Out of curiosity I did a Google search on the above three words in parentheses as a phrase. In the entire internet there was only one hit and it was to this forum in my discussion of ladder, climber, view. It is a unique phrase and even more, a valid contender for what this forum purports. It might even be a misnomer to call something postmetaphysical "spirituality" given what I said in the thread:

[Referencing "to see a world," see link] "As for turquoise, it reinjects 'Spirit' back into the equation. And therein lies the question for an IPS, how to have a nondual spirituality that doesn’t separate spirituality from the mundane, that doesn’t 'include' the metaphysical interpretations from prior WVs. It might even be an expression of a metaphysical WV holdover to call something 'spirituality,' since the very term indicates the metaphysical notion of an absolute world apart from a relative WV. Granted we can re-define it any way we like but nevertheless its etymology is one of a split, dualistic origin. Another term that can be more easily separated from its metaphysical baggage is 'nondual.' Integral Postmetaphysical nonduality? I’ve already made a strong case that the intersection of American Pragmatism with second generation cognitive science is precisely this WV based on postformal cognitive functioning. And AQAL to boot, though they don’t use those terms."

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Compare to this statement by Commons:

"Lastly, in the early 1960s, many others’ work (e.g., Krantz, Luce, Suppes, and Tversky, 1971; Suppes, Krantz, Luce, and Tversky, 1989; Luce, Krantz, Suppes, and Tversky, 1990) introduced the representational theory of measurement. It is the basis for the Model of Hierarchical Complexity" (315).
Here are some interesting excerpts comparing different schools of cognitive science: classical, connectionist, pragmatist, reductionist. From “Intertheory relations in cognitive science” by Jesus Ezquerro (in CRÍTICA, Revista Hispanoamericana de Filosofía. Vol. 36, No. 106, April 2004: 55–103):

"Functional properties have a mathematical nature, and the classical view takes algorithms as the best
way to capture them, because algorithms are specially apt to describe state transitions between formal, discrete, symbol-like representational structures. In this sense, an algorithm would be constituted by a set of formal rules that operate on representations. Yet, algorithm theory is only a part of mathematics. Other mathematical descriptions may be able to account for that intermediate level between mental and physical properties....level-2 explanations are not necessarily algorithmic but they admit of a different sort of mathematics, such as dynamic systems theory.

"The classical view, Horgan and Tienson contend, entails that cognitive functions have to be specifiable by means of general laws about cognitive states. These laws are realized in particular cognitive transitions, which can be specified by rules on the algorithmic level, so a computation can be determined. However, if there are no such general laws, then the cognitive function will not be tractably computable. In fact, they argue, this is the actual situation in cognitive functions (73).

"Connectionist systems could be thus characterized in this mathematical framework: their transitions do not generally conform to algorithmic relations but can be captured by dynamic mathematics (74-5).

"It might be that our mental life can better be modeled by means of dynamic systems mathematics, as Horgan and Tienson contend, instead of algorithmic operations" (77).
Here's a link to a very technical paper called "The 'dynamic turn' in cognitive linguistics." The abstract:

"The introductory sections of this paper ask the following basic questions about the proper goals of linguistic theory: Why did linguistic structuralism fail as an explanatory endeavour? Why is the understanding of the dynamics of language a primordial goal of linguistic theory? In order to give an explanation of the notion "dynamics" basic notions of dynamic systems theory are introduced informally. Following these questions the paper considers major proposals by Talmy, Lakoff and Langacker and asks how they account for the dynamic aspects of causing/enabling (Talmy's force dynamics), for iterated metaphorical mapping (Lakoff) and for syntactic composition ("construal" in Langacker's terminology). The ad-hoc pictorial models proposed by these authors are compared to mathematically controlled models in dynamic semantics (based on catastrophe, bifurcation and chaos theory). Shortcomings and advantages of the informal and pictorial versus the mathematical description are discussed. The dynamics of phrasal and sentential composition is currently one of the central topics of neurodynamic models based on ERP and fMRI brain scanning. This perspective must be further developed in order to specify the possibilities of future dynamic semantics of natural languages."
Manuel de Landa was mentioned above. In his article "The geology or morals" he discusses both hierarchies and meshworks. Of the latter he uses the example of the autocatalytic loop as studied by Varela and Maturana via autopoesis.

