Foundations of Special Systems Theory Chapter 02 C.S. Peirce’s Name taken in Vane1, (i.e. semiotically) Kent Palmer http://kdp.me kent@palmer.name 714-633-9508 Copyright 2013 K.D. Palmer All rights reserved. Not for distribution. FoundationsOfSpecialSystemsTheory02a03kdp20140120a http://orcid.org/0000-0002-5298-4422 2013.7.11-15 edited 2014.01.20 Terrence Deacon uses C.S. Peirce’s philosophy as a starting point for his ruminations on the ententional phenomena caught up in abstential eventities. And that is a good place to begin for out deeper look at the map which Deacon uses to try and cover the territory that is related to the Special Systems. Peirce has three philosophical principles which he calls First (isolate), Second (relata), and Third (continua) by which he tries to understand almost everything. Deacon does not mention these Peircian principles and how they relate to his program of trying to understand absences. One thing we might point to is the idea of the continuum that Peirce says is the basis of his philosophy. By continua he does not mean Cantorian Set Theory and the movement from Aelph0 to Aelph1 and beyond which is ultimately built on some type of discrete foundation. Rather he means a perfect continuum without points but only neighborhoods inspired by Topology. Peirce is a Kantian but who is wrestling with Hegelianism. Peirce is the beginning of the turn toward Logic. Peirce made many improvements that led to Symbolic Logic like adding Existential operator, and identifying abduction as the alternative to deduction and induction. In general, philosophy before Peirce only dealt with Firsts and Seconds and not Thirds although they were implied in Logic and Causation and in other phenomena related to the Kantian categories. One of the things I had been wondering for a long time is where the aspects of Being came from. Then recently while reading Heidegger’s Being and Time (B&T) I realized because Heidegger said truth was relational that perhaps the Aspects of Being were related to the Philosophical Principles2 of Peirce. Thus we can think of Identity as being a First (isolate) and Truth as being a Second (relata) and Presence as being a Third (continua). That means that Reality would extending Peirce’s scheme using B. Fuller’s own principles which include Synergy (Fourth) and Integrity (Fifth). This means Reality would be a Fourth (synergy) and beyond that we can think about Existenz (when related 1 2 Peirce uses a wind vane as an example of a sign. http://en.wikipedia.org/wiki/Weather_vane http://en.wikipedia.org/wiki/Categories_(Peirce) 1 to Dasein) or Being (when related to things other than Dasein) which includes all the aspects as having Integrity. We extend Peirce’s principles also to the Zeroth which is prior to the First which represents emptiness or void. What we notice is that Presence is at the level of the Third or the Continuum. And that means that the anti-aspect Absence is also at that level. This suggests that Presence/Absence would be thought by Peirce as a pure continuum which is to say as a Mass rather than as a Set. In Peirce’s terms instances would be neighborhoods and not points. That means there would be neighborhoods of presence and neighborhoods of absence. But within the overall continuum there would not be any digitization of that difference. It would in fact remain intrinsically vague. Notice that in the Existential Graphs Alpha is a plenum of truth, and to that he adds lines of identity in the Beta graphs. In Gamma graphs he adds possibility and thinks it topologically as the connection between sheaves of pages connected via dotted lines. The surfaces are the places that the true things are presented for analysis much like Russell’s Logical Atomism3 influence by Wittgenstein’s Tractatus 4. Reality is that to which the things must be compared, as map to territory for the truth to be validated. Formal Systems have properties that are the relations between Identity, Presence and Truth, which are consistency, completeness and clarity (wellformedness). When we bring the formal system up against reality then we produce three other properties which are verification, validation and coherence. Peirce’s first attempt at producing a boundary logic ala G. Spencer Brown and Wm. Bricken was perfected by their later work. But the difference is that with Peirce the goal was to understand the various elements as they relate to the aspects of Being and Modality. N. Hellerstein in his Delta5 and Diamond6 Logics perfected the logics of Brown to show how the dual paradoxes A yet B, and B yet A interact as limits within the Diamond Logic. By using these limit paradoxes G. Spencer Brown could simplify electronic circuits as he alludes towards the end of the book. Bricken7 makes Laws of Form8 a full-fledged Boundary Logic9. Masses have their own logic10 which is a pervasion or boundary logic as opposed to the syllogistic logic of Sets. We must also remember that there is also the anti-logic to that of Spencer Brown which reverses his two laws, and