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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From The Democracy of Objects, chapter 6.2:

"Within the domain of formal reasoning, Z-F set theory shows the inconsistency of any attempt to form a totality or whole. Set theory provides a variety of resources for contesting the consistency of any totality or whole, however, here I'll focus on the power set axiom. As we've already seen, the power set axiom allows one to take the set of all subsets of an initial set....If the power set axiom spells the ruin of any whole or totality, then this is because it reveals the existence of a bubbling excess within any whole or collection.... What the power set reveals is the bubbling pluralism of 'the' world beneath any unity or totality. Any totality or whole, in its turn, is itself an object or One alongside all sorts of other ones.

"At the formal level, the real force of the power set axiom lies in the manner in which it reveals the possibility of a multiplicity of relations and objects within any collective. It will be recalled that any exo-relation between objects is potentially itself also an object. If we ask the strange question, 'when is an object?' we can answer this question with the hypothesis that an object is when exo-relations among other objects manage to attain operational closure such that their aggregate or multiple-composition becomes capable of encountering perturbations as information in terms of their own endo-consistency. On the one hand, the power set axiom reveals the possibility of a plurality of other objects within any collective. On the other hand, the power set axiom discloses the possibility of alternative exo-relations among objects, not present in the whole from which the subsets are drawn. Finally, the power set axiom reveals the possibility of withdrawing objects from their relations to collectives so that they might function as autonomous actors, either entering into other collectives, subsystems, or going it alone within the order of being.

"If, from the standpoint of formal reasoning, the Whole is not, the One is not, or the world does not exist, then this is precisely because these subsets, these other possible objects and relations populating the power set of the Whole or alleged One are neither counted nor countable within the Whole or One. In short, every Whole or One contains an excess within it that is not itself treated as a part of the Whole or One. Put differently, such subsets are included in the set from which they are drawn, without belonging to it. Yet it is precisely this absence of belonging or membership that spells the ruin of the Whole, One, or World."

As to the nature and implications of this excess, see this post and several posts and pages following for one of its manifestations as the objet a.

One of the implications of the recent quotes is that members of a set, i.e., objects that are members of a larger class, are not only defined by the endo-structural relations of that class but also continue to evolve on their own. This reminds me of a previous discussion relating this to levels of development, how each lower level (holon or object) within a higher-level structure (level or object) not only retains its autonomy but itself continues to evolve. So part of an 'integral' view would be not so much how a particular higher level object oversees and subsumes all lower levels within its purview but rather how it recognizes that previous levels continued to grow within it, not just laterally but vertically as well. And how it integrates those 'octaves.' See for example this post and following on Goddard's work, and it's relation to spiral dynamics (not 'integral' trademarked).

In mereological terms, each member of the 'set' has an excess that cannot be completely defined by the set or even any subsets, for the so-called empty set is within it as well as the set in which it is a member. This cannot be explained by the MHC, whose math requires that members of the set are fixed, as it were, to their roles in that set so that they can be totally subsumed in the very definition of a higher level set. I.e., they don't 'grow' but are more like the unchanging Platonic forms, replete with fixed essences, that are the very basis of the MHC and it math.

Also recall this post on Luhmann, how he thought the various parts or levels of the human being are separate systems that, while structurally coupled, are nevertheless operationally closed from each other. That is, those independent systems continue to develop on their own while being part of the larger human being.

Which reminds me of Levin's 'bodies,' and my theory about them being a reiterative spiral process of development. To put it in Goddard's or spiral dynamics (not SDi) terms, so-called levels recur in the next tier, coming to the conscious fore again after their temporary subsumption into the background. However while SD and Goddard see them reoccurring in linear sequence, I see them re-emerging in reverse or mirror sequence. For example, with Levin's bodies the ego-logical body is the last stage of the 1st tier and the fulcrum around which what came before and after reflect. Level 2, the pre-personal body, reemerges as a reconstructed transpersonal body at level 4. The primordial body of level 1 reemerges as the reconstructed ontological body at level 5. I.e., the 'lower bodies' have been developing the entire time, but the early phases of level 3 pushed awareness of that development into the background. The last phase of level 3 allowed an opening into awareness of the prior bodies heretofore hidden development back into the foreground.

Now how this process goes on from here I don't know, as I'm guessing that there will be another twist in the reiterative spiral, one which will likely again change its mathematical formula, since the math is part of this embodied process and not an unchanging archetype. Levin noted that stages 1-3 were linear, stages 4-5 were not. What's next? That's the thing with iteration; something novel emerges that cannot be predicted from what came before.