"They are dynamical systems which endogenously generate their own stable states (called "attractors" or "eigenstates"), and they grow and evolve by drift. . {9} An example of the first characteristic are some chemical reactions involving autocatalysis (as well as cross-catalysis) which function as veritable "chemical clocks", in which the accumulation of materials from the reactions alternate each other at perfectly regular intervals . This rhythmic behavior is not imposed to the system from the outside but generated spontaneously from within (via an attractor)."

We've seen this same process described above. Drift happens when a new, unplanned reaction appears from the internal processes thereby complexifying the aggregate, but it isn't generated by an external demand or a higher whole. Again I'm reminded of Bortoft's whole-in-the-parts rather than some overriding whole beyond the parts.

De Landa however is not an apologist for a merely rhizomatic universe in distinction from a hierarchical one. He says:

"The dichotomy between hierarchies and...meshworks, should be understood in purely relative terms. In the first place, in reality it is hard to find pure cases of these two structures....hierarchies give rise to meshworks and meshworks to hierarchies."

This is one reason I like Fisher's approach to altitude in that he combines both. I'm still a little unclear though about the mathematical modeling he uses to measure altitude if it is of the strictly hierarchical type, especially when there is dynamic systems math which seems more appropriate in measuring such dynamic systems as human development.
Wilber doesn't talk frequently about meshworks, except in passing, as I recall, but other Integral theorists do, such as Marilyn Hamilton. Here's something on meshworking from her website:

"What is Meshworking Intelligence?

Meshworking intelligence creates a "meshwork" by weaving together the best of two operating systems — one that self-organizes, and one that replicates hierarchical structures. The resulting meshwork creates and aligns complex responsive structures and systems that flex and flow.

Meshworking intelligences are triggered in the brain by dissonance (ie. constraints) in the environment. The brain's capability of re-organizing itself and releasing new potentials allows for the emergence of new values systems and new capacities. At the same time meshworking intelligence utilizes hierarchical structures and capacities to create sorting and selecting mechanisms that allow the brain to make survival choices. As values systems emerge, a level of complexity develops where our brains can meshwork hierarchies and make hierarchies out of meshworks.

Meshworking intelligence uses imagination, courage and powers of attraction. It articulates designs from the meshing of the diversities in people and thereby releases and reorganizes new intelligences that are currently locked and blocked in silos of sameness.

Meshworking catalyzes a shift in the system, so that new capacities emerge and the system reorganizes itself into something more internally resonant and externally coherent with life conditions.

So What?

Because communities and cities are emergents and artefacts of human life, they are outcomes of the brains that have created them. The meshworks in them seem to be fractal patterns that emerge at all scales of human systems. We can better understand how cities work and evolve by recognizing that their communities reflect evolving capacities to meshwork hierarchies and to make hierarchies of meshworks.

An enormous value of meshworking is that it embraces both the realms of the objective and interobjective space of physical people and built structures, and calls forth the capacities that lie in the subjective and intersubjective zones of the City. These are the inner domains of intention, purpose and culture.

Meshworking intelligences contribute to research, planning and management in the city.

Now What? Three simple rules for applying Integral City Meshworking Intelligences

Catalyze fractal connections within the human hive.
Build communication bridges across silos, stovepipes and solitudes.
Enable meshes and hierarchies that transform, transcend and transmute capacities."
Nice, thanks Balder. That Wilber doesn't is maybe because he equates it with heterarchy only, which only provides "translative" growth. Whereas dynamic meshworks most certainly increase in complexity, aka altitude, but perhaps of a different kind.