together the logic and the anti-logic gives a full picture of the intertransformations that are possible. But the key to Laws of Form is that the ground is taken to be void, not truth. On the void there are the monads of Marks that carry identity. Marks are two dimensional but also appear as parentheses when given a serial presentation. The Horizontal part of the mark we associate with Process Being while the vertical part of the mark we associate with Pure Being. The mark is a splitting of the map written across the void of the Zeroth and this splitting sets up a relation which can be 3 4 http://plato.stanford.edu/entries/logical-atomism/ Wittgenstein, Ludwig, David Pears, and Brian McGuinness. Tractatus Logico-Philosophicus. London: Routledge, 2001 5 Hellerstein, N S. Delta, a Paradox Logic. Singapore: World Scientific, 1997. 6 Hellerstein, N S. Diamond: A Paradox Logic. New Jersey: World Scientific, 2010. 7 http://www.boundarymath.org/ 8 Spencer-Brown, G. Laws of Form. London: Allen & Unwin, 1969 . 9 http://www.boundaryinstitute.org/bi/index.html 10 http://plato.stanford.edu/entries/logic-massexpress/ 2 associated with Truth through the introduction of equalities. Presence and absence enters into the equations though variables. Theorems can be proved in the algebra of Form. In this way a formal system equivalent to Boolean Logic is set up which can be compared to Reality. But Laws of Form is a big improvement over the existential graphs of Peirce from where they obviously take their inspiration. Laws of Form does not start assuming Truth as the ground but instead the Zeroth of Emptiness or Void. The mark is two dimensional but simplified into a single mark that can frame the essentials of a boundary within the ground of emptiness. What is fascinating is how Spencer Brown also defines jumps that are equivalent to Hyper Being in his formulation of his notation, where variables might appear in different places in the nesting. Wild being appears as the symmetry breaking that gives the Laws but not their inverses. We can represent the two rules of law and their symmetry breaking as two different types of marks. We have speculated before that if we consider both laws this may be an image of the Emergent Meta-system that appears most prominently in our tradition in the Monadology of Leibniz. We have also speculated in the past that the four possible corners of the marks could be related to the aspects. If we have all four rotations of the marks then that gives us a box like those boxes by which Peirce represents negation in the existential graphs. The difference in the types of marks could be related to the difference between negation in Alpha graphs and possibility that appears in the Gamma graphs. It is fascinating that the identity lines of the Beta graphs is very similar to the Meta-pattern method of Pieter Wisse in which there is also a line of identity which was treated in my dissertation on Emergent Design. In that work I did not realize that he might have been inspired in part by the Existential Graphs of Peirce. We can see that the Laws of Form start with the Zeroth. And the Mark alone is the first, which Badiou would have called the ultra-one. The Laws of Form and anti-Form establish the relations between double marks and no mark, or single mark and double mark. The fact that the double mark becomes the Zeroth background is the strongest rule shared with the Existential Graphs. The equations of the Laws of Form establish relations. It is when the Laws of form are turned into an algebra that presence and absence is introduced. In China the character for a variable was Heaven, and that is because during the solution of the equation something is rotated out of the invisible realm into the visible realm. The theorems of Laws of Form are the stable turning points of those rotations established by proof. What is interesting is that in Hellerstein’s Diamond Logic is that two paradoxical limits (j, k) are produced that are A yet B and B yet A. The real interest of the Laws of Form is how these limits can be used to simplify electronic circuits. The paradoxes could represent present yet absent and absent yet present, or any of the aspects. In other words they are excellent embodiments of the ententional phenomena that appears as absential eventities. We see this played out in the work of Deleuze Logic of Sense where floating signifiers range within intersecting series. We might see a given logical formation of marks as spanning between the two limits of absent yet present and present yet absent. It is not that the ententional is completely missing. Rather from the perspective of Deleuze it is rather missing in action, or rather the interaction of two series, which causes the floating signifier to move between the series and within the range of the series like a free variable, a gap, or view down to the ground of the Zeroth that signifies in spite of itself. Spencer Brown was not trying to think the topology of Logic like C.S. Peirce was trying to do. Spencer Brown’s