24 This is indeed the deeper creative and evolutionary function of philosophy, because—as Buckminster Fuller would argue—in a world of increasing specialization, if no-one specializes in comprehensive generalization, then who is looking at the big picture?
28 Interface Philosophy is a study of concepts through the use of percepts—or more precisely, a study of the conceptual roots, relations and patterns of concepts where they merge with percepts into vision-logic interfaces. This then, is an exploration of the perceptual embryogenesis of the concept, and thus an examination of the empirical roots of Rationality itself. …Polarity, as well, is key to bothpercept and concept, and all senses are based on the polarity of contrast. And indeed, polarity will be seen as the opposable thumb of the conceptual mind—fundamentally indispensable as the most primitive and powerful form of conceptual relation. Certainly as well, polarity lies at the very heart of a conceptual understanding of nonduality. …This is therefore largely a work about interfacing infinity—boundingthe boundless and unbinding the bounded. It is also about “pulverizing” and rebuilding the categories surrounding the infinite. Indeed,the infinite will no longer be seen as a “disastrous regress,” but as a boundless source of emergence; a fullness to Emptiness, and a“positive infinity,” what Deleuze calls “the secret of Grand Rationalism.” And hence in order to truly transcend-and-include the rational into the “trans-rational,” one must first interface rationally and conceptually—and indeed perceptually and thus empirically—with the nature of the infinite. One thus moves beyond the common confusions and paradoxes of the infinite, by transcending the common pre-rational set of concepts which generate them.
32 From this Deleuzian plane of consistency the esoteric project of Rationalism becomes vibrant and healthy; ready to explode in long forsaken directions, into a completely new toolset of concepts and perspectives.
37 Deleuze, like Nagarjuna, before him, implores us to think “acategorically,” to “pulverize the categories” inherited through a past hermeneutic—the forces of representation—driven by the distorting effects and purposes of power.
46 Thus if a metaphysical system uses logical relation and causality then that system is verifiable by the means of logic and causality which are themselves a priori categories of experience. And, as we will see, these categories themselves are derived through a deep coupling with experience prior to the human modes of experience to which Kant had set his anthropocentric, chicken-and-egg limits. This logical or relational verifiability is in the same way that a mathematical proof cannot be verified by empirical means but only by means interior to its logical relations. Indeed, the notion of infinity itself is purely logical and thus entirely amenable to the understanding, and this understanding underlies all of Kant’s supposed antinomies. Infinity is simply boundless, in any of its forms. It is only the limited imagination that cannot fit the unlimited infinite into its domain. But the forms and details of logic are not bound by the perspectival restrictions of the imagination any more than is a mountain restrained in size by the horizon. And thus a metaphysical system is open to demonstrations and relations of the infinite so long as it unfolds its relations in a consistent and coherent manner. But then it can only “prove” its conclusions in the realm in which it is limited, namely logic and relation, as opposed to empiricism and objectivity insofar as our inter-objective experience with mathematics and logic is neglected.
50 – 51 Thus, post-metaphysics is not ultimately a feature of the metaphysical system itself, but a cognitive or conceptual aperspectival stance which imposes an acategorical imperative—a meta-metaphysical and meta- categorical framework—in which the absolute truth claims of any metaphysics are suspended in the relative world of justification, partly through the rational truth that all truth claims may be subject, endlessly, to further analysis. Indeed, this unbounded stance of analysis is at the very core of the synthesis of Nondual Rationalism, as we will see. It is a resonant thread to the positive infinity and secret of Rationalism. And, as we will see, the Vision-Logic Coordinate System and the Univocity Framework, form a meta-metaphysical framework within which metaphysics can find no foundational ground with which to dogmatize and ism-ize itself.
73 In order to integrate all aspects of rationalism (e.g. philosophical and mathematical) this infinity, boundlessness or Emptiness within number must correlate with the infinity opened up in the mathematical ratio, which is the core of the mathematical definition of the Rational numbers and of mathematical rationalism. But more pointedly, it must explain the meaning of (or define) the “undefined” ratio with zero in the denominator, such as 1/0. Indeed, a key question which we will answer in much more detail later is, “What is this limit on definability for the rational numbers?” Or, “Why, exactly, does placing a zero in the denominator produce these ‘undefined’ results?” And, “Is a limit on definability not in essence a limit on limits themselves, and hence merely the unlimited and Infinite once the double-negative has cancelled out?”
