Foundations of Special Systems Theory Chapter 03 Kantian Categories as a Model of the Six Core Lacunae as the Abstential Eventities of Ententional Phenomena within Autopoietic Symbiotic Systems in a Reflexive Social Field Kent Palmer http://kdp.me kent@palmer.name 714-633-9508 Copyright 2013, 2014 K.D. Palmer All rights reserved. Not for distribution. FoundationsOfSpecialSystemsTheory03a03kdp20140120a http://orcid.org/0000-0002-5298-4422 2013.7.16-18 edited 2014.1.20 Introduction The fundamental problem which we are addressing here raised by pushing back Terrence Deacon’s work into the foundation in Peirce is how it is that the entire field of meaning is produced with local presences with lacunae and global absences that appear in teleodynamics and perhaps sociodynamics as well when we extend our theory beyond the range that Deacon surveys that becomes visible with Special Systems Theory. It is clear that the lacunae come from the conjunction or disjunction between the separate morphodynamic systems. Each of those systems produce a series of repetitions independently. Those series cross as noted by Deleuze producing the floating signifier. However, what our theory tells us is that there are two AutoGen each different that combine into a SocioGen to give various TeleoGen. Deacon has named one composed he believes of Self-assembly and Hypercyles. We don’t at this time have a candidate for the other AutoGen composed of two orthograde processes that are complementary. This is an open problem. But even without knowing what the other AutoGen predicted by the theory might be we can draw some general conclusions about the overall structure. For instance, if each of the Morphodynamic Dissipative Structures is producing a replicated series and there are four of them, that means that there are six possible lacunae between them. That is six floating signifiers each with their own quality and type. What we are looking for are four morphodynamic processes which can productively combine with each other to give us six possible AutoGen to of which are embodied as different possible foundations for Life. The other four could be virtual. But of course it would be best if all six were capable of embodiment. This gives a very stringent condition for life. We are looking for four orthograde negentropic processes that fit 1 together such that each feeds what is needed for each of the three others. And we are imagining them to be such that they produce repetitive series in such a way that each of the floating signifiers is realizable. Now it could be that instead what we will find is a symmetry broken structure which does not completely realize this perfect embodiment. But since the AutoGen itself is an idealization we might as well go all the way and consider the perfectly embodied sociodynamic system. The six lacunae that appear as floating signifiers would then interact with each other at a distance across the sociodynamic system each with their own quality and typology. Each forms patch or neighborhood in relation to the entire set of the other lacunae standing out on that background. But of course all the lacunae are referenced to the zeroth which is the ground of emptiness or void to which each lacunae refers. We know that Domain Walls exist in Condensates and it is possible to distinguish these lacunae from each other by their domain walls. In fact we know that domain walls collapse and stabilize into hexagonal patterns, honeycombs which is the mirror structure of the Autopoietic Symbiotic Special System which is convenient. Three mirrors facing as an equilateral triangle produces a virtual hexagonal space surrounded by myriad other virtual hexagonal spaces. We can see the reflected mirrors within this honeycomb as the domain walls between the lacunae. At any given time two AutoGen are embodied and four are virtual. What we are going to posit is that the lacunae are not related to transcendental absential eventities but that the abstential eventities are from the set of lacunae in every case and thus immanent. We take this imperative of immanence from Deleuze. Transcendence is always an illusion. In a sense this sets limits to the TeleoGen within the SocioGen. It predicts that there are six basic types of TeleoGen with in the SocioGen. Of course, we don’t know what these core ententional phenomena are but let us pretend for the sake of argument that they are reflected in the Kantian Categories. We note that there are four basic higher categories each of which has three lower categories. It is generally agreed that Kant just pulled this structure out of thin air. But of course we note that are twelve of these lower level categories. Twelve has always been a convenient number for dividing. Each of the lower categories in each higher category is thought of as a frozen dialectic. Hegel had a field day setting these dialectics into motion in his logic. One thing that has been clear to me for some time is that wholeness is the nondual between Unity and Totality.  