approach was set-like but we can see how this was an attempt to reach toward the mass3 like boundary logic which was completed by Bricken. It was the introduction of the two dimensional mark that led toward this direction. But Spencer Brown himself was thinking in a Set-like way, and had not yet transitioned to the Boundary Logic of Bricken. Instead Spencer Brown was trying to discover a logic that was between Zero and One of Boole, which was Boolean without being dualistic. The fact that by reducing to a single mark on a Zeroth background could imitate a Boolean Logic is of interest, especially since the various forms of the mark correspond so well to the different kinds of Being, and the orientations of the mark can be seen to correspond to the aspects of Being. In other words even though we can reduce Laws of Form to Boolean Logic there is much there in the simplicity of the Laws of Form as a formal system that appears as a kind of metaphysical insight that goes beyond the isomorphy with Boolean logic when considered deeply. In effect if you take the additions by Bricken (boundary logic) and Hellerstein (paradox logic) and the analogy to Peirce’s existential graphs and the work of Deleuze on Logic of Sense seriously then we have a model of the relation of the physical system to the missing absential eventities and to ententional phenomena in general. And what we see in this model is that what is missing in Deacon is whatever it is that imposes the constraints that give local absences their contextual ententional value. Deacon is talking about the physical infrastructure and how it makes possible negative entropy in morphodynamics and how absential eventities are produced in teleodynamics, but what is missing is the superstructure that imposes the constraints that gives the value to the ententional phenomena. It is like half the world is missing. And also Deacon though he references Peirce does not spend time on the Semiotics of Peirce and how semiotics provides a framework for understanding ententional phenomena. As Heidegger says signs have a special place in the ready-to-hand in as much as they become highlighted as pointing elsewhere-elsewhen via references that need interpreting to absences. But absences are just as much a phenomena as presences, and it is the disregard for absences and the role they play that is part of the reason that the present-at-hand mode is impoverished in a certain way and cannot explain all the phenomena we experience. The present at hand mode of approach to phenomena taken by science is deficient in a certain way that it fails to account for signs and their tying together presence and absence. But the absence is not a plenum. As we know there are many different kinds of ententional phenomena and we need to wonder where this variety comes from, and also we need to know what it is that as a superstructure beyond the physical not only holds the difference between various absential eventities apart but also imposes the differences within a specific kind of abstential eventity on the emergent levels of thermodynamics, morphodynamics and teleodynamics. There has to be a source for those constraints. My answer to these quandaries is that it is the structure of mathematics that supplies the constraints. Mathematics as nomos is unaffected by whether things exist or not. Mathematics is existential in a certain sense in as much as the nomos is set regardless of the universe you are in or whether anything is in that universe. And the thing we know about mathematics after the twentieth century is its immense variety. Only some of that gets used in the organization of actual phenomena in nature. And Science is basically the matching up of mathematical structures with systems of phenomena via theory. But those parts of math that are actually reflected in physical structures are just a small part of the different types of math that exist unused and unneeded by physical structures to organize 4 themselves. Mathematics places constraints on Physical Phenomena as we can see from the various phenomena that are perfectly described by mathematics, once the proper theory has been found to explain the phenomena. The mathematics is a priori, it would be as it is regardless of whether the physical phenomena existed or not. The fact that many physical phenomena correspond to mathematically mappable organizations is what makes science possible. But mathematics in spite of its tremendous variety has in many cases a specific form that is set and cannot be otherwise, and physical phenomena cannot violate the forms of mathematics that are set. In other words we know of no case where physics violates hard limits of mathematics. But we know of many cases where mathematics sets the organization of some phenomena. But finding which part of mathematics corresponds to a given phenomenon may be a hard problem, and is at the core of scientific explanation. But from this we postulate that mathematics which is existential, i.e. is there regardless of whether everything is merely