In my research I came upon this free e-book called Spinbitz: Interface Philosophy, Mathematics and Nondual Rational Empiricism, A Philosophy of Vision-Logic Interfaces. Here's the "spin" on it from the site:

 

SpinbitZ is a playful, whirling, churning, folding and unfolding set of concepts for the illumination and integration of abstract philosophical ideas, through the integrated use of the imagination and its percepts.  SpinbitZ constructs a set of philosophical "graphical user-interfaces" at the vision-logic level of cognition.  It is thus a philosophy of vision-logic interfaces, employing the "triune interfaces," or "cultivated thirds" hidden within the polarities of every duality, dichotomy, controversy and paradox to build a consistent system for the effective understanding and resolution of their key esoteric truths, rather than for their dualistic and reactionary refutation.  In using these interfaces to trace a nondual thread of rationality to its historical roots, it is discovered that only the dualistic, exoteric (or commonly understood) forms of rationality begin with the Greek trinity:  Socrates, Plato and Aristotle.  By reconnecting to the earlier nondual truths of Heraclitus and Parmenides, the conceptual axis-mundi itself (what Lao Tzu called "the door to all wonders") is found spinning at the core of Zeno's paradox, and thus at the core of nondual rationality.  Through a fusion of Art, Science, Mathematics and Philosophy—and with the help of nearly a hundred detailed diagrams and illustrations—this embryogenesis of rationality is traced as it reconnects to the alternative lineage of philosophy uncovered by Deleuze, with a nondual fusion of the systems of Spinoza and Leibniz.

In esoteric Theosophy it is said that in the "shock" of the interface between Spinoza and Leibniz "the essence and Spirit of esoteric philosophy would be made to appear."  Unfolding through these vision-logic interfaces, this Interface Philosophy finally appears to reconcile many of the dualities plaguing the history of exoteric rationality.  In its nondual interface with empiricism and Integral theory, for example, a detailed sketch of an Interface Epistemology is unfolded.  Operating at the crossroads of the ontic-epistemic (reality vs. knowledge) and subject-object polarities, the evolutionary symbiogenesis of the exoteric dichotomies at the foundations of human knowledge is examined—illuminating and reconciling the "ontic-shadow" of post-modernity. 

The process of reanimating these hidden nondual truths of rationality demonstrates that mathematics itself mirrors this holarchic structure implicit in the embryogenesis of the concept.  This is because mathematics, as the art and science of pure relation, employs the most rarefied and abstract form of the concept, e.g. numbers and operations.  Unfolding in layer upon layer, this Interface Mathematics transitions from the "oppositional forces" of dualism, ultimately again to the "intensive," integral or "second-tier" truths, and to the originary axis-mundi of the nondual.  In making mathematics visible, visceral and understandable—a Vision-Logic Coordinate System is constructed revealing two fundamental axes of conceptual thought (one of which is this axis mundi or immanent/transcendent axis).  Spinoza's "three infinities" are then shown as the triune interface, or cultivating third between these binary axes, for illuminating and reconciling the many paradoxes and controversies of infinity—e.g. Zeno's, Galileo's and Cantor's—as they wind their way into the truths of our modern mathematics of the continuum and set-theory.

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This is a great discussion, and thank you guys for engaging in the material.  I gain lots from watching the turbulence at the interface of its reception.  It illustrates to me, however, the problems with the linear format both of the book and of verbal understanding.  I had long internal debates about how to inform the dendritic trajectory of the linguistic lens as it traces the semantic body.  One clear problem with the result is that the underlying epistemological framework assumed and emergent throughout the work, is only expressed fully at the end of the book.  Back to source, as it were.  Which is why I emphasised at the beginning the importance of a full read---invoking the entire semantic body in the mind, the plane of consistency---before attempting (seriously, anyway) a deconstruction.  But then this is why it should be recieved, embodied and dissected much more efficiently (and holistically) in an integral setting.  

 

At any rate, this in mind, I'd like to calibrate a few apparent misalignments.