Quality {Intrinsic, Awareness, Zeroth, Dissipative Structures} o Reality (Quantity sense Plurality)  Negation (Relationflux substance and accident) o Limitation (ModalityconstraintNecessity) Quantity {Extensive, Wholeness, First, Self-Assembly} o Unity (RelationprojectionCause/Effect)  Plurality (QualitysenseReality) o Totality (Modality allExistence) Relation {Extrinsic, Entailment, Second, Hyper-cycle}   2  o Inherence and Subsistence (substance and accident) (Qualityflux Negation)  Causality and Dependence (cause and effect) (QuantityprojectionUnity) o Community (reciprocity, mutual entailment) (Modalityinterdependence Possibility) Modality {Intensive, Actuality, Third, Spontaneous Bipolymerization} o Possibility (Relationinterdependence Community)  Existence (Quantityall Totality) o Necessity (Qualityconstraint Limitation) We notice that each of these four types of dialectic is very different from each other. But supposedly they work together to give us a world in which Newtonian objects exist for science to discover and understand. But each is an ideational reification of something more basic. For instance behind Quantity stands Wholeness. Wholeness encompasses Unity, Totality and Plurality. What the non-reified form of the other Higher Categories might be is unknown. But let’s pretend we know for a moment what they might be. If the difference between the Kantian Categories is like the difference between the four Morphodynamic systems, then we could imagine that the lower level categories are the way that the other three look from the view point of this non-reified substrate. Each of the lower categories is how the other higher categories look from within the non-reified categories. This would mean that any given sub-category should be matched up with an opposite sub-category in order to have views in both directions across that bridge. This means that there would actually be six two way bridges between these four morphodynamic dialectical elements. In the tradition it has been assumed that they are independent from each other. Kant only really believed in Firsts and Seconds with Thirds of the Hegelian style more or less unknown to him. We can think of Quality as what comes before Firsts and Modality as what comes after Relation or Seconds. In a sense Quantity and Quality are mirror images of each other and the same is true of Relation and Modality. But we can imagine Quality and Modality as pre-images of Zeroths and Thirds. These are probably not the lacunae proper, but at least it gives something to stand in for them until they are identified. And this set has the virtue of being the a priori that were posited by Kant and thus are core to the tradition as the strawman for the a priori syntheses we project. The middle term is the dialectical result in each case. We posit that as a first guess that the nonduals are Awareness for Quality, Wholeness for Quantity, Entailment for Relation, and Actuality for Modality. Each lower category is a view point on another of the higher categories and thus we get six two way bridges between the four higher categories. The bridges stand in dialectical relation within each higher category. So all the higher categories stand in direct relation to the others via the lower categories and their bridges to the other higher categories via related sub-categories. But each higher category is realized by the dialectical relations between the subcategories within it that reifies the nondual that stands behind the sub-categories. 3  Quality {Intrinsic, Awareness, Zeroth} o Reality (Quantity sensePlurality)  Negation (Relationflux substance and accident) o Limitation (ModalityconstraintNecessity) In Awareness we sense reality though its plurality in experience. But there is a priori limitations on experience by necessity (i.e. the necessary conditions for the possibility of experience) which places a constraint on sense. Reality under the Limitations of the constraints gives dialectically negation which is the condition for comprehending flux in awareness which is contradictory. That contradiction gives rise to paradox and absurdity, which is the nature of Being or substance.  Relation {Extrinsic, Entailment, Second} o Inherence and Subsistence (substance and accident) (Qualityflux Negation)  Causality and Dependence (cause and effect) (QuantityprojectionUnity) o Community (reciprocity, mutual entailment) (Modalityinterdependence Possibility) Relations become apparent in the flux which alternates between substance and its negation (Nothing) as Hegel discusses in his Logic. But the opposite of the flux is the interdependence brought about by community exploring possibilities. Community here means reciprocity of relations. Flux running though the interdependencies dialectically gives rise to the impression of causality that unifies phenomena through projection.  