empty or void, is an a priori organization for physical phenomena and thus a causal constraint for phenomena. Finding out what part of math is the causal constraint on what phenomena is the basic work of science. But once it is known which part of math acts as a causal constraint on what phenomena in nature is the essence of explaining a given phenomenon theoretically in science. From this we infer that mathematics as a nomos is the source of the constraints on ententional phenomena that governs the relation between absential evenities and the presences that semiotically refer to those absences. From what Deacon has said there are both orthograde phenomena and contragrade phenomena. Orthograde phenomena is what happens naturally and spontaneously in nature. Contragrade phenomena we can characterize as physical work in which we use different orthograde phenomena to drive contragrade phenomena in order to do something that would not naturally happen without an intervention by an agency of some sort. The point is that different parts of mathematics govern different types of orthograd and contragrade phenomena. Thermodynamics has entropy as an orthograde phenomena. Information production is contragrade. Deacon uses Prigogine’s dissipative structures to explain morphodynamics, i.e. systems in far from equilibrium systems that are neg-entropic. Negentropy involves the production of order which is a priori constrained by Nomos, i.e. the structures of mathematics that are set in stone (actually written in the void) in existence. So it is precisely order that is produced by negative entropy, and it is precisely order that is constrained by necessary mathematical structures, and so we can then easily see how existing nomos would constrain order producing entities such as dissipative structures. Dissipative Structures are orthograde within the context of a contragrade environment where energy flows are occurring for instance based on energy from the sun hitting the planet. So it is interesting that dissipative structures tap into exactly what mathematical structures have to offer which are possible orderings that then can be rendered in the ordering of the substrate of the dissipative structure in a physical embodiment. Thus we can say that we call mophodynamics “Form Dynamics”, because it is embodying form which is constrained by the ordering principles embedded in mathematical structures so that Forms take form through the embodiment of what is possible mathematically. The dissipative structures could ideally manifest many different orderings at various schematic levels, thus many different facetings, patternings, formings, systemizing, meta-systematizing, domaining, worlding, kosmosing, pluriversing, can occur with different orders based on different parts of the intrinsic 5 mathematical structures inscribed into existence. We would prefer to call this schemadynamics because there is no reason to limit it to the dimensional scope of the form schema only. But so long in the Western worldview form was the only schema that counted that morphodynamics would have been the default way of looking at the order of things. We can take this as a general term where ‘morpho-’ is considered as an exemplar that stands in for other schemas in the general case, but in specifics we are talking about facet-dynamics, monad-dynamics, pattern-dynamics, form-dynamics, system-dynamics, meta-system-dynamics, domain-dynamics, world-dynamics, kosmos-dynamics, and pluriverse-dynamics. The key is then to understand how we move from dissipative structures and their morphodynamics to teleodynamics where ententional phenomnea based on abstential eventies occurs. It is one thing just to posit it as Deacon does because there must be something like this to explain life and it is easiest to follow up by invoking Aristotle’s other causes beyond efficient cause to explain the appearance of this emergent level; And it is another thing to say why it is that ententional phenomena based on references to absential eventities occur necessarily, i.e. based on an imposed constraint, for instance from the existential nature of order itself given its mathematical infrastructure. And this is where we must appeal to the anomalies in Mathematics such as aliquot numbers, or nonorientable surfaces, or hypercomplex algebras or in physics like solitons which is a reflection of these mathematical anomalies into the functioning of matter in certain circumstances. Dissipative structures channel order to produce schematization. Order itself as an a priori has certain anomalies that constrain the articulation of matter in morphodynamics. It is these anomalies that produce the possibility of morphodynamics, and the possibility of the interaction of morphodynamic systems to create teleodynamics and going beyond Deacon the interaction of teleodynamic systems to produce sociodynamics. And it is the mathematics that dictates that there is no higher threshold of organizational emergence beyond that of the social which is based on consciousness