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Overview of the Core of the Western

Worldview starting from Cassirer and

Heidegger Complementarity

Kent Palmer Ph.D. kent@palmer.name

http://kdp.me 714-633-9508

Copyright 2014 KD Palmer1 All Rights Reserved. Not for Distribution. CassirerHeidegger_01_20140806kdp01

Started 2014.8.6; Edited 2014.12.22 Draft Version 02 http://orcid.org/0000-0002-5298-4422

http://nondual.net http://schematheory.net

Key Words: Cassirer, Heidegger, Kant Abstract: Explanation of Hypothesis W-prime as to the structure of the Western Worldview in the context of the Cassirer-Heidegger complementarity. What is more important than either Cassirer and Heidegger is the context of their complementarity which is the core of the Western Worldview set down by Plato and Aristotle which we still need to learn. Cassirer and Heidegger both are merely taking us back to that Core and showing us how it is still applicable today and their work merely brings our view of that Core up to date. So the thrust of their work and our interest in it should be to reacquaint us with that Core and its importance for us today. The fact that it is still significant to us after all this time, the fact that the core has not changed, and still permeates our existence within this worldview is extremely significant. Appreciating the complementarity between Cassirer and Heidegger is in some sense appreciating the significance today of the core of the worldview established by Plato and Aristotle the fact that they agreed on that when they disagreed on so much else. This fact is obscured by the fact that Aristotle in his Ethics does not introduce the kinds of knowledge in the order of the Divided Line and thus it is not common knowledge that there is a correspondence between the phases of the Divided Line and the kinds of knowledge of which Aristotle speaks. This discovery which is not in the tradition as far as I can find is fundamental to our

1 http://independent.academia.edu/KentPalmer See also http://kentpalmer.name

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understanding our worldview. And the fact that even at the time of Cassirer and Heidegger we were still in the process of rediscovering the way in which the phases of the Divided Line still affects us is significant, and that is because we had forgotten about certain types of knowledge that are essential to our lifeworld within the worldview core and its boundary and limit. And so it behooves us to return to the worldview and to see what we can make of it now that we understand that the complementarity between Cassirer and Heidegger points us in that direction and in fact due to their inverse duality it points to the core as the meta-system within which their systems of thought find their meaning. So let us begin again and attempt to understand the core of the Western worldview more deeply with the help of Cassirer and Heidegger. As we have said our quest begins by understanding that there is a duality between ratio and doxa. Each of them is in turn split into representable and non-representable intelligibles on the one hand, and grounded and ungrounded opinion and appearance on the other hand. With respect to Doxa ungrounded opinion and appearance is related to phronesis of praxis that is formally indicated by Dasein and grounded opinion and appearance is related to techne of poiesis that is ready-to-hand and apprehended though circumspective concern. With respect to Ratio representable intelligibles are related to epistemic knowledge of science that is present-at-hand and non-representable intelligibles are related to Sophia of virtue. Heidegger does not have a modality of being-in-the-world related to non-representable intelligibles because he assumes that this is a priori and thus unchanging. But what we know from Cassirer is that the a prories change and so there should be a designation of being in the world for Sophia.

Figure 1. Stages in development of Spirit in Cassirer

What we note is that there is a relation between the first and fourth phases of the divided line, and a relation between the second and third phases, which is established by Plato himself because the way he formally draws the line the two central phases are equal while the two peripheral phases are unequal, even though that formal drawing of the line contradicts what Plato himself says. Plato says that each section is larger than the last as we go up the line from phase one related to ungrounded doxa, to phase two related to grounded doxa, to phase three related to representable intelligibles, to phase four related to non-representable intelligibles. This contradiction between what is drawn and what is said in Plato is very significant because he is demonstrating the non-representability of the line itself

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and drawing attention to the weakness of our representations. If even the core of the tradition contains a contradiction when it is represented then this should give us food for thought, it suggests that this representation of the core of the Western worldview is not final or fixed or the last word on the subject, even though it has become ensconced as something unquestionable in our tradition. Plato is telling us we must question the representation of the core of the worldview by embedding in his description a contradiction between what is said and how it is represented. And this is probably the most significant thing about the core of the worldview that its founder calls it into question. But also it is important to note that he uses a drawing from geometry to represent the core as if he were doing a proof in plane geometry but it is a proof that goes wrong because the diagram does not correspond to the words describing the worldview itself which is elaborated on in the analogy of the Cave. In fact Plato gives us three analogies: The sun, the Divided Line and the Cave. These correspond to the Egyptian trinity Aten, Ra and Amun. This alerts us to the fact that we are dealing with a desideratum of Egyptian Wisdom, which are encountered everywhere in Plato in disguised forms. But here the key point is that we are dealing with a trinity and as the central feature the Divided Line is what takes us from Aten the manifest face of God to Amun the hidden face of God. The Divided Line is what allows us to distinguish these two faces of God, but it is also the vessel of experience of the manifestation of God as Ra. Aten is the Sun which is the outward sign of God in the Heavens, as the source of everything living. Because the Sun is there pouring its bounty of energy on earth we have experience as living, conscious, and social creatures within the limit and boundary provided by the Divided Line. But that line also teaches us to distinguish between visible and invisible things. And we do that by giving up being men of earth who can only believe in what they can grasp in their hands. It is thus significant that the central parts of the divided lines are names in relation to our hands and their way of relating to objects we discover in experience. There are levels to initiation that Plato tells us which start with the uninitiated which are the men of earth who only believe in appearances, what Hegel calls sense certainty. Then there are those initiated into the lesser mysteries who recognize the invisible but see it as pure flux of Becoming like Heraclitus. Then there are those who are initiated into the greater mysteries and see it as static Being like Parmenides. But this implies that there is the one who initiates into the mysteries, i.e. the Hierophant, who believes in change and changelessness at the same time, which is the supra-rational which is intrinsically non-representable and ungrasped by Being as such, i.e. refers instead to Existence giving rise to the upper limit of the divided line as distinguished from its lower boundary in contradiction, paradox, absurdity, and impossibility. Beyond the Hierophant there is another position which is that of Plato himself the writer of the Dialogues who has an even deeper position. Plato has the position of the one who does not believe in anything that is in the dialogues for his concern is something that after long companionship is like a spark that jumps from soul to soul, i.e. a wisdom that is transmitted beyond words. Thus all words in the Dialogues only exist as a basis for understanding that transmitted understanding with which Plato is most concerned. Most commentators forget this statement which appears in the seventh letter which must be the ultimate basis for all our interpretations of Plato. We are