Quantity {Extensive, Wholeness, First} o Unity (RelationprojectionCause/Effect)  Plurality (QualitysenseReality) o Totality (Modality allExistence) The unity of the projection by which we see cause and effect together with the totality of existence which is all there is gives rise dialectically to plurality which allows us to comprehend the reality of experience which we sense. And this feed back into Quality to give a robust and complete cycle.  Modality {Intensive, Actuality, Third} o Possibility (Relationinterdependence Community)  Existence (Quantityall Totality) o Necessity (Qualityconstraint Limitation) Modality stands outside this loop of projective flux that produces sense. If Community gives rise to possibilities of interdependence by combinatorics and 4 Limitations give rise to necessities that impose constraint, then these dialectically will produce Existence as a totality of all there is to be experienced which then feeds into supporting Quantity. Or on the other hand if the totality of existence breaks up then it would break up into necessities and possibilities that in turn could drive limitations and the creation of communities of reciprocal relations that would support Relation and Quality. We posit that Kant does not think Mediation thoroughly as does Hegel and it remains as modality a subsidiary concept and a degenerate form of the Third. So here we see that Quality, Quantity and Relation form a cycle of the projection of the flux of sense within experience and that is supported by constraint, interdependence and the all of experience. In this way we can see Kantian Categories as producing the six lacunae of flux, sense, projection, constraint, interdependence and the all of experience. Three of these produce a cycle of self-production while the third supports this cycle in terms of the articulation of modalities. This dialectical structure that connects the lower level categories to each other to form the six lacunae gives us a model by which to understand the relation of the AutoGen to each other at a very abstract level. The Hypercycle is like the relation of cause to unity. The cycle of causes gives rise to the unity of the system which is a projection. Self-assembly is like the relation of plurality to reality related to sense. A plurality of parts are put together which we can sense to produce an embodied reality. So the AutoGen which is defined by Deacon represents dialectical synthesis of both Quantity and Relation together. This implies that the other AutoGen is related to the dialectical outputs of Quality and Modality. One morphodynamic would be related to the production of flux by positing substance and its negation. The other morphodynamic would be the production of all of experience by the encompassing of existence by totality. You can see that this is almost a definition of the material substrate as the other AutoGen. If you look carefully at the Deacon AutoGen morphodynamic components what we see is that neither of them are in fact the Dissipative Structures of Prigogine per se and if we look at DL Abel’s article1 which reviews the possible spontaneous structures and denies the existence of self-organization then there are several possible structures listed. Of those listed Dissipative Structures ala Prigogine and Spontaneous Bipolymerization2 seem the most likely candidates for our purposes. 1 Abel, DL & Trevors, J.T “Self-organization vs. self-ordering events in life origin models” Physics of Life Reviews (2006) doi10.1016/jplrev.2006.07.003 Elsevier B.V. 2 “Is polymerization a self-organization process? Namely, is the product (the polymer) the result of the internal rules of the system? The answer is not as clear as in the case of the formation of a micelle or of a crystal. I believe that a positive answer can be given in the case of spontaneous polymerization, as in the formation of nylon starting from a mixture of dicarboxylic acid chloride and alkyl diamines; or the polymerization of styrene induced by heat or by light; or the formation of oligopeptides starting from N-carboxyanhydrides. However, in the case of step-wise polymerization – for example, in the Merrifield synthesis – this is not the case, and I would not include this polymerization process in the category of self-organization.” P. 95 in Luisi, P L. The Emergence of Life: From Chemical Origins to Synthetic Biology. Cambridge: Cambridge University Press, 2006. See also Zhao, Zhitong, "Modeling spontaneous three-dimensional polymerization", Master's Thesis, Michigan Technological University, 2013. http://digitalcommons.mtu.edu/etds/208 5 The dissipative structure projects a boundary and turns what is outside that boundary into the ordering that it imposes inside the boundary. We associate this with Quality. Then given the boundary we can imagine a process of self-assembly and hypercycles occurring with the boundary. Deacon more or less assumes that self-assembly leads to a boundary naturally which is unlikely. Given that a boundary is established as a dissipative structure in a medium we can see that the structural organization could further undergo self-assembly of structures within that boundary, and that