More on postmetaphysics

Continuing the last post, Tom replied: "I’m not sure I would take it quite that far Edward. What prototype theory does is not so much invalidate hierarchies, as show that, assuming they do roughly approximately capture some aspect of reality (which I think they do), they are imperfect maps. In the same way that simple concepts (as categories) are partial truths but err in forcing clean boundaries (and clean hierarchical relationships). I do think that prototype theory and the theory of “natural kinds” in concept formation is incredibly important for all theory makers and users to know about."

I replied:

Lakoff also noted in Women, Fire and Dangerous Things:

"The classical theory of categories provides a link between objectivist metaphysics and and set-theoretical models.... Objectivist metaphysics goes beyond the metaphysics of basic realism...[which] merely assumes that there is a reality of some sort.... It additionally assumes that reality is correctly and completely structured in a way that can be modeled by set-theoretic models" (159).

He argues that this arises from the correspondence-representation model, a metaphysical system.

And this one is significant, which was made apparent in my discussions with Commons:

"In objectivist cognition, concepts by definition exclude all nonobjective influences.... For example, the properties of basic level concepts [their embodiment]...cannot be true properties of concepts in an objectivist theory" (165).

Hence the complete avoidance of Lakoff's (and company) work; it is not "objective" and proven (i.e., circle-jerked) with so-called objective, mathematical, set-theorectical axioms.

And this one that nails the MHC's categorization structure:

"The classical theory comes with two general principles of organization for categories: hierarchical categorization and cross-categorizaton. [In the former] a partition of a category into sub-categories such that all members are in one, and only one, subcategory.... [In the latter] a number of hierarchical categories at the same level.... [these] are the only organizations of categories that exist" (166-7).

A key reason Lakoff is ignored by hierarchical complexifiers:

"It is the classical concept of a category, the concept that contemporary research on prototype theory claims is untenable as a fully general approach. If that concept changes in an essential way, then most, if not all, of objectivist metaphysics and epistemology goes. What is at stake is a world view" (174).

Yep, a formop worldview dressed up as postop and integral, with the math to prove it. Never mind that the math is also formop based on classical category theory. Lakoff challenges the  unconscious presuppositions and premises upon which such theory is based and taken as given.