I posted the following in the Yahoo Adult Development forum and am cross-posting here. I'll keep you apprised of some key responses, provided I get any: 

Building on the post below* regarding Lakoff's embodied reason, he seems to call into question the type of abstract reasoning usually found at the formal operational level. This appears to be false reasoning based on the idea that reason is abstract, literal, conscious, can fit the world directly and works by logic (also see for example this article ). If formal reasoning is false wouldn't this call into question some of the assumptions of the MHC? That perhaps this "stage" is a dysfunction instead of a step toward post-formal reasoning? 

Now Lakoff has his own hierarchy of how embodied reason develops: image-schematic, propositional, metaphoric, metonymic, symbolic. (See for example "Metaphor, cognitive models and language" by Steve Howell.) So I'm wondering how the MHC takes into account Lakoff's work here and how it answers his charge of false reason? Terri Robinett noted in his Ph.D. dissertation (at the Dare Association site) that "work has already begun by Commons and Robinett (2006) on a hierarchically designed instrument to measure Lakoff’s (2002) theory of political worldview." So perhaps you can shed some light on this? 

* This is the referenced post: 

Since Michael brought up Lakoff as perhaps being "at right angles to the stage dimension" I read this by Lakoff this evening: "Why 'rational reason' doesn't work in contemporary politics." He distinguishes between real and false reason, the former being bodily based and the latter existing in some sort of objective, abstract realm. Very interesting indeed. Here are a few excerpts: 

"Real reason is embodied in two ways. It is physical, in our brain circuitry. And it is based on our bodies as the function in the everyday world, using thought that arises from embodied metaphors. And it is mostly unconscious. False reason sees reason as fully conscious, as  literal, disembodied, yet somehow fitting the world directly, and working not via frame-based, metaphorical, narrative and emotional logic, but via the logic of logicians alone."
"Real reason is inexplicably tied up with emotion; you cannot be rational without being emotional. False reason thinks that emotion is the enemy of reason, that it is unscrupulous to call on emotion. Yet people with brain damage who cannot feel emotion cannot make rational  decisions because they do not know what to want, since like and not like mean nothing. 'Rational' decisions are based on a long history of emotional responses by oneself and others. Real reason requires emotion."

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I don't know. After about a year of study I'm finally just beginning to get a handle on L&J's work. I can't say I understand much about Meillassoux at this point, so I'm not qualifed for this comparison. Although some of these same issues were addressed in the original Meillassoux thread and my first response on that thread was the following:

Just a quick comment this morning. Rayburn's review at Amazon said:

"Guided by Badiou's use of set theory, Meillassoux argues that Hume's probabilistic reasoning rests upon the dubious assumption that the set of possible outcomes of an event can be totalized. Probability as a metaphysical fact is undermined by Cantor's discovery of "transfinites"--that is, the multiplicity of infinities that cannot be gathered into a single 'meta-set.'"

This seems to be related to my prior critique [in this thread] of holarchical complexity?
Here’s an interesting excerpt on Meillassoux and Badiou from The Black Swan: The End of Probability by Elie Ayache (Wiley, 2010):

“How could the thing-in-itself…be even remotely sensitive to a theorem which obtains within the confines of mathematics? It is here that Alain Badiou’s meta-ontology lends Meillassoux the support he needs. ‘The thesis that I support,’ he [Badiou] writes, ‘does not in any way declare that being is mathematical, which is to say composed of mathematical objectivities. It is not a thesis about the world but about discourse.’ Mathematics is a thought (and not just a calculus), and it is thought that asserts existence through the orientation of its discourse” (146-7).
The following on Badiou’s math doesn’t sound anything like how it’s used in the MHC. Or in Plato, the foundation of MHC math theory. From Wikipedia:

