., where a so-called smaller holon is not subsumed in a larger one but in which they share a 'space-between' as Mark Edwards calls it. It offers an entirely different approach to hierarchy because the interacting holons retain their autonomy. They structurally couple and create another holon altogether instead of one being subsumed or nested in the other. This is especially significant when you take into account basic categories, which are in the middle of typical taxonomic hierarchies. That is, a hierarchy does not start with the most particular type which is subsumed into the most general type. Those two abstract ends of the spectrum are literally tied together by the basic category in the middle, the most concrete and thus the most closely interactive with the world. Hence this hierarchy is in effect from the middle up and down so that the very nature of hierarchy is entirely different than the typical one. Hence hier(an)archical synplexity.

Rosch's seminal work on prototype theory is still fundamental in cogsci, in that categories have fuzzy boundaries that do share some space with other categories; they are not strictly delineated by necessary and sufficient conditions. Rather basic categories are grounded in our afforded experiences with external objects and provide a base from which to extrapolate more abstract categories. The lines between categories remain graded, with some sharing of qualities. Varela's autopoetic systems are similar in that one's boundary both sustains its closed autonomy yet also allows some open communication and exchange with its environment.