 
Upfront, it's important to understand the general implicit epistemic view here.  Conceptuality, in all its forms, is representational.  It's all really (and real) metaphor, projection, and reflection.  Spin on/in bitZ.  When I invoke Koestler's 'holarchy' spell it is always in this sense.  Terms are terminals; windows into wasteland catacombs of categories; lenses slicing through branches and worms by the sheer differential of their frequency of propagation.  The rules of connection and degrees of freedom at one level are not those of the other.  But the one can be used to invoke revealing echos and resonances of the other's interiors.  And so the evolutionary power in the return stroke of 'holarchy' emerges into stabilized form...and we press it into action.  So again, yes, all is holarchy in the same sense that all is not holarchy.  All is one in the same sense that it is not.  Omni-non.  That's the basis of the univocity framework in the integration of the absolute and relative scopes at the heart of the nondual form of rationality...as lensed in this work, at any rate.

 

Regarding the discussion on the holarchical underpinnings of post-Cantorian set theory (and perceptual/conceptual representation) theurj says:  'It seems that Morrison's notions of "natural" hierarchies assumes that the container metaphor is "real." I.e., because our natural image schemas are so close to the thing-in-itself he, like so many others, assumes it is in fact the thing-in-itself.'  

 

In the later discussions of the underlying meta-paradigm epistemology, it becomes more apparent the function of the evolutionarily formed and informed ->percept->concept->symbolic metaphors emergent from empirical contact with holarchical reality in human embodiment.  The container/holon metaphor is a metaphor, yes.  It is an epistemic or representational construct.  But the epistemic transcends and includes the ontic, in terms of depth (and in terms of span, is a subset of it).  The container metaphor is "only" a metaphor, but it is nonetheless real.  Its reality comes from its usefulness in conceptuality, which in turn comes from a multi-billion year sensory-mnemonic training period of the human pheno-/genotypic trajectory through evolution.  Why does the concept of the holon afford so much usefulness to the imagination?  Because, as is relatively apparent (relative truth) from our collective empirical explorations, it evolved in contact with reality, which, in part, *is* holarchical.  This is what is being demonstrated in revealing its presence also (along with in physics, cosmology, biology, etc) in the mereological underpinnings of modern post-Cantorian set theory.  But not *everything* (ALL-ONE or absolute) is holarchy, or is best understood with that concept.  There are 'heaps' as well as subtillions of other more apt concepts to be used as needed.  This is no holarchical absolutization.  And the absolutization of *any* concept is contradictory to the tenets and structure of the underlying system (e.g. univocity framework).

 

theurj also states: "Hence he argues against notions of the empty set and mathematical infinity in this section because they don't fit in the container schema."


I demonstrate why the embodied symbol-conjunction of 'empty' and 'set', in naieve set theory ends up generating confusion and paradox, yes, and why naive set theory came to adopt again the mereological (holonic) form, even if unwittingly so.  But this is not the same as arguing against the concept of the empty set in general.  As you say, "abstract categories somehow lose the connection to this natural, implicit holoarchy."  They can often become abstracted away from this embodiment in percept and evolution.  Floating nipples can be arranged any way you like on the body, regardless of any supply of milk, their "evolutionary peduncles" having been "suppressed" and forgotten.  And so inconsistent conjunctions are allowed in this new state-space; forms that no longer have grounding (or haven't yet been adapted as such) in an epistemic correlation to the ontic (as a map).  But this is not to say that the "empty set" has, or could have no usefullness.  It simply enables a new perspective from which to see the nature of its power.  Being a computer programmer, I understand quite well the value of non-empirical abstractions.  


theurj also states: "Morrisson doesn't see the error in our intuition but rather with the mathematical notions of infinity."

 

I'm not aware of any point at which I argue against mathematical notions of infinity, but rather quite the reverse.  What I show is *why* they are valid in understanding the nondual nature of perceptual->conceptual->rational reality, as well as how they can be better understood in this context, implicitly and explicitly revealing the resolution to the core paradoxes of the infinite already implicit in the body of modern mathematics.  In my view I validate the mathematical notions of infinity, along with post-Cantorian set theory, including Cantor's corpus as well.

 

So, no, I don't "see the container metaphor itself as a literal expression of truth," any more than ALL metaphors are an expression of truth...and they are, in my view.  But yes, "...Spinbitz is leaving out some serious research for his mathematical project...".  Such is the nature of expansion.  Always room to grow.  