77 Numbers began their evolution at one and transcended or ascended into higher and higher values. Counting was their purpose, their “fitness function,” and reason for coming to be. The Rational numbers came later, transcending-and-including the integers, as a function of the relation between two of them, but fundamentally operating on a new “axis;” immanence vs. transcendence. The ascending- transcending bias is therefore a natural and pervasive feature of the number-system in general, as the number-system is indeed a transcending-and-including holarchy [a hierarchy of holons, or wholes that are always parts of higher level wholes, and so on] of functions built on other functions, ultimately built on numerical identities serving the very human function of labeling and inventorying increasing agglomerations of real objects. This is the transcendent-bias in stark relief.
78 Transcending and including (recognizing and accounting for) this transcendent-bias, to get to the nonduality and neutrality, the open ground of rationalism, this must be seen as a true polarity, and the qualitative differences between the values that seem so absolute through the active frame of reference of the transcendent numerator, must be seen, in a sense, as relative to the active frame of reference of the inherited interpretation. In other words, the differences in quality between immanent and transcendent positions are a function of the active frame of reference and order of operations of division. The numerator’s frame of reference is active as the determinant of value, and the denominator’s is passive as the context for its meaning.
79 This transcendent-bias in operation in mathematics—and human thought in general (as we will see)—manifests in our tendency to see infinitely increasing values as normal Infinity, and infinitely decreasing values as undefined or approaching an actual limit at zero, as is the case with the errors of interpretation surrounding Zeno’s paradox and the infinitesimal of the calculus.i* This immanent infinity, however, is the inverse pole of the infinite axis specific and unique to the rational numbers, and critical to Nondual Rationalism. And similarly, opening up the meta-mathematical understanding of this polarity to its true relative and reciprocal nature, is the key to understanding the thread of rationalism as it winds its way through the labyrinth of history.
95 – 96 It is from this evolutionary focus on the outside—this arms race to accumulate the intelligence of directionality in the senses—that the imagination is born. This symbiogenesis of subject and object, a process, which we will cover in much greater detail later, directly encodes the trans-bias into human conceptual thought. This is why we find it so difficult to conceive of infinite immanence, and why we always feel a sense of cognitive vertigo when we can’t find a final resting place, or footing for the mind; an ultimate foundation, a fundamental substratum, a “ground of Being.” The power of intelligence and therefore of transcendence granted to the agglomerative, evolved organism in sensorially mapping his exterior transitively, in lines (axes) of direction, encodes the transcendent-bias directly into the gene-pool of all organisms with sensory functions, as this is translated into the differential reproductive success that (among other intelligent properties) drives evolution forward into higher and higher levels of transcendence. This transcendent-bias can also be seen in the phenomenon of group-mind. We have a bias for transcending ourselves and merging into a larger whole(or holon), and we tend to spurn (at least collectively) the lone individual—exploring his own infinite differences in immanence—until, perchance, the fruits of individual difference make themselves readily apparent to, and accepted by, the group at large. The power and bias stemming from this tendency can be startling when we come face to face with the irrationalities and atrocities that can manifest when the effect gets magnified and corrupted, such as in cults of personality. This effect shows up as, for example, the willingness of individuals to do things for the group that deeply violate their own individual morals, such as the Nazi effect, and the public ridicule—and even violent ritual murder and dismemberment—of “unorthodox” and “heretical” geniuses. The transcendent-bias here can be embodied and called forth readily in theimage of a herd of animals, driven by fear, back to back, fiercely facing their external enemy, encroaching on all sides.
100 – 101 The last century of ontology and epistemology, coupled with the discoveries of quantum and complexity science, has rendered moot the lingering, peculiarly medieval, fear of the infinite regress and thrown it into positive relief. Instead of viewing the problem from the negative point of view of looking backward or inward to find an origin in space, scale or time, and fretting when these hypothetical beginnings can’t be found, the problem is turned on its head. If there are no origins to begin with—in other words, if, contrary to our tacit predispositions, the universe is eternal and infinite (as conceived in Buddhist nondual schools of cosmology), in both depth and span,then the search for an origin is itself a false problem engendered by the false premise that such an ultimate beginning or ultimate foundation necessarily exists. The problem of the regress itself is seen to be merely aprojection of a regressive, point of view on the infinite or the unbounded nature of reality.
