Fuzzy sets

Continuing the last post, in chapter 2 of Sattler's book, Wilber's AQAL Model and Beyond, he reiterates a point I've long made in the "Real and false reason thread" regarding set theories: Some sets are fuzzy, meaning a member can be both partially in and out of a defined set. Hence a part is not completely subsumed in a larger holon as in the typical nested concentric circles. One kind of set theory does that, another kind (fuzzy set) does not. The former nested set forms one kind of hierarchy, the fuzzy kind form what I've come to call hier(an)archical synplexity. Both are internally consistent depending on which set axioms you choose, yet both are inconsistent with each other.


Then again, which set axioms are more consistent with cognitive science given its own methodological axioms? It depends on which cogsci you use. The 1st generation is built on what Lakoff calls the necessary and sufficient categorical conditions of disembodied, abstract reason. The 2nd generation is built on the fuzzy categories of embodied reason. The question becomes which is more empirically accurate given advances in the field?