Mathematics as ontology

For Badiou the problem which the Greek tradition of philosophy has faced and never satisfactorily dealt with is the problem that while beings themselves are plural, and thought in terms of multiplicity, being itself is thought to be singular; that is, it is thought in terms of the one. He proposes as the solution to this impasse the following declaration: that the one is not. This is why Badiou accords set theory (the axioms of which he refers to as the Ideas of the multiple) such stature, and refers to mathematics as the very place of ontology: Only set theory allows one to conceive a 'pure doctrine of the multiple'. Set theory does not operate in terms of definite individual elements in groupings but only functions insofar as what belongs to a set is of the same relation as that set (that is, another set too). What separates sets out therefore is not an existential positive proposition, but other multiples whose properties validate its presentation; which is to say their structural relation. The structure of being thus secures the regime of the count-as-one. So if one is to think of a set — for instance, the set of people, or humanity — as counting as one the elements which belong to that set, it can then secure the multiple (the multiplicities of humans) as one consistent concept (humanity), but only in terms of what does not belong to that set. What is, in following, crucial for Badiou is that the structural form of the count-as-one, which makes multiplicities thinkable, implies that the proper name of being does not belong to an element as such (an original 'one'), but rather the void set (written Ø), the set to which nothing (not even the void set itself) belongs. It may help to understand the concept 'count-as-one' if it is associated with the concept of 'terming': a multiple is not one, but it is referred to with 'multiple': one word. To count a set as one is to mention that set. How the being of terms such as 'multiple' does not contradict the non-being of the one can be understood by considering the multiple nature of terminology: for there to be a term without there also being a system of terminology, within which the difference between terms gives context and meaning to any one term, does not coincide with what is understood by 'terminology', which is precisely difference (thus multiplicity) conditioning meaning. Since the idea of conceiving of a term without meaning does not compute, the count-as-one is a structural effect or a situational operation and not an event of truth. Multiples which are 'composed' or 'consistent' are count-effects; inconsistent multiplicity is the presentation of presentation.

Badiou's use of set theory in this manner is not just illustrative or heuristic. Badiou uses the axioms of Zermelo–Fraenkel set theory to identify the relationship of being to history, Nature, the State, and God. Most significantly this use means that (as with set theory) there is a strict prohibition on self-belonging; a set cannot contain or belong to itself. Russell's paradox famously ruled that possibility out of formal logic. (This paradox can be thought through in terms of a 'list of lists that do not contain themselves': if such a list does not write itself on the list the property is incomplete, as there will be one missing; if it does, it is no longer a list that does not contain itself.) So too does the axiom of foundation — or to give an alternative name the axiom of regularity — enact such a prohibition (cf. p. 190 in Being and Event). (This axiom states that all sets contain an element for which only the void [empty] set names what is common to both the set and its element.) Badiou's philosophy draws two major implications from this prohibition. Firstly, it secures the inexistence of the 'one': there cannot be a grand overarching set, and thus it is fallacious to conceive of a grand cosmos, a whole Nature, or a Being of God. Badiou is therefore — against Cantor, from whom he draws heavily — staunchly atheist. However, secondly, this prohibition prompts him to introduce the event. Because, according to Badiou, the axiom of foundation 'founds' all sets in the void, it ties all being to the historico-social situation of the multiplicities of de-centred sets — thereby effacing the positivity of subjective action, or an entirely 'new' occurrence. And whilst this is acceptable ontologically, it is unacceptable, Badiou holds, philosophically. Set theory mathematics has consequently 'pragmatically abandoned' an area which philosophy cannot. And so, Badiou argues, there is therefore only one possibility remaining: that ontology can say nothing about the event.
Hey, Edward, thanks for digging those excerpts up. That's clarifying for me. I can't say completely clarifying, as when it comes to math I'm mostly in the dark. But I can follow those arguments enough to gather that Badiou and Meillassoux aren't appealing to mathematical concepts as Platonic forms or involutionary givens.
Here's a good wikipedia article on the philosophy of mathematics, giving a general overview of the various schools. We can see how the origins and results of math depend on a particular philosophical perspective. For our purposes we could ask which are more or less postmetaphysical?
In my continuing inquiry into this topic, I was re-reading the "ladder, climber, view" thread, wherein I said the following on p. 2:

"Gidley talks about the difference between research that identifies postformal operations (PFO) from examples of those that enact PFO. And that much of the research identifying PFO has itself 'been framed and presented from a formal, mental-rational mode' (109). Plus those enacting PFO don’t 'necessarilty conceptualize it as such' (104), meaning the way those that identify it do, i.e., from a formal operational (FO) mode. Which is of course one of my key inquiries: Is the way PFO is identified through FO really just a FO worldview interpretation of what PFO might be? Especially since those enacting PFO disagree with the very premises of the FO worldview and its 'formally' dressed PFO?