hypercycles might catalyze that process. But ultimately if we want replication of polymers3 then we must rely on something like spontaneous bipolymerization to produce those structures given that various self-assembly structures have been produced which are the materials for spontaneous production of polymers. This may lead into Amino Acid production via free energy binding. What can be seen in this model is that none of the spontaneous processes on their own is enough to give rise to life, but all of them together at their proper level of complexity might have a chance to go beyond order into organization. The organization of Kantian sub-categories into the six lacunae gives a template pattern to the whole process that differentiates the levels and shows the symmetry breaking between them. All we are saying is that there are enough differentiated spontaneous orthograde processes that can be combined and they appear to operate at different levels physical ordering. The using the Kantian model as a template for understanding the core Ententional phenomena of abstential eventities seems to suggest the same number of levels of ordering and give a path from ordering to organization at the conceptual level. Whether these specific orthograde spontaneous processes would ultimately fit together to form life is unknown. But Abel does not seem to consider the possibility of the various spontaneous orthograde processes cooperating each at their own level to move from selfordering to self-organization the possibility of which he denies. What we get out of it is the concept that there is a projected self-organizing structural template that relates the six possible lacunae (sense, flux, constraint, projection, interdependence, all4) in an immanent structure of mutual dialectical constitution and mutual reference. The fact that we get this structure of self-organization out of the Kantian categories which are supposed to deliver a priori synthetic projection is of great interest. The question that we are asking here as a thought experiment is how it is that the various orthograde spontaneous processes might combine together to produce life, 3 Pross, Addy. "Causation and the Origin of Life. Metabolism or Replication First?" Origins of Life and Evolution of the Biosphere. 34.3 (n.d.): 307-321. 4 The possible relation of gaps to source/sink holes in the aspectual field. sense’fragmentation, flux’emotion, constraint’abyss, projection’exclusion, interdependence’inclusion, all’synthesis. These six lacunae may be related to the six holes (source/sink) in the Aspectual Field. See “Dreamtime Structure of Inception: An Introduction to the Aspectual Field based on the movie Inception as a cultural object that contains the entire field of anamorphic entities with anagogic affects” by the Author 6 and how at the teleodynamic level we get the production of interdependent references between lacunae without transcendence. One question is at the physical level and the other at a semiotic level in which interacting morphodynamic systems produce projections of distinctions that refer to ententional phenomena by referring signs that are present to abstential eventities. Terrence Deacon really does not have answers to these questions in his present work. His work is truncated by only considering two orthograde spontaneous processes within his AutoGen hypothesis. He does not consider the possibility that there are multiple coordinated spontaneous orthograde processes at different levels that are brought together to produce life and Abel the critic of this concept does not consider that either. But how is it possible for various spontaneous orthograde processes to be coordinated in a fashion that leads to life. We are talking about a very rare event since it only occurred once on Earth and nowhere that we know of in our solar system. When we consider the functioning of every cell on Earth since the earliest proto-cell the fact that all these are derived from the proto-cell means that this is an incredibly rare event even if we just take earth into consideration, because at any moment a new proto-cell could arise, but it has never happened in a way that led to a lasting line of living things which might leave a fossil record. To all intents and purposes if we take the criticism of Abel seriously it would appear that Life is a miracle. However, we would not want to accede to this conclusion without first exhausting every possible scientific explanation. Once we accede to a miraculous origin to life, social and consciousness then our search for plausible rational answers would cease. But something extraordinary would have to be appealed to explain a unique genesis for life, consciousness and the social. We are looking for something just as rare and unique as life, consciousness, and the social itself. We know that dissipative structures exist in far from equilibrium situations. But these are very special circumstances, however it just so happens that because of the relation of the sun to