The following are my responses to date on a FB thread by Trisha Marie.
I agree with Tom that Platonic forms (and math itself) are part of a metaphysical, misplaced concreteness projected as independent of our cognitive processes. This is what Lakoff calls ‘false’ reason. And yet as I’ve shown in the Ning IPS thread on “real/false reason,” the model of hierarchical complexity, with its objective (and Platonic) math, is itself guilty of this very same false reasoning.
E.g. What I find most revealing is Common’s discussion of Plato, Aristotle and Thales. The MHC “follows in the tradition,” being “a mathematical theory of the ideal. It is a perfect form as Plato would have described it” (315). I wonder whether the MHC itself, assuming such formal, metaphysical characteristics as the above–even being a literal Platonic ideal–isn’t itself just an extension of formal operations.
That discussion also covers what Lakoff calls real reason and embodied realism/metaphysics, a different animal.
Lakoff’s embodied realism though is not ‘just’ constructivist. E.g. see Philosophy in the Flesh (1999), pp. 5-6, where he criticizes such a view. Also Lakoff said the following about math in this interview:
“What our results appear to disprove is what we call the Romance of Mathematics, the idea that mathematics exists independently of beings with bodies and brains and that mathematics structures the universe independently of any embodied beings to create the mathematics. This does not, of course, result in the idea that mathematics is an arbitrary product of culture as some postmodern theorists would have it. It simply says that it is a stable product of our brains, our bodies, our experience in the world, and aspects of culture. The explanation of why mathematics ‘works so well’ is simple: it is the result of tens of thousands of very smart people observing the world carefully and adapting or creating mathematics to fit their observations. It is also the result of a mathematical evolution: a lot of mathematics invented to fit the world turned out not to. The forms of mathematics that work in the world are the result of such an evolutionary process.”
In the Lakoff interview above he discusses that different metaphors of causation produce different inferences. Hence it is a version of integral methodological pluralism (IMP). The mistake comes when philosophers “pick their favorite metaphor for causation and put it forth as an eternal truth” (11).
Which of course reminds me of Edwards’ multiple lens needed for an IMP. In this post I showed how he wondered if there was some explanation why human experience always showed up as these multiple lenses, which I related to image schema. Edwards concludes that AQAL theory places far too much emphasis on the developmental holoarchy lens. Lakoff likewise sees the objectivist paradigm as being too reliant on hierarchical set/category theory based on particular image schema. That is, getting caught in a favorite metaphor of causation and assuming it as an a priori eternal truth.