"This is also part of the problem with a strictly mathematical model of hierarchical complexity based on set theory. Phenomenon, including human cognitive structures, do not fit nicely into one 'set' or category so that they can be completely included and subsumed into the next higher set or category. At best each phenomenon interacts with another more like a venn diagram, overlapping with some area in common, but other areas that are not included and subsumed in a higher synthesis. Which is why I wonder whether the formal study of postformal enactments in methods like the MHC is itself a formal or PF enactment. Or some venn combination between, sharing partial sets from both?"

[The Gidley article is at this link.]
In my research I came upon this free e-book, Think Again: Alain Badiou and the Future of Philosophy (Continuum, NY: 2004). It contains a variety of critical responses to Badiou's work with contributions from Zizek, Brassier, Laclau and Nancy, among others. Here's a brief excerpt from the Introductin by Hallward , which nicely sums up the idea of math as ontology:

"Badiou explains in the difficult opening meditations of Being and Event, mathematics is the only discourse suited to the literal articulation of pure being qua being, or being considered without regard to being-this or being-that, being without reference to particular qualities or ways of being: being that simply is. More precisely, mathematics is the only discourse suited to the articulation of being as pure multiplicity, a multiplicity subtracted from any unity or unifying process. Very roughly speaking, the general stages of this argument run as follows: (i) being can be thought either in terms of the multiple or the one; (ii) the only coherent conception of being as one ultimately depends on some instance of the One either as transcendent limit (a One beyond being, or God) or as all-inclusive immanence (a cosmos or Nature); (iii) modernity and in particular modern science have demonstrated that God is dead, that Nature is not whole, and that the idea of a One-All is incoherent; (iv) therefore if being can be thought at all, it must be thought as multiple rather than one; (v) only modern mathematics, as founded in axiomatic set theory, is genuinely capable of such thought. Only mathematics can think multiplicity without any constituent reference to unity. Why? Because the theoretical foundations of mathematics ensure that any unification, any consideration of something as one thing, will be thought as the result of an operation, the operation that treats or counts something as one; by the same token, these foundations oblige us to presume that whatever was thus counted, or unified, is itself not-one (i.e. multiple).

A ‘situation’ as Badiou defines it is simply any instance of such a counting operation, whereby a certain set of individuals things are identified in some way as members of a coherent collection or set.... Now as Sartre himself understood with particular clarity, truly radical change can in a certain sense only proceed ex nihilo, from something that apparently counts as nothing, from something uncountable. Every situation includes some such uncountable or empty component: its void. What Badiou’s ontology is designed to demonstrate is the coherence of processes of radical transformation that begin via an encounter with precisely that which appears as uncountable in a situation, and that continue as the development of ways of counting or grouping the elements belonging to the situation according to no other criteria than the simple fact that they are all, equally and indistinctly, members of the situation (3-4)."
Zizek’s article, “From purification to subtraction,” examines this idea of the empty set as foundation, with a “supernumerary element which belongs to the set but has no distinctive place in it” (162-3). This plays out in politics with those marginalized groups that are part of a system, say its slaves, but have no voice within in. Hence their seeking equality represents that missing part in (but not of) the set that represents the “empty” virtue of equality, whereas the notion of a unitary whole called “equality”, like some Platonic ideal or metaphysical form, has no meaning apart from the missing part that represents it. Hence sets, to put it in Buddhist terms, are “empty” of inherent existence and exemplify dependent origination (multiplicity). More later.
The link with Buddhism was not in Zizek but my inference. Which brings me to a recent addition to Integral World, a re-printed tract by Elias Capriles called "The transreligious fallacy in Wilber's writings." He first discusses how Wilber erroneously transfers the teachings of one tradtion onto another, as in Vedanta unto Vajrayana. And how the former agrees with the dualistic, Orphic roots of Wilber's own edifice, particulary as it refers to the dichotomy of absolute and relative. While I don't understand all the Dzogchen jargon Capriles effuses, his main points sound resoundingly similiar to my own critiques of Wilber's dualistic nondualism. Of specific pertinance to this thread is how Ploninus, continuing in the Platonic-Orphic tradition, views the relation of the One to the Many, and how this differs from both Badiou and Capriles' version of Vajrayana. While I might draw some similarities in the latter two relating Buddhist emptiness with Badiou's interpretation the mathematical empty set, in my inexperience I have no illusions of equating them in yet another transreligious fallacy. In that light let's see what Capriles says about Plotinus and the One, which he parallels with Wilber's own absolute, transcendent Spirit. As well as how the MHC interprets-uses sets and the Platonic ideal, differing from Badiou and Meillassoux thereafter.