103 In the context of the Principle of Nondual Rationalism, we can see the bundle views as correlating with infinite division of substance into its deeper properties, and the bundle views as the assertion that the absolute is fundamentally indivisible with respect to properties.We saw that in the case of numbers, this infinite divisibility actually gave rise to the fundamental indivisibility of the absolute, in that there can be no end to division and therefore the absolute cannot finally and ultimately be divided. As an analogy, we can say that because there is, and can be, no final propertyless substrate, and therefore there are always deeper levels of modification leading to properties, then substance, at all levels, can have the property of further modification, or dissolution. This means that the substance-bundle dichotomy, asshould be expected, is purely a function of the foundational bias in modern thinking, which has only begun to wind its way out from the abstractions of the ancient monasteries of nondual practices and the modern ivory towers of academic epistemology.
104 This is essentially Spinoza’s Substance, the positive infinity as the secret of rationalism, and the single “axiomless-axiom,” which renders Spinoza’s system a “foundationless-foundationalism,” in that its very foundation is foundationlessness, or Emptiness, itself, i.e.the absolute scope.
111 In Interface Mathematics we will differentiate Unity into two different kinds, according to the difference in scope, from relative to absolute.i These two kinds of Unity are then finite “unity” and infinite “Unity,” because finity and infinity (apeiron) are the mathematical aspects of the relative and absolute scopes, respectively.
119 Furthermore, Science, with its premature abandonment of rationalism, and indeed metaphysics, in the enlightenment, has gotten stuck in a medieval foundationalist outlook, always looking for the smallest, simplest, most “fundamental particle” (foundational solid),the absolute “building blocks” of existence. …Nonduality, however—not to mention the ultimate quest of modernunification theories in physics—necessitates that ALL is fundamentally ONE “substance”—a unified field. It is commonly assumed that a foundational atom-void, particle-based model is a postulation of a single substance—that stuff which makes up the a-tomoi—but this is incorrect. The atom-void is a tacit polarity between two substances with opposing absolutized (yet minimally inter-expressive) properties; the solidity of particles and the fluidity or non-solidity of amorphous space (such as air), the uncuttable and the infinitely cuttable, and ultimately between thingness (form) and no-thingness (Emptiness). Perhaps it is tacitly assumed that since nothingness does not exist then to postulate its existence (?) as space or the void, in addition to the fractured somethingness or substance of the atomos, is still to assume a singular substance—the atomos. But since this nothingness (this now existing non-existence of the real void), is what defines the limits of the myriad atomic somethingnesses, then this nothingness plays a causal role in the very identity of the atoms as well as providing the causal context for the atoms, the field of interaction and inter-expression of the “laws of motion”. The existing non-existence of the void,the Emptiness, in a sense, limits, forms and cuts the uncuttable substance of the atomos into its fractured multiple identity.
120 So we already see that Form, when taken to the absolute scope, the infinity of infinite smallness, becomes the non-form of Emptiness. And we can see that this is a resonance of our Principle of Nondual Rationalism, that the infinite divisibility in the foundational search for the “fundamental particle,” the inverse-ultimate form, has ended in the non-particle, the non-form of the mathematical point—the implicit singularity of Emptiness.
121 By the Taoist identity of opposites and its extension into the PAR, if you place one opposite at the absolute level, you must place its opposite there as well. Thus infinite freedom must equal infinite causation, and vice versa. This ancient operation in the identity of opposites may indeed be the source and resolution of all our cherished paradoxes. We will see the above as a pre-echo in the concept“Infinite determinism equals indeterminism,” yet another resonant strand in our Ariadne’s Cable of Nondual Rationalism.