I see one of my raisons d'etre as the first injuction above, that of dissonant fractal catalysis. Let me stir the stew, make things meshy and ready for change. Create an emerge-an-see. This is for your own highest good people!
That Wilber doesn't is maybe because he equates it with heterarchy only, which only provides "translative" growth.

Yes, that may be the case. But I think "meshworking intelligence" (and the dynamic models you are discussing above) make it clear that heterarchical change is not "just" heterarchical; that hierarchical-developmental and rhizomatic-meshworking movements give rise to each other, so the distinction between them is not final or absolute.
Let's take a closer look at the Commons article I cited above. The MHC describes two kinds of complexity, horizontal and vertical, which is often translated as heterarchy and hierarchy. The latter type of complexity is described in 3 principles:

"The hierarchical complexity of tasks, or actions, is defined in words as follows. Actions at a higher order of hierarchical complexity: (a) are themselves defined in terms of actions at the next lower order of hierarchical complexity; (b) organize and transform the lower-order actions; (c) produce organizations of lower-order
actions that are new and not arbitrary. These next higher order actions cannot be accomplished by those lower-order actions alone" (308).

The kinds of meshwork processes described above "produce organizations that are new and not arbitrary," and contrary to one of the MHC tenets, are "accomplished by those lower-order actions alone," not a "higher-order action." MHC modeling is to me a fine example of, in Commons' own terms, using a linear model to describe non-linear processes. Hence we get such "representational" limitations.

The catalyst in the meshwork process is an "attractor," which arises from within the process, not without like a higher-order action coordinating the process.
Are you posting these critiques on the Yahoo adult development forum? Are you getting any responses from Commons or others there?
I gave up this inquiry at that venue a long time ago, as Commons was getting overtly hostile to my persistent questioning. Since then I've seen some posts from followers (with tacit Master approval) that are pulling a Wilber, i.e., if you don't buy the MHC program in toto as laid down by the Master then you must be interpreting it from a lower than post-formal "performance." This kind of insular hegemony is part and parcel of such metaphysical, representational models of "altitude."
My research led me back to Visser's ITC presentation on evolution. He reiterates Wilber's insistence on Spirit as skyhook pulling the process of evolution upward, since it existed apriori and "came down" via involution. Or in more materialistic terms, teleos is the driving force, or eros. It's the same idea in the MHC, with its ideal Platonic forms existing apriori and pulling up simpler parts into higher whole, the latter initiating the process mysteriously before they were actually created by the simpler parts in known evolution.

Visser explores Darwin's natural selection as a better explanation, as does Dawkins in The God Delusion. All of which is supported by scientific evidence on how chemicals react via autopoeisis to create novel, more complex stews. Note that natural selection is not random chance, the boogeyman of teleosiacs like Wilber and Commons. What drives or motivates change in natural selection, instead of God, is, well, nature. Things change in the environment and to survive processes and beings must adapt to those environmental forces. I am reminded of the "original" Spiral Dynamics model (before integral) that placed emphasis on life conditions as what drives evolution, not some inner (or spiritual) structures pulling it up. More later.
So how does one develop to a higher stage, if the higher stage is not pulling it up? See this article by Sara Ross discussing the fractal nature of transition steps. An excerpt:

"Adaptation characterizes the transition steps, and is the process by which changes in stage come about. The steps describe the process of adapting: learning to perform tasks at the next order of hierarchical complexity" and

"The stages of hierarchical complexity are the axiomatically defined, mathematically specified performances of tasks. The empirically based transition steps’ dynamics are not yet mathematically specified (although they are partially described by signal detection theory)" (365).

More later.

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What paths lie ahead for religion and spirituality in the 21st Century? How might the insights of modernity and post-modernity impact and inform humanity's ancient wisdom traditions? How are we to enact, together, new spiritual visions – independently, or within our respective traditions – that can respond adequately to the challenges of our times?

This group is for anyone interested in exploring these questions and tracing out the horizons of an integral post-metaphysical spirituality.

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