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right to suspect that the contradiction in the form of the divided line itself and what is said about it has to do with the pointing at this deeper perspective in which the core of the Western worldviews representation as a diagram contains a contradiction. In other words it is clear that the Divided Line is not the whole story as it is normally taken to be by the commentarial tradition. However, what we need to focus on here and now is the fact that Plato is telling us that we need to comprehend the invisible in order to approach Amun the interior hidden God when we start from the external visible aspect of God which is the Sun. But what we need to keep in mind is that just as we cannot look at the external Sun in the Sky without going blind so to we cannot look at the hidden God directly either. And it is this fact that God cannot be looked at directly in either of its appearances to us, either externally or internally that is the key to understanding the nature of the Divided Line. What we can look at is Ra manifestation of the world within the phases of the Divided Line itself. This is interesting because it is Ra who was never taken as a Monothesitic God exclusive of its other characteristics. Akhnaten converted Aten to an monotheistic god and excluded both Amun and Ra. Moses converted Amun into a Monothesitic God and excluded Aten and Ra. But Ra itself was a characteristic of God that was never historically converted into a monotheism. And that is because Ra is the Pantheistic aspect of God which is identical with experience and which is immanent and never transcendent and which is broken up into the phases of the divided line and appears to us only as an A priori that we can infer from experience after the fact but cannot reduce to an extreme or nihilistic opposite that can serve as a monism. Ra is inherently pluralistic and marked by discontinuities in experience that the divided line characterizes2. Ra is neither the Unity of Aten nor the Totality of Amun who is associated with the non-representable concept of the Good. Amun is the invisible interior Good that underlies everything as the source of variety in experience. Amun is the source of Good Presence and the Presence of the Good which is called Ousia. Ousia is what goes beyond either Pure Being of Parmenides and Process Being of Heraclitus which is both change and changelessness at the same time supra-rationally, which contains all the differences that make a difference that well up as a cornucopia of difference that provides every being what it needs which is good for each in themselves and which provides experience with its diversity to which every being is adapted intrinsically. With the Divided Line analogy Plato is teaching us how to transition from the extreme of Aten to the extreme of Amun. But there is a deeper wisdom than just climbing the ladder of the Divided Line embedded in the Divided Line itself. One way to recognize that deeper wisdom from the position beyond the hierophant that Plato himself takes is to realize that once we understand the supra-rational as having two things that are distinguished that appear at the same time without interfering with each other like Change and Changelessness then we can understand the nature of the non-representables like the Good which is nondual. And the other deeper teaching is 2 See Seung’s interpretation of Thus Spake Zarathustra by Nietzsche which sees Zarathustra as identifying with the Spinoza-Hero who becomes one with Nature as God. This is close to the idea of Ra as Manifestation. Seung, T K. Nietzsche's Epic of the Soul: Thus Spoke Zarathustra. Lanham, Md: Lexington Books, 2005.

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about the nature of nonduality which we understand once we turn to interpret the crossing lines of the Divided Line which is not normally done in the commentarial tradition. What stands out in the divided line is the discontinuities between the phases of the divided line, and these are not interpreted in the tradition, and for good reason because they contradict the principle of Excluded Middle or non-contradiction which is the fundamental principle that Aristotle sets up in his Metaphysics that is contrary to the Tetralemma. The tetralemma was developed in Buddhism to indicate emptiness a non-representable non-experience non-concept. Lets call it a Notion3 using the terminology of Hegel. Emptiness is a notion which goes beyond the logical possibilities which have been exhausted in the Tetralemma itself. Normally notions represent sub-ideas of the complete and final idea, i.e. various sub-philosophies that are taken up into later philosophies. But here we take notion as also something that goes beyond the Idea and all its permutations of sub-ideas which is the nihilistic opposite of the concept of the notion. We might more rightly call emptiness a proto-notion or an Ur-notion that leads to the idea of emptiness as nondual. Nondual means not One, not Two, not Three, not Many, we may call it non-cardinal to be more exact, in effect it is a unique position that recognizes the possibility of Zero, as that which is not in the number series but is the necessary background to generating the number series. Emptiness is the interpretation of Existence given by Buddhism. There is another dual interpretation of Existence called Void given by Taoism. Emptiness and Void are the two ways that nonduality can appear and do appear in our tradition and all traditions. Thus we can see that this distinction also appears in the discontinuities that inform the Divided Line. There is the nondual of Void that divides Doxa and there is the nondual of Emptiness that divides Ratio. The only difference between Void and Emptiness is the difference between the nondual being enclosed or not enclosed. So for instance if we take a jar then the void is the space around the jar, while emptiness is the space within the jar. Similarly with the Divided Line there is the nondual exterior that we apprehend as underlying appearances within nature, which is global spactime. On the other had there is the nondual interior of consciousness that is the ground of the rational, i.e. ordered consciousness with unity, which is apparent to awareness below the level of intentionality and this interior nonduality divides ratio into the representable and the non-representable. But it is clear that Emptiness and Void are dual nonduals, and so it makes sense that there should be also an utterly nondual, and that we can see as the middle crossing line of the Divided Line that separates Ratio from Doxa. We call that Manifestation (Sifat) which is completely nondual. And logically there must always be the opposite of even that which we name the Amanifest (Dhat). Going back to Henry and the Essence of Manifestation we can see manifestation as the fullness of experience within the Divided Line called Ra by the Egyptians. But there must be something hidden in manifestation that never manifests, the unconscious of manifestation called by Henry the Essence of Manifestation. If we want to find the deeper nondual which we call the Amanifest we must distinguish the anti-manifest from the non-manifest using the Greimas square. The anti-manifest is what is hidden from manifestation. The Unmanifest is what 3 https://www.marxists.org/reference/archive/hegel/help/mean06.htm

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never comes to manifestation but is not specifically hidden. Then there is a chiasm between the Anti-Manifest, i.e. the Secret, and the Unmanifest which is unknown unknown. And this chiasm points to the Amanifest which is the next deeper level of nonduality beyond manifestation. The A manifest is a limit of thought beyond which we cannot think meaningfully. The Amainfest is what was before the manifestation of experience within the divided line, and thus the source of all experience. The Chinese have a good term for this which is there term for Void which is Wu Ji, which means without tentpost. In other words in the Amanifest the whole tent of experience collapses that is represented by the Divided Line itself and which is beyond all experience being prior to it in the most original possible way. What is striking is how these nondual Ur-notions are coded into the Divided Line itself. The nonduals of Emptiness and Void are coded in as the divisions of Ratio and Doxa. The Ur-notion of the utterly nondual is coded into the division between Ratio and Doxa itself. And the Amanifest is coded in via the contradiction in the representation of the divided line and what is said about it, which revolves around whether the central phases of the Divided Line are equal or not. The representation of the Divided Line calls itself into question as stated by Plato, and this is the key to understanding the Divided Line analogy. When we know that the core of the Western worldview is cut into pieces discontinuously by nonduality and that this differentiates various kinds of Ur-notions of nonduality, then we suddenly see that despite Aristotle’s dictum of Non-contradiction and Excluded Middle Plato has given us a way to recognize nonduality within the Western tradition which is the most dualistic tradition after that of the Zoroastrianism in Persia (which was one of the Others of the Greeks the nihilistic opposite of the Scythians) which inherits from it its dualistic tendency from Indo-European sources. Once we understand that the extreme dualistic tendency of the Western tradition that denies all possible forms of nonduality, is undercut by having nonduality inscribed in its core as the discontinuities between the phases of the Divided Line then we see that as with any other tradition the Western Tradition needs to come to terms with nonduality and accept it as inevitable and unavoidable. We call this acceptance of the inevitability of nonduality the Homeward path. It is a spiritual path intrinsic to the Western worldview that recognizes the intrinsic nonduality embedded in the Western worldview which is like the various forms of nonduality we see in other traditions. For instance, Taoism in China was a reaction against the dualisms of Confucianism, or Buddhism in India was a reaction against the dualisms in Hinduism, and more significantly DzogChen in Tibet which was part of the recognition of the deeper utter nonduality of manifestation, which has its counterpart in China with Fa Tsang in Hua Yen Buddhism. Recognizing Nonduality as Supra-rational is in its own way an extreme and we need to realize that and come back to the middle way which is between all extremes even the extremes of the recognition of nonduality. Here is the key. The utterly nondual fullness of experience as manifestation is at the center of the divided line not at its limit. Comprehending supra-rationality as the opposite of the mixture of contradiction, paradox, absurdity, and the impossible is a prelude to recognizing the different kinds of nonduality in existence, i.e. emptiness and void, which is a prelude to recognizing the utterly