The following are excerpts from this link and relevant to this thread. Commentary to follow later. Quote:

Complexity can be formally defined as nonlinearity. As a matter of fact, the world is mostly nonlinear. The "linear" world studied by classical Physics (Newton’s equations are linear) is really just an exception to the rule. The science of nonlinear dynamics is also known as "chaos theory" because unpredictable solutions emerge from nonlinear equations.

The first "strange attractor" was "discovered" in 1963 by the USA meterologist Edward Lorenz: it was due to a nonlinear system that evolves over time in a non-repeating pattern. In phase space its evolution looks like an infinite series of ever-changing patterns that seem to be attracted to a point but never repeat the same trajectory around it.

An "order" is a multiplicity that becomes a unity in virtue of its internal organization (in virtue of the pattern of relatedness among its components). Buchler’s "principle of ordinality" states that every natural complex is an order. Basically, the principle of ordinality asserts that every complex must be constituted by other complexes, and that every complex must be one of the constituents of some other complex. Every complex is relative to some other complex, is conditioned by and conditions other complexes.

Von Bertalanffy's "systems"… are those entities ("organized complexities") that consist of strongly interacting parts, usually described by a set of nonlinear differential equations.

Nonlinear systems driven away from equilibrium can generate instabilities that lead to "bifurcations" (and "symmetry breaking" beyond bifurcation). When the system reaches the bifurcation point, it is impossible to determine which path it will take next. Chance rules. Once the path is chosen, determinism resumes.

Eigen came up with the concept of an "hypercycle". A hypercycle is a cyclic reaction network, i.e. a cycle of cycles of cycles (of chemical reactions). Then he argued that life can be viewed as the product of a hierarchy of such hypercycles…. Formally: "hypercycles" are a class of nonlinear reaction networks. They can originate spontaneously within the population of a species through natural selection and then evolve to higher complexity by allowing for the coherent evolution of a set of functionally coupled self-replicating entities. A hypercycle is based on nonlinear autocatalysis, which is a chain of reproduction cycles, which are linked by cyclic catalysis, i.e. by another autocatalysis. A hypercycle is a cycle of cycles of cycles.

In the early 1960s Monod and others discovered gene regulation: genes are assembled not in a long string of instructions but in "genetic circuits". Within the cell, there are regulatory genes whose job is to turn on or off other genes. Therefore genes are not simply instructions to be carried out one after the other…. The genetic program is not a sequence of instructions but rather a regulatory network that behaves like a self-organizing system…. For example, the Danish physicist Per Bak studied the pile of sand, whose collapse under the weight of a new grain is unpredictable: the pile self-organizes. No external force is shaping the pile of sand, it is the pile of sand that organizes itself.

The MHC admits that it measures nonlinear processes, but does so with linear math. Per above nonlinear dynamics appear to use nonlinear differential equations, not linear math. Given I know next to nothing about math is anyone out there familiar with nonlinear math, and how it might differ from the math used in the MHC?

Nonlinear systems also evolve in a non-repeating pattern. I like the idea of hypercycles expressing this, akin to my recent posts. And how genes do not follow a sequence. And the example of a pile of sand, as previously discussed in terms of heaps and holons.

I’m pasting this post over here as well:

Cilliers references Morin in this article, where he says:

"In the first place one has to acknowledge that the 'discipline' of Complexity is a house divided. There are serious differences between different approaches to complexity. After about two or three decades of work explicitly dedicated to the understanding of complex systems, it has become crucial to reflect critically on the value of these different approaches. One way of distinguishing between these approaches is provided by Edgar Morin (2007) who distinguishes between 'general' and 'restricted' complexity. Restricted complexity refers mainly to the mathematical and computational approaches to complexity, often strongly informed by chaos theory. This approach, Morin argues, acknowledges the non-linear, relational nature of complex systems, but seeks to tame it in ways which reintroduces positivism and reductionism. General complexity on the other hand, argues for the limits of all approaches to complex systems and urges that we acknowledge these limits and recognise that we need a new language* in which to do this, a language which moves beyond Enlightenment ideals of neutrality and objectivity."

I also noted this about the "science wars" referenced elsewhere, where Prigogine was on the more general, philosophical side of the debate. One main issue is the idea of math being a Platonic ideal or not explored in depth in the "real and false reason" thread.

And the following post:

Cilliars' article "Complexity, deconstruction and relativism" is instructive is confronting the ill-informed arguments of relativism and performative contradaction within a complexity frame. This passage reveals the hidden positivist and objectivist (i.e., formal) assumption of the argument, one I examined in the real/false reason thread above.