earth we happen to live in a stable far from equilibrium situation. The fact that dissipative structures can arise on a regular basis in the far from equilibrium environment that exists on earth is established. It should be noted that the whole universe is far from equilibrium in as much as dark energy is pouring into the universe keeping it accelerating in its expansion, so far from equilibrium situations are universal in our own universe. Earth is no exception here, and probably there are myriad worlds with similar situations as our own and that is why we believe that there may be alien life somewhere. But given the fact that it only arose once in the entire history of earth we can say that it is an incredibly unique situation that must produce life and so if it occurs anywhere else it is liable to be an extremely rare situation. But if we are looking for a rare anomaly to support the appearance of self-organization from self-ordering spontaneous orthograde phenomena that occur in physics then one place to look is in Mathematics. This is because dissipative structures which are possible are negatively entropic and are thus creating order, and order is constrained by mathematics which is the source of all order. It turns out that there is a rare anomaly in mathematics which we have called the meta-anomaly. The meta-anomaly occurs apparently because as we move from plurality and large numbers to small numbers and unity there are various 7 fusions that occur at different levels of complexity that are in themselves anomalous. We postulate that this meta-anomaly in mathematics comes to shape the orderings that are possible for dissipative structures and therefore defines the nature of morphogenesis. Given this situation and also the situation that we are physically in four dimensional space and also that there are macro-Quantum Mechanical phenomena. We combine these four different configurationally circumstances to explain the miracle of life, consciousness and the social arising. Deacon says he will not appeal to Quantum Mechanics and ignores the fact that everything he is describing in terms of thermodynamics takes place in a four dimensional environment. Four-dimensionality and macro-Quantum Mechanics are of a piece. In other words it is almost the same thing to say that we are living in a four dimensional environment as to say that we are making use of the ubiquity of Quantum Mechanics. However, there are some interesting ways in which Quantum Mechanics goes beyond four dimensionality. For instance the fourth dimension has no set topology and that could be the way that relativity and quantum mechanics are reconciled. But in general it is almost the same to say that we are living in a four dimensional space, appearances to the contrary, and that we are immersed in a macro-quantum mechanical physical environment. When we consider that the dissipative structure is a four dimensional structure operating in a quantum mechanical and relativistic four dimensional space this greatly enhances the types of processes that are available to us to explain the arising of life. And then when we note that the dissipative structures are drawing on the kind of order that is represented by the macro-anomaly to turn self-ordering into self-organization then that conjunction of the rarity of self-ordering phenomena and the rarity of the mathematical structures that are inherent the panoply of possible mathematical orderings is important to recognize. In effect the macro-anomaly is what creates the structure of the fourth dimension as a unique dimensionality among the ndimensions that are possible. However, this dimensional structure anomaly is at a very low dimension, in fact the same one as the physical environment in which we live which is one dimension away from the three dimensions that we experience as our apparent habitat. If anything is a miracle it is that the anomalous fourth dimension is low dimensional, and happens to be the same physical dimension in which we dwell as living creatures. Thus what is being invoked are anomalous structures that appear in mathematics that are active in the very dimension in which we live, and which is the dimensionality that quantum mechanics expresses as well as relativity theory express themselves within. Thus it is not farfetched to say that life is a relativistic and quantum mechanical phenomena that exists in the fourth dimension which is anomalous mathematically expressing the structure of the macro-anomaly in math. What is unique is the situation which allows all these factors to align, i.e. to have contained spontaneous orthograde processes, that are partaking in the configurational space of the relativity and quantum mechanics as well as the four dimensional structure of physical nature giving rise to a creature with limited experience of that physical situation which apparently exists in a three dimensional space with an asymmetry that produces time (nowhen), or with a three dimensional time and a single dimension of