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nondual fullness of manifestation at the heart of the Divided Line, which is a prelude to recognizing the Amanifest source of nonduality as such which is at the limit of what thought can think. These steps are what Plato is alluding to in the Seventh Letter as being a position beyond the recognition of supra-rationality as such. This train of thought leads us to a surprising conclusion which is that not only is the Western worldview’s core definitive of Nonduality its various modes or expressions but that the Divided Line itself needs to be expanded and extended. The expansion comes from the questioning of Ratio as the only criterion for judging experience. Blake questioned that in the Four Zoas which was contemporaneous with Hegel’s Phenomenology of Spirit. Blake in his unpublished and thus hidden book attempts to explore the prequel to the Bible in which the various types of Gods that appear in the Bible interact with each other as Zoas (principles of Life). Each of them has four phases which includes the Zoa, its female emanation, its shadow and its spectre. There are four Zoas that appear from Albion who is asleep like Vishnu, which are Urizen (reason), Tharmus (emotion), Luvah (love) and Urthowna (closeness to the earth). Blake suggests in his literary masterpiece that reason is not the only criteria for the judgment of experience but we need all the Zoas to work together as they do within the nondual Albion, which is like Vishnu in India and Hun Tun in China. Therefore from the perspective of Blake there are four Divided Lines not one. And we need to expand the set of possible divided lines if we are going to cope with the variety of nature. Hegel on the other hand believes that we need to generate a principle beyond reason to reign it in and control its excesses that leads to the Terror of the French revolution and later to genocide in ideological times like the Twentieth Century. Hegel develops the idea that consciousness in man evolves though philosophy though stages starting with Sense Certainty, then Consciousness, then Self-Consciousness, then Reason and then into Spirit, where spirit is the consensus of opinion of the community of man as it evolves though history related to the Holy Spirit which is the community of the believers in Christianity after the death of Christ, i.e. the ideal church. Developing a higher criteria by mutual consensus of the tradition to control the excesses of reason is Hegel’s solution that goes to a higher logical level beyond reason which has its own emergent properties gained from surveying the history of mankind and the history of ideas and the phenomenological development of man through time. Hegel develops the idea of a dynamic a priori but which is still closed into a circle at the end of time, i.e. at the time when Hegel lived and conceived of the absolute as the limit of the evolution of spirit. Kant’s a prori was static and did not change and was based on the table of judgments. Hegel in his logic turned the categories into a whole world with its own internal dynamic based on the negation of negation starting out from the difference between Being and Nothing where nothing is conceived as Buddhist Emptiness. When we combine Being of Parmenides and Nothing as emptiness together into a Synthesis we get the Flux of Change of Heraclitus. And then from that we posit the determinate something which he called Dasein. It is no accident that Heidegger seizes upon this term as the core of his philosophy and the formal indication of the Facticity of Life. In Being and Time Heidegger attempts to reconcile the phenomenology of Husserl with that of Hegel and distances himself from Husserl by

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embracing the phenomenology of Hegel and the problematic of historicity that Husserl understands though genetic phenomenology that recognizes the world as a horizon of experience and does not need bracketing. Heidegger adopts the orientation of genetic phenomenology but then attempts to find a way to approach the haecceity (Thatness) facticity of life using formal indication which attempts to radicalize phenomenology beyond the distinction between abstraction and essence perception opened up by Husserl that allows us to distinguish present-at-hand from ready-to-hand views of objects. In order to solve the problems of Husserl’s phenomenology Heidegger attempts to go to a place prior to the arising of the difference between subject and object. And it is this move that makes Heidegger’s philosophy so groundbreaking in the Western tradition.

Figure 2. Properties of Systems are relations between Aspects of Being

But beyond enhancing the divided line by recognizing a principle beyond reason, i.e. the social in history, and expanding the divided line by recognizing other criteria for judging experience other than reason, like agape love that appears in the Sermon on the Mount which maps to the Divided Line structure, and the natural emotions of man explored by Darwin, and the position of the one who is close to the earth eschewing all transcendences who was called the Uberman by Nietzsche and risen as an ideal in Thus Spake Zarathustra4. There is another option that needs to be explored which is the extension of the Divided Line. We can see that extension on the one hand in the distinctions between contradiction, paradox, absurdity and the

4 Seung, T K. Nietzsche's Epic of the Soul: Thus Spoke Zarathustra. Lanham, Md: Lexington Books, 2005.

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impossible that appears at the lower boundary of the Divided line. The question is whether there is a similar extension on the other supra-rational extreme of the limit of the divided line. To explore this we must become more technical about the content of the divided line. The Doxa is associated with the Aspects of Being which are Identity and Presence which are related to ungrounded appearances and opinions. On the other hand it is Reality and Truth that are related to grounded opinion and appearances across the divide of the Void within Doxa. Thus the aspects are what is related to Doxa. We can see that the aspects of Being are related to the Peirce/Fuller Principles in as much as Identity is a First (isolate), Truth is a Second (relata), Presence is a Third (continua) and Reality is a Fullerian Fourth (synergy). Thus the relation between Doxa and the aspects does not follow the order of these in terms of the ordering of the philosophical principles. However, Ratio is related to the nonduals within the Western tradition which are Order (First), Right (Second), Good (Third), Fate (Fourth), but these continue to Source (Fifth) and Root (Sixth). Order and Right are related to representable intelligibles. Good and Fate are related to Non-representable intelligibles. But then we must see that Source and Root are projected beyond the limit of the Divided Line which is Nous of the Numinous by which we recognize the gods in experience. That tends to suggest that there is some fourfold distinction beyond the limit of the supra-rational that extends the divided line. When we think about this we realize that sources and roots suggest the primal scene of the Well and the Tree, where the roots of the tree holds a dragon and are wrapped around the three wells. And if there are roots and wells then there must be soil and water, and thus by this analogy there must be something that fulfills the role of soil and we see that as the Sifat (the attributes of God) and the Dhat (which is the essential oneness and uniqueness of God beyond the diversity of His attributes). But this implies that the extended Divided Line is seen as the natural evolution of the world tree from the primal scene and this means that the utter limit of the extended divided line can be envisaged as the Lote Tree of the Furthest Limit. Given this image from Islam for the limits of all experience in relation to God. Seeds appear in the interspace between soil and water at the outer limit of the extended Divided Line. Monads or leaves appear at the level of the inner limit of nous of the divided line. Flowers or views appear at the level of Metis which is the internal boundary of the Divided Line. Candidates or Fruits appear at the other outer boundary of the divided line. The image of the tree is upside down and the wind is represented by contradiction, paradox, absurdity, and contradiction. That is the wind that carries the fruits of the tree. The imaginal tree is upside down within the normal series of the divided line. The Lote tree of the furthest limit5 is encountered at both extremes of the extended divided line. It should be noted that the extension beyond the boundary into contradiction, paradox, absurdity and impossibility is divided by Emptiness, while the extension beyond the limit into source, root, soil, and water is divided by the Void, and the divisions of these extensions compensate for the appearance of emptiness in Ratio and void in Doxa, so that each side of the central cross line of Manifestation is balanced by both emptiness and void ultimately. The extensions of the divided line are illusions of course, merely the mirror image of the 5 http://en.wikipedia.org/wiki/Lote_tree