123 Often, therefore, to make this aspect of the absolute-relative interface explicit, it will be invoked with the term ‘omni-non,’ as in omni-non-locality or omni-non-directionality. We saw already how the idea of omni-locality is essentially identical with the idea of non-locality, given that a location necessitates a separation and exclusion from other locations which both the omni- and non- view negate. In other words, locality is an implicit polarity,and when this polarity is violated in either omni- or non- directions (affirmative or negative, respectively), we pass through the PAR and reach the identity of opposites underlying the concept as a whole. The omni-non simply recognizes the identity between the omni and the non at the absolute scope.
127 – 128 …it would appear that vision is the most nonlinear, massively parallel and sensorially precise for the purpose of “simultracking,” and interrelating (networking) many spatiotemporal phenomena at once. This unique quality of vision is likely the reason for its inclusion in the term “vision-logic.” Vision-logic is, in a sense, a meta-vision; it is taking the “networking” capacity of the visual sense and transposing or transcending-and-including it at a higher (meta-conceptual) level (e.g. the level of logic) in the networking of perspectives themselves. This is why it is also called “network logic.” But with “vision” at the meta-level in “vision-logic,” we are not excluding, but transcending-and-including the other senses and their training (and even creative listening or interpreting) modalities in the full spectrum of the arts. Vision at this level, in a sense, simply means “percept,” and so, accurately speaking, we might call this a “Percept-Logic Coordinate System,” though this would lose the unique network connotations that vision-logic has come to embody. Vision-logic, therefore—with its integrated concept-percepts—becomes opposed to “blind-logic,” where “concept is divorced from percept, and thought moves among [mere] abstractions.” Blind-logic has a limited, hollowed out, semantic foundation and so it lacks the ground or medium within which to move, so to speak. Unable to find a ground within which to find subtle reconfigurations and variations, it is stuck in a single perspective. It can’t, therefore, find new modes of “seeing” the whole. Blind-logic generally lacks the ability to lift itself out of the rooted perspective of mere words, syntax; it cannot escape the “word-binding” so common to abstract, sophistic, logic (e.g. lawyer talk) which can “prove” the “truth” of even the most obvious of absurd conclusions; thought, such as this, easily becomes “spell-bound” to its surface-level machinations, as does its unwitting audience.
129 The aim of vision-logic interfaces, such as the Vision-Logic Coordinate System, is to reconnect concept and percept; to reawaken the “eyes” of modern thought which have been put to sleep by the paucity of sense in intellectual abstraction; to reinvigorate the anemic, disfigured forces of imagination in modern intellectual discourse. This is what Buckminster calls for in his idea of a “return to modelability” in geometry, mathematics and ultimately science.
133 “Vision-logic,” a term borrowed from developmental psychology, denotes a stage in intellectual development, a “meta-vision” whereby one can transcend the limits of singular perspective and attain an understanding, simultracking, integrating many perspectives at once, i.e. “integral-aperspectival.” It is also called “network logic,” in the sense that it can actually begin to make networks of perspectives; moving among them, forming comparisons, higher-level systems of inter-perspective translation, co-operation and conjunction, integrating and transcending.
146 The uni-axis is always centered on a single position, whose “infinitely small” Euclidean point is its unbounded immanent pole,and whose transcendent pole “reaches to” the unreachable transcendent infinity of the ONE-ALL. The uni-axis, therefore, is always conceived through the relative aspect of position or finite locality (relative to any other) and, therefore, ultimately through the “eye” or aperture (boundary or spherical “yard-stick”) of the transitive unit i.e. the spherical coordinate making up the linear directionality of the transitive-axis. The I/T uni-axis is the immanent and transcendent, internal and external boundless dimension of this spherical, a priori-extended unit.