 

Thanks again, theurj and everybody for engaging this subject.

 

Welcome to the forum Joel. It's always good to engage the author if possible to get to the intended meanings. I must admit that math is not my bailiwick so my comments were at best meager and tentative attempts at understanding your text. And I admit that I did not complete the reading of your book, only getting as far as I've referenced in this thread. Perhaps your presence will motivate me to pick up my reading again and take advantage of your participation.

Hey, thanks.  I'd love to help in any way I can.

theurj said:

Welcome to the forum Joel. It's always good to engage the author if possible to get to the intended meanings. I must admit that math is not my bailiwick so my comments were at best meager and tentative attempts at understanding your text. And I admit that I did not complete the reading of your book, only getting as far as I've referenced in this thread. Perhaps your presence will motivate me to pick up my reading again and take advantage of your participation.

For anyone interested, Joel is currently conducting an online SpinbitZ course at Bonnie's Magellan site:  SpinbitZ Course

I shared my "Sophia Speaks" paper with Joel, the author of SpinbitZ, and I wanted to share one of his comments about it here.  (It was on a Facebook group page, so I don't think everyone here can access it.) 

Layman, I think you might find his work to be a powerful example of what you call the Metaphysics of Adjacency (which he terms "Interface Philosophy").  A link to his book is in the opening post of this thread.

~*~

"AQAL is one particular evolutionary foray into the field of onto-epistemic lenses (generated and generative maps), which does indeed represent a significant portion of the evolving Story of Philosophy, even if it has inherited shadows and blindspots from an Orthodox and Mythic collective reading of History (center of gravity). But given the AQAL map itself, and KW's own words, we should indeed expect to see a distorted image of the Rational in the social holons of a proto-Rational age.

In such an age, however, AQAL's power and freedom stems from its focus and limitation in the categorical simplicity of its form (mythemes). To the extent that it speaks at the dominant level(s), it gains traction. But AQAL is only *locally* simplex, in the interfacing here at the mythic-rational collective interface and transition. There are deeper and wider simplexes in its vicinity.

A key one that I just got excited about comes from the limits on what I'll call the "linguistic lens," in an "Aspect Oriented Philosophy". Bruce Alderman's recent article, "Sophia Speaks: An Integral Grammar of Philosophy" (ITC 2013) has really inspired me here. [[I got a sneak peak and highly recommend it. And I hope you don't mind my sharing of enthusiasm for it here prematurely, Bruce.]] So according to Bruce's Integral Grammar method/model, and as should be apparent, AQAL is essentially a Pronoun Philosophy, in emphasis not in exclusion or principle. It is simply an exemplar of the form. And such a philosophical focus represents only one type of onto-epistemic lens in the whole landscape of an implicit and embodied (and embryogenic) integral grammar, which Integral Philosophy (the *involutionary mode* of philosophy in this global transition) in general is exploring.

As a testament to the generative capacity of Bruce's work, I am seeing my own work in Interface Philosophy through a very helpful new onto-epistemic lens. I see it more clearly now as what Bruce calls "onto-choreography" and "heno-ontology" (iirc) with a (heretofore largely implicit) "aspect oriented" focus on the linguistic lens and grammar primitive in many of its forms. Most clearly, however, it appears largely as a Prepositional, or even Meta-Prepositional Philosophy, with a visual and nounal languaging: An "interface" being the dynamic "between" (cultivating third) of positions, perspectives, and critically directions and motions. But the prepositional interface also mediates other key prepositions couched in nouns, such as Substance (within, below, or Immanence) and God (without, above, or Transcendence), as well as critically, the absolute and relative scopes. And I also use it to interface the AQAL pronouns, in SpinbitZ.

Anyway, that's what I am seeing now, and I'm pretty excited about all the new bits and pieces coming together from all over."

I'm reading this book now.  It's very dense reading.

Joe

Indeed, it is!

Very cool -- Joel Morrison's visionary art (for his "interface philosophy") is being featured on Integral Life, wtih commentary by Michael Schwartz.

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