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divided line reflecting in the mirrors of its boundary and limit. But the fact that this model is an image of the Emergent Meta-system which appears in the Monadology of Leibniz and which was taken probably from the idea of temporal atoms of the Muslim theologists is significant. We don’t have to justify these excursions into the extension, expansion and elaboration of the Divided Line here. We mention them only to get a perspective on the various ways that the divided line as the core of the Western worldview may be elucidated further to suggest a position that Plato might have had on it that goes beyond what he has said in the dialogue that might be related to spiritual transmission such as that we see in Zen Buddhism for example. These elucidations give depth to the nondual treatment of the Divided Line we are offering. These various adumbrations give us some structural clues how the worldview might be changed from a structural perspective in order to express its inner logic more clearly. For instance, the crucial problem with the worldview is the over emphasis on reason as a criterion for judging experience. From what has been said there are several possibilities, one is to have other criteria that compete with reason such as love which turns out to have been the origin of Christianity as a Greek Jewish cult, which we see in the Sermon on the Mount filling the structure of the core as Luvah in the eyes of Blake. another possibility was Tharmas, or emotion that leads to glory by filling the thymos with berserker rage as in the example of Achilles. Or there is the possibility of Urthowna who in immanence only is close to the Earth as Zarathustra’s Uberman who becomes the guardian of the earth. But another completely different approach to controlling Reason is the development of a higher power Hegel called Spirit based on the learning of the community through its history. A completely different path is the one which emphasizes the extension of the line into the upper reaches beyond the limit of nous into the supra-rational or nondual arena, where we find the source, root, and then sifat and dhat as transcendent, as mirrored across the limit from the central position of the middle crossing line and prior to the unfolding of the line altogether. In this the central nondual is seen as controlling reason from the outside, and the Dhat is embodied in the line rather than being prior to the line. This option controls reason by making the ineffable active rather than passive and gives rise to illusion of transcendence.

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Figure 3. W-prime hypothesis for the Structure of the Western Worldview

What we need to be aware of is the fact that there are three parts to the Western worldview which are the shell, core and kernel. The shell is the outward aspect of the worldview which we are caught up in as the They which is steeped in Nihilism. There wherever you look is some form of nihilism, and this forms the background to the Emergent Event. The emergent event causes a discontinuity in the tradition to be formed at some scope via a fact, theory, paradigm, episteme, ontos, existence or absolute change. When this occurs all the kinds of Being have to form a face of the world together, and then the background nihilism is cleared. If however not all the kinds of Being are together in the emergent event then it becomes an artificial emergence and merely intensifies the nihilism. In the emergent event the transcendentals become immanent within the world and the worldview ceases to be a structure of headlands above the world. This precipitates a transformation in the organization of the world as a whole which eventually leads to a new unfolding of transcendences after the emergent event.

Figure 4. Inner Shell of Worldview

We can think of the worldview as meta-dimensions. The zero meta-dimensions hold the schemas (facet, monad, pattern, form, system, meta-system, domain, world, kosmos, pluriverse) which are templates of space time comprehension. The first meta-dimension is the standings which are the five kinds of Being, one of which overlaps with existence which then is interpreted as empty or void at the fifth level, and then manifestation (the sifat) and then the amanifest (Dhat). Void divides doxa,

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and Emptiness divides ratio, and manifestation which is full is the central crossing line, and the a manifest is prior to the line unfolding. Then at the second meta-dimension are the aspects of Being which are identity, presence, truth and reality. Beyond that meta-dimension three and four give us the world soul, and five, six and seven give us the trinity. For the trinity there is only one member at each meta-dimension. For the worldsoul there are two and three elements which together gives six relations connecting the aspects, or the existentials as the case may be. The worldsoul is the moving image of eternity in time as expressed by Plato. It has the structure of the powers of two and the powers of three both emanating from the one. The inner shell is the aspects and kinds of Being. The core is the world-soul, and the kernel is the trinity. But these can be construed as underlying the structure of the divided line, so the trinity can be seen as the crossing lines of the Divided Line.

Figure 5. Standings in the First Meta-dimension of the Worldview

The World Soul can be seen as the relations between the aspects or the relations between the existentials. There are four aspects and four existentials and the Worldsoul as a tetrahedron mediates between these based on the multiplication of the elements to give six which is the prefect number of relations within the minimal solid of the third dimension. Indulging in a bit of numerology we can say the following. If we multiply the aspects and the standings we get 28 (4*7) which is the second perfect number and the number of relations between 8 things. The next perfect number is 496, which is 16*31 or the number of relations between 32 things. The number of relations between 16 things is 120 and is not a perfect number. So the relations between 4, 8 and 32 things gives a perfect number but not the relations between 16 things. This is significant because 16 is the number of the arche in the negative first meta-dimension. Jung calls this the quaternion of quaternions and relates the pattern to the relations between archetypes that form a field. We can see this field in chess as the 8 players on each side that are not pawns and thus have rank. The two sides give us 16 ranking players and then we have the

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pawns which are also 16. Pawns are the men and ranking players are the gods such as those on Olympus. This leads to more numerology which tells us that in chess the amount of information in the distinctions embodied in the pieces is equal to the amount of information in the board, and this is the number 64 which is the next number beyond 32 which again does not give rise to a perfect number but has 2016 relations. The next perfect number is 8128. But the next number which is intertransformable without loss between two and three dimensions is 729. The fact that 16 and 64 do not yield perfect numbers of relations while 4, 8 and 32 do is very significant to the structure of the worldview. The combination of the levels 3 and 4 with elements 2 and 3 in the Worldsoul gives us a tetrahedron that mediates between existentials and aspects. The existentials come from Egypt, Semite, and Sumerian sources. Relations between them give the four points of the tetrahedron which then also has the surfaces that relate to the aspects. Then when we take the aspects times the standings we also get 28 which is another prefect number of relations between eight things. The eight things can be seen as the trigrams in the Chinese worldview which are the various possible connections between heaven and earth based on three oppositions. For instance these may be Inward/Outward, Sensory/Meaning & Celestial/Terrestrial. When you multiply the trigrams by themselves you get the hexagrams in the Chinese worldview. They use the binary information infrastructure to describe the differentiation of the fourfold which is Heaven, Earth, Mortals and Immortals in the West. But in the West this structure is related also to the negative fourfold which is abyss, covering, night, and chaos, which when we reverse them we get grounding, uncovering, light and order. Order is the first nondual. Uncovering is the nature of Aletheia which is primal truth of disclosure. Light is the basis of vision that comes from the sun during the day and the moon at night. Grounding is the giving of basis, i.e. reasons. It is the negative fourfold that tells us the most about the nature of the worldview and its core.