155 – 156 This section operationalizes the concept of Univocity into a rigorous and intuitive framework that provides a simple conceptual “space” for open and honest ontological speculation, maintaining the necessary nondual relativity of this ontological space and its resident or emergent concepts and relative truths in polar contrast to the Truth of the absolute scope. This operationalization of Univocity enacts and softly enforces the principle of nonduality by explicitly recognizing the fundamental Nagarjunan/Spinozan/Deleuzian polarity between the absolute and relative “scopes.” …Univocity is explained by Deleuze as “the idea that all events are compatible; they are ‘inter-expressive’. Being has one voice but can only express differences.” And Todd May says, “What univocity implies is not that everything is the same, or that there is a principle of the same underlying everything, but, instead, precisely the opposite. With univocity comes difference, difference for the first time taken seriously in itself.” …Univocity means that every expression of existence is different in a fundamental sense from every other. And yet the unity aspect of the concept signifies that these differences are fundamentally causally intercompatable, or ‘inter-expressive.’ This is the identity of opposites of difference and similarity, because indeed without this inter-expression or inter-relation, differences could not interface or relate in order to really differ. And thus, with univocity, difference (or relativity) is “taken seriously in itself” and given a framework for actualization and understanding.ii It is this basic, or “fundamental,” framework, expanded and operationalized herein, upon which any healthy and “holistic,” or integral rationality must be built (insome form or other), and we have already seen it as the implicit essence of ancient and esoteric nondual/perennial philosophy,i such as Taoism, Advaita Vedanta Hinduism, Madhyamaka Buddhism. It is also seen in the West in some forms and levels of Christianity, Neo-Platonism, esoteric Spinozism, and in some of the pre-Socratics, such as Heraclitus.
167 In short, a nondual and univocal monism is an infinite pluralism via the identity of opposites of the One-All or Unity-Multiplicity. Univocity is the monism=pluralism identity of opposites in Nondual Rationalism.
175 Polarity is the essence, or defining feature of the nondual and of univocity. And univocity, we will see, is the very limit of polarity; where polarity (the core relation of the relative) self-referentially applies itself to itself to form the absolute scope in identical opposition to the relative. This is where relative thought grounds itself in its engendering other; its identical- opposite which gives it context and meaning; the absolute.
178 Through the identity of opposites in the ontic and epistemic we can see also that ontology is epistemic and epistemology is ontic. In other words, speculation about the nature of reality is necessarily representational, and representation is necessarily real. Or even simpler, the map of the territory is a feature of the territory itself.
182 Because the absolute scope (e.g. the nondual or the ‘‘axis of Tao”) enfolds and unfolds all polarity, univocity is actually the positive negation, or the acceptance, affirmation and transmutation of opposition; the negation of negation in the positive infinite. The root-polarity, the positive infinity of esoteric rationalism, is the polarity of polarity vs. non-polarity—in other words, the relative/absolute polarity, the univocity axis or the dialectic of univocity whose synthesis returns us to the positive infinity (logical Emptiness) of esoteric rationalism. This is the root polarity because the absolute has returned home, from its journey through the world of form, the relative and sub-representational, to its engendering other in the ineffable absolute. The concept has returned to its source through the non-concept,the sub-representational or the plane of immanence. In this root conceptual polarity, where concept opens to its annihilating/generating antithesis/pre-thesis, the absolute unfolds and then enfolds polarity itself.
183 In Leibniz-Kant-Hegel, the univocity pendulum has swung the other way, from the medieval relativization of the absolute in ascribing anthropomorphic qualities to God, to the post-modern absolutization of the relative, in lifting the properties of the dialectic (or hermeneutics, or social construction, or whatever) to the absolute scope. In the Univocity Framework, however, these two opposites, as all opposites, are seen necessarily as identically opposite anthropocentrisms. They both attempt to dissolve the core of nondualism in the absolute/relative polarity through conceptual encapsulation of the absolute in the relative, or populating the absolute scope with conceptual mono-poles, but from two different sides of the same operation. The Hegelian, post-modern, transcend-and-negate dialectic is the inverse identity of the pre-modern negative-regressive foundational infinite. They are both functions of the transcendent-biased modes of absolutized representation (relativity) and are therefore also epistemic absolutisms.
191 The fundamental relativity—where the relative scope finally points outside itself to the absolute, forming the absolute/relative polarity of univocity and Nagarjunan nondualism—serves to balance the transcendent-and representational-bias and to deflect any unconscious attempt at absolutization by the relative (e.g. reductionism) by reminding us of its identical-opposite in the ineffable absolute. This includes absolutization of the immanent-transcendent omni-axis itself as actually being the absolute scope, rather than merely pointing to it as an enfolded and unfolded tautological aspect or identity in the ONE-ALL.