"The performative contradiction is predicated on the assumption that one can adequately distinguish between the performative and the locutionary levels, and, in the terms Habermas uses to criticize Derrida, between logic and rhetoric. However, in order to make this distinction clearly, one would need to take in a position that can characterize what is being said from an external vantage point. In the language of complexity, that would mean that one has access to a framework that is not the result of a strategic choice, i.e. some objective meta-framework. This is exactly what the view from complexity is sceptical about."

We see the same formal assumptions underlying the mathematical model of hierarchical complexity as well as the "restricted" chaos theorists. Again, see the referenced thread [this thread].

* And a new math.

From Morin's paper, "Restricted complexity, general complexity":

"Restricted complexity....still remains within the epistemology of classical science.... Actually, one avoids the fundamental problem of complexity which is epistemological, cognitive, paradigmatic. To some extent, one recognizes complexity, but by decomplexifying it. In this way, the breach is opened, then one tries to clog it: the paradigm of classical science remains, only fissured.

"But then, what is 'generalized' complexity? It requires, I repeat, an epistemological rethinking, that is to say, bearing on the organization of knowledge itself.... In opposition to reduction, complexity requires that one tries to comprehend the relations between the whole and the parts. The knowledge of the parts is not enough, the knowledge of the whole as a whole is not enough, if one ignores its parts; one is thus brought to make a come and go in loop to gather the knowledge of the whole and its parts. Thus, the principle of reduction is substituted by a principle that conceives the relation of whole-part mutual implication.

“Concerning this, the old formula is known that the whole is more than the sum of its parts…. But there is also a substractivity which I want to highlight, noticing that the whole is not only more than the sum of its parts, but it is also less than the sum of it parts. Why? Because a certain number of qualities and properties present in the parts can be inhibited by the organization of the whole…. Thus, the notion of organization becomes capital, since it is through organization of the parts in a whole that emergent qualities appear and inhibited qualities disappear.

“If we think already that there are problems of irreducibility, of indeductibility, of complex relations between parts and whole, and if we think moreover that a system is a unit composed of different parts, one is obliged to unite the notion of unity and that of plurality or at least diversity. Then we realize that it is necessary to arrive at a logical complexity, because we should link concepts which normally repel each other logically, like unity and diversity. And even chance and necessity, disorder and order, need to be combined to conceive the genesis of physical organizations.

“I believe that the word chaos must be considered in its deep sense, its Greek sense. We know that in the Greek worldview, Chaos is at the origin of Cosmos. Chaos is not pure disorder, it carries within itself the indistinctness between the potentialities of order, of disorder, and of organization from which a cosmos will be born, which is an ordered universe…. Chaos and Cosmos are associated—I have employed the word Chaosmos—there is also a circular relation between both terms. It is necessary to take the word chaos in a much deeper and more intense sense than that of physical chaos theory.

“The hologrammic or hologrammatic principle should also be advanced, according to which not only a part is inside a whole, but also the whole is inside the part; just as the totality of the genetic inheritance is found in each cell of our organism, the society with its culture is inside the spirit of an individual…. It is here that the principle of the excluded middle reveals its limit. The excluded middle states ‘A cannot be A and not A’, whereas it can be one and the other. For example, Spinoza is Jewish and non-Jewish, he is neither Jewish, nor non-Jewish. It is here that the dialogic is not the response to these paradoxes, but the means of facing them, by considering the complementarity of antagonisms and the productive play, sometimes vital, of complementary antagonisms.

“It is certain that the idea of a pure objectivity is utopian. Scientific objectivity is produced by beings who are subjects, within given historical conditions, starting from the rules of the scientific game. The great contribution of Kant was to show that the object of knowledge is co-constructed by our spirit. He indicated us that it is necessary to know knowledge to know its possibilities and limits. The knowledge of knowledge is a requirement of the complex thinking.”

Also recall this thread on Desilet, a few excerpts following. Similar information can be found in his Integral World article, “Derrida and Wilber at the crossraods of metaphysics,” to appear in the forthcoming book Dancing with Sophia: Integral Philosophy on the Verge, in which I think Balder will also be appearing.

"A restricted economy imposes a structuring principle that establishes a strong polarity of opposites and clear lines of choice. The structural tension between opposites such as true and false or fact and interpretation operates with a clarity that facilitates either/or alternatives and simplified decision-making. In a general economy, however, every oppositional structure submits to a reversal and a displacement. This displacement involves an extraordinary reconfiguration of the structure or dynamic play between opposites.