time (nowhere). In effect the nature of the Matrix (4sx4t) of spacetime is eight dimensional with four dimensions of space 8 and four dimensions of time, and there are various symmetry breakings of spacetime that are possible within the Matrix. Our 3sx1t symmetry breaking of appearance is just one possible symmetry breaking within the Matrix. The Matrix is contained within the series of Schemas that make up the S-prime hypothesis of General Schemas Theory. That hypothesis goes from dimension -1 to 9 after which String theory occurs in the tenth dimension, then M-theory in the eleventh dimension and F theory in the twelfth dimension. In F-theory there is an orthogonal time line that physicists do not know what to do with that occurs. We count this fourth moment of time that arises in orthogonal time as extremely important. Its reappearance ushers in the heterochronic era after the loss of that fourth moment of time in the metaphysical era. It is this fourth moment of time which was lost in the meta-physical era that is extremely useful for understanding the source of life, consciousness and the social. We follow Pico in his conjecture that there are relativistic frames associated with not just the thermodynamic processes but also with the teleodynamic, morphodynamic consciousness, and sociodynamic. Each emergent level produces its relativistic frame based on its clocks at that given level of emergence. One way to understand life is through the fourth moment of time. This is a virtual co-now that is mythic associated with the social and language. However, at the level of life the fourth moment of time allows the unification of the other four ecstasies of time because it stands off in orthogonal time and can have a view of the other three ecstasies of time together. Life is future oriented as both Heidegger and Deacon say. However we have to explain the binding of time that occurs at each emergent level and the best way to explain that binding is via orthogonal time. The rarity of life which is conscious and social is based on the rarity of that binding, not just the conjunction of the orthograde spontaneous negatively entropic processes within a dissipative structure. The order of the dissipative structure tapped into the meta-anomaly and had the opportunity to use the other orthograde spontaneous negative entropy processes that are physically viable. It is readily understandable how the juxtaposition of all these conditions could be rare. But we do not think that the dissipative structures appearing is rare. In fact we think that there were many different dissipative structures tapping in to different orders and exploring the possibilities of those orders until one hit upon the use of the meta-anomaly and the fourth dimension of time together with the other various spontaneous orthograde process that were available to it. The space of physical ordering possibilities is huge but the point where the imaginary opens up from there is only one point in the entire design space. But it just so happens it occurs at negative one, and thus close to zero, but in a negative range. So the production of that negative value would also probably be rare. It is only the facet schema that goes down into the negative first dimension. Therefore we are looking for something faceted which is participating in orthogonal time such that it binds the three moments of time together for the proto-living system that arises from the conjunction of two dissipative structures in a configuration space that contains multiple spontaneous orthograde processes that are negatively entropic and which spontaneously gives rise to the projection of the six lacunae that come from the conjunction of four dissipative structures giving rise to a virtual spacetime that is symmetry broken in a 3sx1t and 1sx3t way but is based on the organization of the 9 fourth dimension, quantum mechanics and relativity in as much as a new clock structure is produced and thus a new reference frame. Precisely how this can occur physically is unknown. Science has a hard time dealing with origins of rare events. But science is giving us some clues as to what we must consider in order to understand those origins, and the limits that Deacon is setting on his own enterprise is too narrow and Special Systems Theory does not set those kinds of limits excluding Quantum Mechanics and Relativity Theory as well as fourth dimension. Our own project is not to explain the specific physics of the proto-life situation, but rather the a priori background that makes the physical situation possible. In general proto-life draws upon the meta-anomaly as an a priori structure that makes life possible and provides the meta-theoretical framework that makes it understandable. We live to the physicists to use this framework to fill in the specifics of how the spontaneous orthograde processes combined to work within this framework to bring about life, consciousness and the social as emergent levels of phenomena of which we are exemplars. 10