which is based on the living. In other words once a physical system starts channeling order though negentropy then it is constrained by the existential structure of the mathematics and it turns out that that structure has certain anomalies within it that can be taken advantage of to produce life, and then consciousness and then the social, but in fact all three of these come into being as simultaneous constraints and thus simultaneously constrain the special system that breaks free locally and ever so marginally from the onslaught of entropy. In effect evolution takes advantage of anomalies within mathematics to do things that normally would not be considered possible in entropic systems and in this way mathematics and its anomalous structure supplies the constraints that when adhered to produce the possibility of teleodynamics and sociodynamics out of morphodynamics. But our theory of Life, Consciousness and the Social then must adhere to the mathematical structures that appear within mathematics as its intrinsic structure. And in fact this supplies us with a complete framework within which to understand the phenomena, and that is because the anomalies in mathematics are mirrored in different types of mathematical structures, but are in fact just reflections of the same meta-anomaly within mathematics which interestingly fit together to give us a very precise theory with a specific signature, and thus does not suffer from the normal problem of trying to decide what mathematical structure applies to a given phenomenon, for this meta-anomaly is 6 unique and its various reflections are unique in their own domains within mathematics and the fact that the same meta-anomaly has many reflections that fit together to produce a very precise signature for the theory is something that is really amazing and almost inexplicable because it suggests an almost premeditated design to mathematics which produces this unique structure that is multifarious despite family resemblance across the different field within mathematics yet fit together like a subtle and finely crafted mechanism to describe the various unique thresholds that make life, consciousness and the social possible. We call the teleodynamic level of organization where ententional pheonomena arise autopoietic symbiotic. It is a conjunction of two dissipative ordering or morphodynamic special systems. Because it is a conjunction or juxtaposition of the two negative order producing systems that means there is intrinsically a gap between them each creating a different order in an orthograde fashion. It is when two such orthograde dissipative structures that create order by negative entropy are conjuncted and interact to feed each other or to support the functioning of each other in a symbiotic fashion that an autopoietic special system is created. The autopoietic system is a site where two different ordering processes intertwine in such a way that they perfectly support and feed each other the inputs that each needs to continue functioning. This produces a stable boundary in space and time within which we see the fusion of life, consciousness. And when autopoietic symbiotic systems are conjuncted or are juxtaposed then that produces the next emergent level where the social arises. The difference between these thresholds of emergence that have special properties is defined by anomalous mathematical structures, and the fusion of these special systems is also defined by other anomalous mathematical structures. There is only one meta-anomaly within mathematics and it is as if dissipative structures converge on that meta-anomaly and use it to bootstrap life at the autopoietic level though the symbiosis of different dissipative structures channeling different orders that are complementary to each other such that what Deacon calls an AutoGen can appear. In the AutoGen Deacon picks out hypercycles and self-assembly as two orthograde processes that could be complementary in order to posit a possible origin of proto-life. However, I would like to suggest that the theory of Special Systems would maintain that there must be four of these orthograde processes that in juxtaposition produce the complete structure and that Deacon has only identified one of the AutoGen combinations, and there should probably be another one which then would produce the SocioGen field of four orthograde processes that probably would be the origin for life consciousness and the social. Deacon defines Autogenesis as the juxtaposition of different orthograde processes that are negentropic to give the possibility of a teleodynamic system. Deacon defines all higher levels as TeleoGen, but in fact this is according to Special Systems theory probably a matter of hubris because there should be at least another level associated with the Reflexive Social Special System that leads us to think that there is a possibility of a SocioGen level that organizes the AutoGen pair at a higher level beyond the TeleoGen. And this is the value of having a theory based in