Figure 6. Structure of the WorldSoul from Plato

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The worldview is a progressive bisection of dualities that are mediated by nonduals. Those nondual mediations are order, right, good, fate, source, root. The 16 arche or archetypal traces of the gods that are adumbrated into male and female deities as we see in Chess do not have perfect relations to each other but instead with men (pawns) have interdimensional transformation with respect to the 64 squares on the board and the information in the pieces, and the 64 does not have perfect relations either. Thus the gods are incommensurate with each other and represent a pure multiplicity in the sense of Badiou. But 25 (32) is again perfect and that is related to the Pentahedron in four dimensional space the next higher minimal solid. What we are saying is that the worldview is a combination of the relation of perfect numbers to non-perfect numbers on the one hand and the minimal solid of three and four dimensions on the other hand. Perfect numbers are very close to each other at the beginning. Standings times aspects gives us 28 which is a perfect number. Existentials and aspects are connected by six relations within the Worldsoul.

Figure 7. Elaboration of the WorldSoul with addition of Matrix Logic

At the zeroth meta-dimension we have ten schemas which is the base for our number system. As we get to the negative first meta-dimension there are 16 arche but these are not related to any perfect number either. So note the trinity is a triangle which is the minimal figure in the second dimension. Then we have the worldsoul which multiples two elements times three to give six prefect relations between existentials and aspects which is the core of the worldview.

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Figure 8. Kernel of the WorldSoul

The kernel of the worldview are the three nondual crossing lines or these may be reified into a trinity. But the tetrahedron in the structure of the worldview is the minimal solid in the third dimension which has the lattice 1-4-6-4-1 connecting existentials to aspects. Then when we multiply aspects times standings we get 28 relations which is again a perfect number relating eight things or three progressive bisections. 10 schemas are not related to a perfect number nor are the 16 arche which are the traces of the Gods. The next meta-dimension is negative two with 25 elements. This is the next deeper level of trace that Buddhism focuses on with its 5 Buddhas. Buddhism is a heresy of the Indo-European Hindu worldview and it goes beyond the level of the Gods to a deeper level of trace. But of course these five are related to the pentachora which then is again level 32 which is related to a perfect number of relations which are 2^5 levels of progressive bisection. In the Pascal triangle there is a relation between the progressive bisection at each level to the minimal solid lattices at each level as two ways of interpreting the Pascal triangle. The lattice for the penta-chora is 1-5-10-10-5. There are five points and ten relations which give us 5 tetrahedrons one of which is emergent over the four tetrahedrons at the level of the arche which are 4*4 that are related to the third dimension with a lattice 1-4-6-4-1. Tetrahedrons can be fused to create the octahedron or interpenetrated to create the cube. Two pairs of tetrahedrons make up the structure of the arche with sixteen elements grouped in fours. When we transition to the icosa-dodaca-hedron structure and the pentachora that share the A5 group then we have the relations between 5 tetrahedrons. Each one has a different signature with respect to the five points that give us the pentagram in which those tetrahedrons are inscribed. Also inscribed in the pentagram is two Mobius strips that do not make up a klienian bottle. Each of the five signatures on the pentagram are immersions in the third dimension and there are five of them each one leaving out one point and using the 6 relations between the remaining points, selecting four at a time. It is these signatures of immersion that give us the five points times five selections which is the imprint of the pentachora at the second negative meta-dimensions. At the third negative meta-dimensions there are 40 elements. And so on. Four the purposes of describing the worldview these first two negative dimensional levels are enough because they capture the transition from the tetraheron in the worldsoul to the pentachora which is in the fourth dimension but also leaves its trace in the second negative meta-dimension as a square matrix of 25

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elements instead of the 16 at the level of the arche. We can call these twenty five elements nexes but by the ability to have perfect relations at 25 bisections and a lattice structure 1+5+10+10+5+1=32 we know these are a trace of the pentachora that appear as trace nexes in the negative second meta-dimension. Pentachora is related to the 5 Hsing in Chinese medicine and exist as a hypercycle following the two Mobius strips within the autopoietic system. Thus this level is related to the autopoietic special system which is relaed to the quaternions, the klienian bottle, the perfect numbers and other mathematical anomalies. There is a transition from the pentachora with its five tetrahedral and the four tetrahedral at the next lower meta-dimension seen in the arche. The production of another whole tetrahedron by the addition of just one point going from tetrahedron to pentachora is an emergent abundance worth noting and this is the basis of the difference between the quadralectic and the pentalectic as seen in the Emergent Design dissertation. The arche are the positions of the Gods or the pawns that appear in chess and chess is perfectly transformable across the second and third dimensions. This perfect transformability is like the relation between the icosa-dodacahedron and the pentachora though the shared group A5. But in the case of 64 elements arranged in an 8x8 square as the chess board gives us or the progressive bisection defining the solid pieces there is transformability between the second and third dimension and back again. A5 locks the pentachora and the iscosa-dodacahedron into the same lock step dance between fourth and third dimensions. In the worldview we see the transformation between the triangle in the second dimension and the tetrahedron in the third dimension. The tetrahedron has a perfect number of relations between its four elements, existenials and aspects. But then the worldview has seven heavens, and these can be seen either as the standings or the transcendentals levels that are meta-dimensions. We see these seven heavens for instance in the ascent of the pilgrim to the heavens in Dante’s Comedy. Dante’s comedy has a structure that perfectly exemplifies the meta-system organization. The precursor for this is unknown. But the seven heavens related to the visible planets plus sun and moon is inscribed into the worldview. They can be seen as either standings or transcendental levels. Numerologically that means the whole matrix has 49 possible elements of which only 19 are filled in as existing. There are 7 knots with 7 crossings, 21 of 8 crossings, and 49 of 9 crossings. All knots with 7 crossings or fewer are relational. The worldview is based on the fibered rational knots6 out of the entire set of possible knots in the table of knots. In the mythopoietic era all the possible knots were available to organize the transcendent, but in the metaphysical the current worldview structure was formed by a catastrophic collapse in which only the fibered rational knots were possible as the basis for the worldview. So the mythopoietic worldview structure was much richer. The schemas represent knots

6

Fibered rational knots with n crossings. https://oeis.org/A051449

+60

1

1, 1, 1, 2, 3, 4, 7, 10, 16, 25, 40, 62, 101, 159, 257, 410, 663, 1062, 1719, 2764, 4472, 7209, 11664, 18828, 30465, 49221, 79641,

128746, 208315, 336872, 545071, 881638, 1426520, 2307665, 3733880, 6040746, 9774133, 15813587, 25586921, 41398418