To be continued...
Capriles see's Plato's use of the One as dualistic. One is posited as the absolute source of everything, the transcendent principle which steps down into manifest form, an involutionary given from which form depends. Hence the stark division between the transcendent and the immanent characteristic of what is defined as metaphysical. Interestingly Capriles finds this view in alignment with Shankara; hence Wilber's use of both Shankara and Plotinus to fit his own dualistic agenda.

Capriles argues though that the one so defined can only be understood in relation to another concept. It is therefore not transcendent but relative, hidden now beneath the veneer of godhood. He asserts that Buddhism refuses to even broach the subject of the transcendent, that it is delusion. Instead the goal is liberation from such delusion and the method is to rest in empty void, which is none other than the manifest world sans such transcendent roots. However Capriles makes clear that his Buddhism is also not a strictly immanent conception, since that too partakes of the dualism. His nondualism is one that goes "beneath" this divide in the void of emptiness, an emptiness which is itself void of any such distinction.

Which sounds, not surprisingly, similar to Badiou's use of the empty set. Recall from above:

"What is...crucial for Badiou is that the structural form of the count-as-one, which makes multiplicities thinkable, implies that the proper name of being does not belong to an element as such (an original 'one'), but rather the void set (written Ø), the set to which nothing (not even the void set itself) belongs."

Interesting new threads in your inquiry, Edward. Capriles' work is unwieldy reading, as usual, but I'm interested in his perspective. I've been a bit confused by recent equations between "dharmakaya" and notions of spirit as the metaphysical ground of creation that I've heard from Integral Buddhists, since that didn't match my understanding from Buddhist teachers, so it is interesting to read Capriles' views on this. I'm not sure I agree with his overall perspective -- he's a bit of a Dzogchen zealot -- but I think he brings up some important cautions here regarding transreligious comparisons.

Concerning the links between Capriles, Madhyamaka, and Badiou's reading of set theory -- yes, that seems fruitful to me, but I need to read a lot more closely to get a better sense of this. Badiou's work is still very new to me.
More from Hallward's Intro referenced above, where similarities with Capriles can be drawn:

"As the name implies, a subtractive ontology is to be distinguished from a discourse which pretends to convey being as something present and substantial, something accessible to a sort of direct experience or articulation. By subtractive ontology Badiou means a discourse which accepts that its referent is not accessible in this sense. As Badiou conceives it, being is not something that shows itself in a sort of primordial revelation; still less is it the object of some divine or quasi-divine act of creation.... The ontologist knows that the ground of being eludes direct articulation, that it is thinkable only as the non-being upon which pivots the whole discourse on being....in mathematical set theory (the theory of consistent multiplicity) the ultimate ‘stuff’ presumed and manipulated by the theory is itself, as we shall see in a moment, inconsistent – it can be presented only as no-thing. In other words, ontology does not speak being or participate in its revelation; it articulates, on the basis of a conceptual framework indifferent to poetry or intuition, the precise way in which being is withdrawn or subtracted from articulation."

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