mathematics rather than merely a conceptual theory empirically derived because based on the Special Systems Theory we can predict that there are at least two Autogen conjunctions. Now maybe that is a conjunction of two Autogens, but given that there are several different orthograd negentropic phenomena to choose from then there is a good chance that the other 7 AutoGen has a different structure than the one that Deacon defines which mates hypercycles and self-assembly. At this time we have no idea what this second Autogen configuration might be. This is an open question whose possibility is suggested by the theory that goes beyond the conceptualization of Deacon because he lacks a mathematical basis for his theorizing. The key point to be emphasized here is that these systems are channeling via their negative entropy anomalous orders inscribed into the bedrock of existence and intrinsic to mathematics in order to produce the special ordering of Life, Consciousness, and the Social. The meta-anomaly in mathematics gets used to give some extra efficiency or extra effectiveness to these systems over mere mechanisms. But because it is a mathematical anomaly it tends to produce fused structures within the systems themselves which are inexplicable mechanistically and thus the difference of life from mechanism or computationalism. Such systems are constrained to follow the form of the meta-amomaly and that is what produces the necessity of their organization at a meta-theoretical level but it is also what produces the precision of the theory with its unique signature. In other words life, consciousness and the social have a specific general form that is imposed on them by the existence of the meta-anomaly in math that is being multiply channeled by the dual Autogen. There are four dissipative structures in the dual Autogen and they are each channeling a different from of the anomalous ordering of mathematics in a specific embodiment such that the various orthograde processes feed and supported each other in a symbiotic way. They are all running downhill together but differently in such a way that their symbiotic interaction produces simultaneously the conditions for life, consciousness and the social. They can run downhill because they are in a fairly stable far from equilibrium energy flow that is sustained within limits that can support life. They are each using physical processes that are orthograde to produce different types of order but which circle round and have been organized a priori based on the meta-anomaly in mathematics that determines the self-ordering of order itself. Essentially the metaanomaly appears to come from the fact that as we approach one and then zero from some very high numbers there are various fusions that occur that produce different anomalous mathematical structures on the way to one but not quite there. These various anomalies in different types of mathematics seem to are compensatory in relation to each other in such a way that the structures in different parts of math that reflect the anomaly actually fit together to give us more information about the special systems than we would have otherwise. Obviously the dissipative autopoietic reflexive systems do not know math except as we come to know them though our scientific progress in history as beings who can know mathematics. What the reflexive autopoietic dissipative ordering systems know is that the math gives them an extra efficiency or effectiveness if they take the anomalous order rather than some other possible order. And thus the evolving dissipative structures naturally adhere to this lower energy possible structure as closely as possible to make their decent toward orthograde optima faster and more efficient. Following the contours of the meta-anomaly is equivalent to approaching laminar flow within the Adrian Bijan “Constructal Law” way of looking at how flow architectures evolve. Following the contours of the meta-anomaly in mathematics is the most efficacious way to dissipate the energy bound up in the ordering of the multiple dissipative structures in their complementary reciprocity. But this laminar limit to the intertwined flows is then the 8 source of the constraints that produce the possibility of ententional phenomena that binds through semiotics absential eventities to present eventities through reference and interpretation into a whole. Saying precisely how that works is the necessary next step once we understand where the superstructure that constrains the physical processes to produce ententional phenomena come from, i.e. from the existentially inscribed nomos that is channeled and intertwined by the multiple dissipative structures that are conjuncted or juxtaposed channeling different but complementary orders. To understand how this is possible and even necessary we must get into the various anomalous forms of mathematics that are part of the meta-anomaly. In other word we must explore the mathematically based theory. Our prime directive is to follow the mathematics no matter