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with ten crossings and there are ten of them in fibered rational knots. In the first meta-dimension there are the knots of nine crossings and it goes down from there as we mount to higher transcendental levels. But 9 crossings relate to 49 knots, and so we can see the space of fibered rational knot formations as just being the first meta-dimension for the whole table of knots. The mathematics that defines the worldview is not straightforward but convoluted. It is caught up in the differentiation of the Pascal Triangles and the levels related to perfect numbers in contrast to those that are not perfect. The worldview in the positive dimensions are organized around the perfect numbers 6 and 28. Then there is a gap and the next number is 429 but that is related to the pentachora. The fact that the pentachora shows up at the second negative meta-dimension is significant. This is the negative meta-dimension that the Buddhists associate with existence and emptiness. The gods inhabit the first negative meta-dimension. For instance there are five mudras for the five Buddhas and if you say that each Buddha can make all the mudras then we get the 25 nexes. Of course there are ultimately more mudras that the main five but this gives the 5x5 matrix of differentiation suggesting the reflexivity of the pentachora, just as the 4x4 matrix suggests the reflexivity of the tetrahedron. In the positive meta-dimensions are the triangle and the tetrahedron, and then the tetrahedron is ramified in the first meta-dimension into four tetrahedrons and in the second transformed into the pentachora. The ramified tetrahedron in the first negative meta-dimension can be taken as an image of the Emergent Meta-system and that means that it is here that we get the extended divided line, or the four divided lines related to the Zoas or the realm of spirit related to the social community over time. All the elaborations of the divided line appear in the first negative meta-dimension. The fact that the divided line has four phases places it back into the schema of the tetrahedron, and the fact that these four phases have three crossing lines is where we get the triangle which represents the three highest meta-dimensions. Engaging in some more numerology we can say. The empirical image of the worldview is the Ark in the Epic of Gilgamesh. Gilgamesh itself has a structure reminiscent of the Divided Line. But the Ark has 7 levels and 9 compartments. Here we can relate the 9 to the crossings and the 7 to the number of elements at the first meta-level that is seven. 7X9 = 63 which is one shy of 64, i.e. all hexagrams other than heaven, all the earthly hexagrams. The point is that the ark of the worldview floats on the surface of the zeroth meta-dimension, i.e. n-dimensional space and the Ark goes up 7 levels of transcendence or has 7 standings at the first meta-dimension. Beyond that first meta-dimension there are six other decks. The 9 compartments are related to the number of crossings at that meta-dimension one. The upshot of all this is that the negative meta-dimensions each has an interesting meaning. The gods are in negative meta-dimension one. Buddhism encompasses the gods in Hinduism and moves to negative meta-dimension two thus changing the whole discussion. This suggests that Manifestation or the utterly nondual might be in negative meta-dimension three with its 40 elements. Just like the Five Buddhas

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and their mudras give us 25 nexes in Islam these forty ‘saints’ are called the Abdal7. Mystical coincidences aside it is quite clear that the negative meta-dimensions are a good place to look for an understanding of nondual concepts as they underlay the structure of the worldview. And it is fairly clear that negative meta-dimension one would have the quality of being a singularity and thus open up into an imaginary space which would be a likely home for the gods. Gods are sometimes thought about at the representatives of Pure Being. They are our projections of what pure spirit might be out of ourselves as our opposite: The immortals. They are definitely part of the fourfold as defined by Socrates and elaborated by Heidegger. The Fourfold contains Heaven, Earth, Mortals and Immortals. This is Socrates answer to the question what is the world. This is the mythopoietic answer. In the Metaphysical Era kicked off by Thales the answer given by Anaximander includes a Cosmology, A map of the Earth, the first prose book which was on Architecture, and the Apeiron which was the Metaphysical Principle. The meta-physical principle eventually under the influence of Parmenides became Being. Corresponding to Heavens we have Cosmic model. Corresponding to Earth we have the map of the Earth. Corresponding to Gods we have a metaphysical principle, and eventually the Gods come to exemplify Being in its purist form. Corresponding to Men we have prose books which men write about these subjects and which capture knowledge and which give us the basis for our civilization.

7 In Sufism, the Abdal are placed in a cosmic hierarchy with other orders of saintly individuals. Two

descriptions of the hierarchy come from notable Sufis. One comes from the 12th Century persian Ali Hujwiri. In his divine court, there are three hundredakhyār (“excellent ones”), forty abdāl (“substitutes”), seven abrār (“piously devoted ones”), four awtād (“pillars”) three nuqabā (“leaders”) and one qutb.

[7]

The second version is from Ibn Arabī, who lived in Moorish Spain. It has a more exclusive structure. There are eight nujabā (“nobles”), twelve nuqabā, seven abdāl, four awtād, two a’immah (“guides”), and the qutb.

[8]

https://en.wikipedia.org/wiki/Abdal

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Figure 9. Anaximander’s Definition of the Kosmos in the Metaphysical Era

What we want to do here is attempt to get the big picture of how the structure of the worldview can be modeled speculatively and see how that model points back to the Divided Line and its various possible elaborations. When we talk about the divided line we are really talking about cognition of experience and the different possible cognitions by which we understand the experiences we have within the world. The whole point of the Divided Line is to point us to the importance of invisible things to our understanding of the world. Once we set out to be initiated into the lower and higher mysteries that have to do with Becoming and Being in the invisible realm then we learn about the position of the Hierophant who wants change and changelessness at the same time and thus points our way to the supra-rational, i.e. that which goes beyond the law of non-contradiction and does not exclude the middle but seeks the middle way in all things. Once we achieve that position where we know there is cognition beyond what is rational then we can seek to modify the divided line to bring in other criteria to judge experience by, or by seeking higher criteria like spirit to control the excesses of reason, or we can think about extending the divided line in order to discover its transcendental grounds or roots. However, what we understand is that it is not the extremes beyond the pale of the divided line that the middle way is to be found but between ratio and doxa there is the utterly nondual which is manifestation. The projection of this difference outside the divided line suggests transcendence but what we would project out is also immanent within the divided line. There is something, i.e. manifestation out of which the difference between ratio and doxa appears that is prior to reason and doxa, just like Dasein is prior to Subject and Object. Out of that manifestation comes the other possible criteria that are associated by Blake with the other Zoas (urthona, luvah, tharmus). Each Zoa is fourfold with its emanation, shadow and spectre. The shadow is what the Zoa looks like to its emanation, while the spectre is what the Zoa looks like to itself. The nondual self as a whole which is Albion breaks up when it dreams into the Zoas that unfold their emanations, shadows and spectres which then engage in strife with each other. All this happens in negative meta-dimension one prior to any actual appearance such as we have in the bible where the various personas of god appear within history to the chosen people. In this way we see that the divided line has a precursor in the negative first dimension which is what Jung calls the Quaternion of Quaternions. Out of this field of possible divided lines comes the actual divided line that teaches us to take account of the invisibles. Once we have the concept of the invisibles then we are prepared to set up the worldview as a headland above the world. The metaphysical principle becomes a point of contention and various are suggested like Air, Water, Fire and Water but eventually it is a linguistic singularity of Being that is accepted at the insistence of Parmenides to become the metaphysical principle par excellence within the Metaphysical age. Thus the first meta-dimension becomes the differentiation of Being within the Ramified Logical Types. Continental Philosophy discovers their properties based on their elaboration of the work of Heidegger started in Being and Time. It turns out that there are five meta-levels of Being which are Pure, Process, Hyper, Wild, and Ultra.