"General economy displaces discrete and essential difference between opposites with a new structure that sees the opposition as presenting a tension between elements both different yet connected, both penetrated to the core each by the other yet irreducible one to the other. Plotnitsky calls this structure complementary—after Niels Bohr and the quantum theory of wave/particle duality.

"Applying the principle of complementarity to any oppositional pair yields a structure in which the two sides of the opposition penetrate each other in every instance such that there is no pure instance of either. As will be discussed in the next section, this complementary structure of oppositional relations has profound consequences for the concept of transcendence.

"In a general economy there is no crossing over from one pure instance to another pure instance since no clear boundary separates one instance from the other. This circumstance of structure supports the notion of a universal law of contamination. This universal contamination cannot be explained in simple degrees of mixture, gradation, or shades of difference. Instead, this law of contamination presents the circumstance of superposition—superposition of continuity (irreducible dependence) and discontinuity (irreducible separation).

"The possibility for unique and irretrievable loss inherent in a general economy is theorized at the philosophical level by Derrida in his notion of the trace—a term he uses to describe the nature and quality of being. The trace is an absenting presencing, disappearing as it appears.

"From the language Wilber uses in characterizing his view of Spirit and his view of enlightenment it becomes clear that his spirituality remains within what Derrida calls a restricted economy. There are two primary indicators for assessing Wilber's approach to spirituality as consistent with a restricted economy: 1) the implicit assumptions about the deep structure of basic oppositions such as Emptiness and Form, timeless and temporal and 2) the dominant role of notions such as unity and union.

"Wilber speaks of the overcoming of this dualism in the union of Emptiness and Form and time and timelessness as if each side in the pair were in some sense separate, as if the Emptiness and Form aspects of Spirit could be approached separately in paths that then lead to partial enlightenment. The mere notion of the possibility of partial enlightenment in the sense Wilber suggests is symptomatic of an organization or structuring of oppositional relation in a manner consistent with a restricted economy."

Morin talks mereology, which is also included in the MHC/Wilber models. But so does Bryant and DeLanda talk mereology. The difference being, as explored at length in different threads, how this complex mereology is approached. Morin notes that restricted forms still cling to "classical science," and I'd add classical math. Strange mereology allows for the fuzzy boundaries of members is a set, and the absences within the set, which change the very dynamic of its complexity. All of which allows for not just cosmos but chaos, which must be eliminated at all costs in restrictive models demanding the excluded middle with pretenses to pure objectivity. In a general complexity knowledge of knowledge generation is prerequisite, the kind of work done by L&J and others, and the kind of work ignored by the restrictors.

I’m pasting the following from this post the OOO thread, as it responds to the above. See that post and above for references to the Borromean rings.

Tying together some of the above posts--yes, intentional pun--perfect circles, spheres or cubes cannot tie into Borroean knots. There has to be some twists that don't fit into those perfect abstract and/or Platonic forms, forms which do not allow for the ties that bind. Hence such projected perfection is exemplified by a restricted complexity or economy, where suobjects have very clear and strict bi-valent dividing lines as in formal logic. No excluded middle. Everything is in its place within a perfect Whole. Whereas the twists of real suobjects allow the to meld in a general complexity or economy, blurring the strict distinctions while simultaneously forming inseparable bonds where the middle is included.

And it is this 'middle' which also attests to the different views. In the restricted version it is 'creative' side of the oppositional poles, i.e, causal over relative. Whereas in the general version it is that which ties the knot of the oppositions, being both and neither so that they can never fly apart. And as I've discussed ad nauseum, this kind of middle is entirely immanent, being created and constructed per any machine. In humans it takes the form of image schemas, where we've seen that they arise in the middle of any classical abstract hierarchy. They are khora, differance, and also tie together the various aspects of a human holon: real, symbolic, imaginary. Or the 4 quadrants, if you prefer. In non-human suobjects khora expresses differently particular to their forms. Hence I changed the phrase to image stigmata as a more general rhetaphor for this process.

The following is from Protevi's review of DeLanda's book Intensive Science and Virtual Philosophy. For this post I'm only concerned with Chapter 1, which is about a math where multiplicities replace essences using the concept of the manifold. This allows for “a variable number of dimensions and the absence of a higher embedding space.” Hence concrete universals replace general essences, the former of which do not have sharp borders but rather mesh “in a continuum of yielding zones of indiscernibility, the source of novel ‘becomings.’” These are modeled mathematically via state spaces, attractors and trajectories, a very different language than set theory, the latter of which is caught up in Platonism and which DeLanda seeks to overturn.

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