where it leads even if it takes us in counter intuitive directions. And it is the idea that we are going to follow the mathematics not our intuitions or common sense or scientific dogma that makes this process scientific, and what makes it empirical is that the mathematical anomalies have physical exemplars which are also unique. So everything is there that is needed for this to be a scientific theory of the constraints on Life, Consciousness, and the Social. But generally, without yet going into all the nuances of the mathematics the metaanomaly in mathematics provide non-intuitive non-commonsensical means for the production of the gaps in physical phenomena that become overlaid with ententional values and then the channels for the communication at a distance between what is present that are used as a reference and can be interpreted semiotically to connect with the absential eventities. The fact that the ententional phenomena have such variety also can be explained by the variety of different types of mathematics involved. In other words it is possible that with different substrates made available to provide these linkages at a distance that this gives rise naturally to various kinds of ententional phenomena. And of course we also see this even more clearly in Quantum Mechanical phenomena in the form of super-position and entanglement which we have linked to the limits of the Divided Line of Plato. Morphodyanical phenomena each with a different ordering being embodied produce distinctions by their conjunction and juxtaposition. Those gaps, lacunae, missing elements etc. which show us the ground of the Zeroth which is empty or void actually can display superposition and can become entangled with other distinctions elsewhere. So we posit that the enentional phenomena made up of absential eventities are not transcendentals but are indeed networks of immanent entanglements which sometimes can overlap to produce superpositions. Our position has always been that there are macroQuantum Mechanical phenomena and so the very substratum that Deacon excludes which is an appeal to the Quantum Mechanical is precisely the medium by which the various absential eventies are tied together and the various ententional values are superimposed on each other to produce the mutual constraints that explain the infrastructure of the semiosis that occurs at the teleodynamic and sociodynamic levels. So in general we are going to appeal to mathematical and physical anomalies which by analogy set the constraints on the possibility of the emergent thresholds of Life, Consciousness, and the Social. But for the dynamics we are going to appeal to Macro-Quantum Mechanical phenomena which is more and more being recognized as a possibility by contemporary physical science. But what is interesting is that we can see a precursor to this type of explanation in the formalisms related to Laws of Form. For instance N. Hellerstein has 9 both delta and diamond logic. In Diamond logic there are two paradoxes that serve as limits, but in Delta logic he found he could project both of these on one limit, which is like a superposition of X yet Y and Y yet X on one limit. In a sense this gives us a simple formalism that expresses what we were just talking about with respect to Macro-Quantum Mechanics which is to say there are ways to represent these limits and their relations such that we can understand the floating signifier within multiple crisscrossing series between the limits of absent yet present and present yet absent. But we can also project absent and presence as a superposition on a single limit. And in fact this is what we see in the divided line what spans from supra-rational to paradoxicality as the limits of experience. One side the supra-rational is a real hard limit while the other is more a boundary that moves from contradiction, to paradox to absurdity by stages. The divided line is the field in which these ententional phenomena are traditionally understood within our tradition. Physical science traditionally only considers the representable intelligibles and the empirically grounded opinions or appearances. We leave the non-representable intelligibles and the ungrounded appearances or opinions to religion. Thus the dualism between religion and science in our tradition which is the basis of their conflict. But essentially science does not cover the whole spectrum of possible experience and concedes its own limitations. Having a real theory of phenomena has to cover the whole range of experience between the limits of the divided line. But that means bringing Phenomenology and Hermeneutics as well as Ontology and Dialectics in to fill out the lacunae left unaccounted for by purely present-at-hand scientific theories. Heidegger attempts to teach us in Being and Time that Human Beings have more than a present-athand relation to phenomena. And it is only by the recognition of that which makes possible a full account of experience that includes ententional phenomena related to abstential eventities. 10