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Figure 10. Meta-levels of Being

Ultra is at the level of existence and it differentiates and distinguishes the two interpretations of existence as Empty and Void. Beyond that is the utterly nondual manifestation and beyond that the Amanifest. Seven Standings appear at the first meta-dimension which is the first level of transcendences beyond the immanence of the schematized things that appear in spacetime. Once we have the multifarious kinds of Being then we have the substance to apply the rational criterion to when judging our experiences. But we discover that all the standings relate to just four aspects which are presence, identity, truth and reality and so we can consider these four to be within the second meta-dimension. They pose a new level of headland above the world where Being is differentiated. At each higher standing these aspects are transformed. There are 28 relations between the aspects and the standings which is a perfect number, so that all of them together add up to the whole and thus are autopoietic symbiotic in their relations to each other. When we bring together the nonduals and the aspects of Being then something interesting happens if we realize that both of them are related to the philosophical principles of Peirce and Fuller. Identity and Order are Firsts. All dissipative structures establish their own identity though their own ordering of themselves. Truth and Right are Seconds and between them they define orthogonality. It is orthogonality that gives us the idea of dimension and by extension meta-dimensions. When we recognize the fact that Being is Static and Becoming is Eternal Return and is a karmic trap then we eventually see that what we want is Ousia which is Good Presence or the Presence of the Good which is a combination of Thirds. Ousia is not just presence but Good Presence, i.e. a presence in which variety unfolds as at the mouth of a cornucopia. The Good by itself is variety production, but with Presence then we get the variety that we need as presented to us. Following this logic we can see that Fate and Reality are Fourths which relates to synergy of Fuller so where the center of the Republic is about the analogy of the Good outside the cave, so at the end there is the myth of Er which everyone ignores that tells us about fate. Fate is neither arbitrary or a pre-determined destiny but a dreeing of the wyrd. Nietzsche calls it Amor Fati, the Love of ones own fate. What ever happens there you are and it is about you.

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Figure 11. Assignment of Aspects and Nonduals to phases of the Divided Line along with the naming of the

Crossing Lines as Emptiness, Void and Manifestation which are the deeper Nonduals within the Kernel

But the key point of this analysis is that Fate and Reality are fourths, i.e. synergies and thus include within them the other elements that came before at the lower levels. In our analysis we have speculated that the fifth aspect is meaning and the sixth is necessity, that means that meaning has to do with integrity and sources and necessity has to do with poise or attitude and roots. The necessity is that there is a single cause for everything and all secondary causes are illusions. It is a matter of poise whether we look to the single cause or are caught off guard looking at secondary causes. This follows the principle of no secondary causation and that leads to a logic of disconnection as explored in my first dissertation called The Structure of Theoretical Systems in relation to Emergence (LSE, 1982). When you are poised to look at things in terms of no secondary causation then you derive meaning from that inclusive viewpoint and that implies fatedness or amor fati. Fate is loved because it is the source of meaning in the world and thus the antidote to nihilism. Nihilism takes meaning out of the world. If you actually accept the idea that there is no secondary cause then that means all good or ill comes to you from a single source. That generates meaning for events, and it makes you recognize your fate which is a reality to you. Meaning is generated when you connect things to their sources, i.e. where they come from and how they carry along with them their provenance and legacy. By sources we mean the upwelling resources of nonduality that are the basis of life. Shaykh al-Akbar call them the ayn al-Thabita. For him either exist or do not exist and they switch off and on in existence thus establishing the connection or disconnection from God and thus make way for understanding the transcendence or immanence of the self. Nonduals come from Ratio and the Aspects come from Doxa when we combine them like this we get a glimpse of what comes before their duality.

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Figure 12. Various ways of looking at the WorldSoul in terms of Physus and Logos ad their relation to the

Quadralectic

Before this inner shell of the worldview there is a higher level set of transcendences at meta-dimenions three and four that relate to the WorldSoul. There are three elements at level three and two at level four. We see this in the two series that appear from one in Plato’s description of the Worldsoul. 8-4-2-1-3-9-27. On one side are powers of two and on the other side powers of three. On the one side we have the information infrastructure which is a binary progression and on the other side we have the meta-levels of mediation. This model of the WorldSoul has been explored in my dissertation on Emergent Design. The key is that the two and three are multiplied to give six relations, and those relations exist between the four points and four surfaces of the tetrahedron, or minimal system. The points of this tetrahedron are the existential that derive from Egypt, Semites, and Sumeria which then combine in a synthesis to yield the four aspects. This is the soul of the Worldview because it is this combination of the different features from the different cultures that were in the Middle East that were the basis for forging the Western worldview. This is covered extensively in my book on the genesis of the Western worldview. The key point here is that the core structure of the Western worldview is forged from the interaction of existentials. Of course, these exisentials are now forgotten but they underlie the basic structures of the aspects and the standings in the lower meta-dimensions. And the key point is that the six relations between the four existentials and the aspects is a perfect number, the first perfect number and associated with the minimal solid in the third dimension, which happens to be the dimension in which we find ourselves in space. On the side of Phusis the four things can be seen as the Causes (Aiton) of Aristotle, and on the side of Logos they might be the master tropes (metaphor, metonymy, synecdoche, and irony). The distinction between Physus and Logos is the core duality for which the nomos (Order) is the nondual. Logos is the root of rationality, which is based on the Legein of language. Because of the four virtues we associate the rationality of giving reasons with

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temperance and thus the ratio in mathematics. If we take the physus as the source of sensations and thus appearances and then our opinions when these appearances are introduced into language by the one trapped in sense certainty then we see that Doxa and Ratio are merely repetitions of the distinction between Physus and Logos internally thus conditioning the subjective experience at the same time as distinguishing it from the objective. It is the ramification of the dualities within the Western worldview that generates the nonduals as non-excluded middles.

Figure 13. Nonduals within the Western worldview in relation to their Dualities

Beyond the WorldSoul is the trinity which are at meta-dimensional levels 5, 6 and 7 with one element at each level. We can take the trinity as that absurdity that Kierkegaard embraces as the exemplification of paradox taken to an extreme which posits the impossibility of the incarnation of God, i.e. the avatarism of Paulist Christianity. The Hindu equivalent Krishna is so much more humane and interesting than the Western avatar but the inhumanity is also there with the sending of the Pandavas astray. But the three ones at each of these highest transcendental levels does not have to be seen as a trinity of paradoxicality but can be seen supra-rationally as the basis for the distinction between emptiness and void on the one hand and manifestation as utter nonduality on the other. The point is that triality i.e. three way complementarity that Arkady Plotnitsky talks about actually exists in the Octonion. It is very rare and is the central feature of the Reflexive Social Special System. So just as the fourfold nature of the tetrahedron can be associated in the fourth dimension with the quaternion, so the triality of the octonion can be associated with a different type of trintarianism that as Cassirer says is functional rather than substantial. Thus each of the levels of the Worldview transcendences is associated with different Special Systems. Triality is a unique three way complementarity that appears in mathematics and we can take that as the basis for understanding the trinity in the worldview instead of the religious dogma that defies reason that haunts our worldview. The key point is that there really is a Trinitarian structure at the kernel of the worldview at the highest transcendental

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planes but it is not necessarily an absurd and impossible religious doctrine that indulges in mixture, but can be seen instead through the lens of suprarationality to be the three ones that separate the phases of the divided line instead. Triality of the octonion allows the quaternion to fold back on itself and it produces the Fano Projective space which is the topological structure of the worldview. The octonion allows us to be reflexive and so it also shows up as the aufhebung (sublation) of Hegel and his ideas on mediation. You need three things in order to have thesis, antithesis and synthesis. By seizing on the trinity and using the Holy Ghost as the basis for the dynamic of the community spirit in history then Hegel uses the trinity at the core of the worldview as the basis of his philosophy, and that is why he seems to understand everything and be able to dominate everything in the world in his system of philosophy. But his system has an obverse side that Plotnitsky explores In the Shadow of Hegel that relates to the General Economy that he discusses in Complimentaries where he first suggests that multi-complementarities are possible. They are possible but they are rare and the worldview seizes on this rarity to produce its own organization. It seizes on triality to produce its inner dynamic that revolves around impossibility or achieves supra-rationality and it seizes upon Quadrality that appears in the Quadralectic that is related to the Emergent Meta-system that can be seen in the extension of the Divided Line. Heidegger rages against worldviews as does Cassirer in his own more urbane way. But in point of fact they would not be rejecting them if they were not powerful ways that we use to understand ourselves. This speculative model of the Worldview allows us to map the territory and gives us a strawman with mathematical structure to reject. If we are going to rage against worldviews then at least let’s have a good example of a model of one to tear down. Worldviews for Heidegger are hated because they cover up what is really happening which is closure and disclosure. They are at best reifications that get in the way of understanding what is really happening. For Cassirer they suggest relativity and a lack of objectivity. But if we don’t recognize what the model of the worldview could be and what its structure actually might be then we cannot challenge it adequately. I call this hypothesis W-prime which says that above the Schema level of abstraction there has to be another structure within which the schemas can be understood. We take the idea of meta-dimensions as a point of departure for constructing a model of the worldview, and then we find the series of the fibered rational knots as a clue to what the actual structure of the worldview might be. Then we elaborate it and connect it back to what Plato and Aristotle have said and agreed upon, and then we have an idea of what the Transcendental superstructure of the world might be, and that helps us to understand the emergent event. Because in an Emergent event that transcendental superstructure disappears and the kinds of Being become immanent taking on the configuration of a face of the world. We do not have infinite powers of projection, and so if we are to believe Kant that we project spacetime and the categories that projection process better be finite otherwise it would take an infinite amount of energy which we do not have. We can imagine ourselves projecting just seven transcendental levels because we see that in our traditional cosmology. We can imagine that the Trinity is fundamental to the worldview because that is what we

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see in Christianity and its impact on the worldview. Christianity creates an avatarism based on Paul’s reading of the meaning of the death and resurrection of Jesus as Christ. We can see the early believers in Jesus propounding a doctrine of Agape Love that fills up the divided line in the Sermon on the Mount. But we also see Jesus in the Gospel of Thomas as presenting a nondual doctrine that is related more to Buddhism and Taoism than to Christianity and Buddhism. We need to account for that nonduality and we find we can use the Divided Line to do that and we can see that nonduality Jesus speaks of in the Gospel of Thomas as the kernel of the Divided Line. After we accept the formulation of the Divided Line and the kinds of Knowledge that Aristotle talks about as the core of the Western worldview then we can begin to understand how that core has a nondual kernel and how that can be related to the trinity interpreted in a supra-rational rather than absurdist way that Kierkegaard prefers and takes to heart in a leap of faith. We can see the aspects of Being and the kinds of Being as a version of the Ramified Higher Logical Type theory created by Russell and described succinctly by Copi, and we can understand how it could be that continental philosophy explored that territory discovering its emergent levels after Heidegger showed the way by identifying the first to levels as the Present-at-hand and Ready-to-hand.

Figure 14. Higher Logical Type Theory

This gives us a context in which to study the Schemas as a part of the worldview that is modeled as having a specific structure given in the W-prime hypothesis. This becomes the context in which to explore the possibility of the S-prime hypothesis.

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Figure 15. Schemas Theory

Then we can put that into the context of the framework developed by Cassirer.

Figure 16. Cassirer’s Evolution of Spirit

And that allows us to see how Schemas relate to the Foundational Mathematical Categories, the Order View Hierarchies and the Philosophical Principles which make up the key elements of Schemas Theory. We can thus make use of the philosophical complementarity of Cassirer and Heidegger as a framework for further exploring the context of Schemas Theory within our model of the Worldview. In the following figure we see the Worlds of Penrose and Popper along with the Intersubjective World of Carnap from the Logical Structure of the World. The Worlds of Popper and Penrose are combined in the basis for the Foundations of Systems Science by Kenneth Lloyd. But we find this model of the Popper/Penrose Worlds to be an image of what we call the Quadralectic in Emergent Design. And the addition of the Intersubjective objective world gives us an analogy to the Pentalectic also developed by adding the bystander as another position in the dialectic of Author, Reader, Character and Narrator.

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Figure 17. Worlds Theory

Once we have mentioned Worlds then it behooves us to mention Badiou’s “Logic of Worlds” which is the second volume of Being and Event. Badiou attempts to formulate a rigorous theory of worlds based on Logic. His book demands a thorough critique which I intend to undertake elsewhere. The idea of Foundational Mathematical Categories (FMCs) comes out of the critique of Badiou who thinks that Sets are the only foundation of Mathematics. With FMCs we instead accept all the foundations and we arrange them in relation to each other based on the Peirce/Fuller Philosophical Principles. Thus the first volume of Being and Event led to an advance in the understanding of mathematical foundations which provided the basis for understanding Schemas. Schemas draw on the various FMCs to articulate their contents while remaining essentially transparent. We have also recently noted that there is a meta-logic associated with the various FMCs which give us models of Subjectivity. Badiou also conceptualizes Logic narrowly and does not explore the various possible deviant logics. For all of his pretense of being radical politically he is very conservative in his thinking about Mathematics and Logic. Rather than limiting foundations of mathematics to Set Theory which has basically failed as a foundation due to Russell’s Paradox we accept multiple foundations and attempt to understand how the possible foundations may relate to each other. Similarly with Logic we accept many different logics including deviant logics and attempt to understand how they relate to each other and that opens up to a fundamentally different theory of the Subject and its relation to the hypothesized worlds of which it is a part and which it is schematizing. We have engaged in some numerology in this paper because we are still struggling to understand some of the structural features of the W-prime hypothesis that the worldview has a particular structure based on the Fibered Rational Knots. Structure means that the actual numbers matter, and they are not just arbitrary. Attempting to understand how they matter and what they mean is the purpose of a benign numerology, i.e. it is not just numerology for the sake of numbers themselves but rather for the sake of unearthing the meaning of certain numbers that show up in this model of the worldview hoping that these structural relations will be enlightening in some way. The point of hypothesizing a particular structure to the

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worldview itself is to attempt to understand in a more mathematically sound way what the physiognomy of the worldview actually is like. In other words the worldview is not just vague, amorphous, indistinct, indeterminate, ambiguous but has particular structures that we may prescind8, i.e. that we can ferret out if we are bold enough to speculate as to the worldview’s actual structure. To the extent it tells us what we would know if the worldview had a discrete structure then it is successful. The model allows us to attempt to explain various features of the worldview in which we find ourselves which is dominant worldwide that could not be explained without the model, or at least that is the hope.

8 prescission – Cf. Peirce See Volume 5-6, p.303 in Peirce, Charles S, Charles Hartshorne, Paul Weiss, and Arthur W. Burks. Collected Papers of Charles Sanders Peirce. Cambridge: Belknap Press of Harvard University Press, 1960.