The paper starts from an unlikely source by tackling the Kantian problem. The problem posed by Kant was that of developing knowledge that was totally free of any a priori experience or definitional scaffolding. Kant called such science metaphysics. In the paper, it is named Generic Science. The paper resolves the Kantian problem by developing a science that is free from any determined attributes, the science sans attributs. From pure reason alone, the elementary generic structures of the science are developed. The resulting generic language is claimed to be the reverse engineered version of the genetic code and is claimed to articulate the generic semantics of its “second articulation.”
Central to the development of this new science is a very old philosophy, that of the Stoics. In this respect, the Generic Science presented in this paper is a modernised and reconstituted version of the Stoic paradigm. A core concept involved is gender. For the ancients, their science involved a gendered world. Even the Four Elements were gendered. Can the gender notion be formalised.? Is there a gender calculus? Is there a relationship with the four lettered genetic code unearthed by the moderns?
In addition to the genetic code implications of the science, the paper also includes some examples of applying the same generic language to provide new insights into quantum mechanics and elementary particle physics based on a new kind of relativity principle, generic relativity.
Needless to say, the material in this paper goes in the countersense, or is orthogonal to practically all accepted tenants of the present day sciences and philosophy.
There are two kinds of knowledge. On the one side, which we will call the left side for discursive convenience, we find all of the traditional sciences including mathematics. These sciences all have a common epistemological structure, which can be summed up by saying that they specialise in conditional knowledge, knowledge that is conditional on such things as empirical data, hypotheses, axioms, and in many cases even opinions. In this paper, we reopen the age-old case for the other kind of knowledge, which does not depend on any antecedent factors at all. A science capable of providing such knowledge we will call right side science. It was Kant that asked the question concerning “the possibility of the use of pure reason in the foundation and construction of all sciences.” Turning this possibility into reality requires the development of right side knowledge. The object of this paper is to argue that the construction of right side scientific knowledge is possible, to show how it is done, and to explore some of the practical repercussions.
Characterisation of left side scientific knowledge
A common characteristic of the left side sciences is that they are all attribute based. All knowledge, without exception, is expressed in terms of the attributes of entities: attributes can be anything from measured properties, defined properties, just to human attributed labels. Many philosophers claim that this is the only kind of scientific knowledge possible. They effectively declare that there is no other way to know the “real thing” behind the attributes other than via and in terms of the attributes themselves. Thus, knowledge has to be preceded by attribute acquisition in some way, either by attribute harvesting, as is the case for empirical sciences or by proclamation, as is the case in axiomatic mathematics. This is what characterises left side science as conditional knowledge, conditional on having the prerequisite attributes on hand before any reasoning can begin.
The “attributes only” paradigm of left side sciences imposes important limitations including the impossibility of a fundamental explanation of differentiation and distinguishability of objects as the possession of both mechanisms are assumed to be a fait accompli before any serious investigation ever even starts.
Right side science is founded on First Classness
Non-conditional knowledge by definition cannot rely on being kick started with a bunch of attributes. However, like any science, right side science needs something from which to start. Since this kind of science is to bootstrap itself up from pure reason alone, it will need to predicate, right from the beginning, all the logical development on the very central principle of pure reason. In other words, knowledge must be conditioned by the principle of pure reason. Since the task is to develop knowledge that is totally non-conditioned, this may seem an impossible contradiction. Rather than a contradiction, what is involved here is a specification of the principle itself. The principle, applied to its object, declares that the object is and must be totally unconstrained by anything other than itself. There is no one in the shadows pulling strings.
Such a principle is extraordinarily difficult to describe let alone formalise. However, examples of such an amorphous but powerful concept appear in many present day scientific disciplines. Computer Science provides some good illustrations of that concept we are searching. There, it is called First Classness (FC). One illustrative example of FC is the Object Oriented (OO) paradigm in Computer Science where the mantra is “everything is an object.” An object is defined as being an “instance of a class.” In this case, there is an apparent violation of FC as a class is not an object. The OO paradigm answers that a class is in fact an instance of a meta class and so is an object. The same argument applies to the meta class that is an instance of a meta-meta class. Infinite regress is avoided though as it turns out that the meta-meta class is an instance of itself and so are both a class and an object in the same instance. The OO paradigm resolves the dichotomy between specification (class) and implementation (object) and provides a useful, concrete way of beginning to understand FC. Note the objects at the base level, the class level, meta class level, and meta-meta class level construct described here. The overall structure is a Three-plus-One structure, where the meta-meta level is the One. We claim that any serious attempt at a system based on FC, be it a left side or right side science, will employ Three-plus-One structures.
Another Computer Science example of FC is the programming language LISP invented by the mathematician McCarthy as an outcome of his theory of mathematical recursion based on anonymous Lambda functions. In this case, the mantra was that any entity is a list. Procedures, arguments, return values, values, and value placeholders were all instances of lists. In this way, McCarthy’s paradigm eliminated the rigid dichotomy between program and data. The Three-plus-One structure in this case is built around atoms, lists of atoms, lists of lists, where the One corresponds to the Lambda functions implemented as lists. “Everything is a list” was the mantra.
Perhaps the most abstract examples of FC comes from mathematical Category Theory which merits a claim to FC by eliminating the rigid dichotomy in Set Theory between the sets of elements and the elements they contain. Instead of sets of elements, Category Theory concentrates on mathematical structure represented in the form of arrows called morphisms. A collection of such structured arrows is called a category. Many different branches of mathematics can be lumped together by thinking of them as instances of common mathematical categories. In their turn, these mathematical categories reveal higher order structure that can be represented by arrows between categories themselves. This leads to meta categories based on meta morphisms called functors. The abstraction does not end there. Mathematics admits of yet another meta level, what we can think of as meta meta categories with meta functors. These meta functors were first defined by Eilenberg and Mac Lane. They coined the term natural transformations for these meta meta arrows. They later wrote that their express aim in developing Category Theory was to study natural transformations. There is no higher meta level above natural transformations. Mathematicians use natural transformations to discover new mathematical objects. Despite its power in the providing new understanding of mathematics, Category Theory is built on an axiomatic framework itself and so is only a left side science. However, we will use some of its arrow theoretic thinking to construct right side science and in so doing we will discover some of the generic entities underlying any system whatever as long as it is based on FC and only FC, no axioms allowed. The Three-plus-One structure in the Category Theory case is realised in the form of the category objects, the morphisms, functors, and finally the natural transformations.
The earliest scientific approach to FC can be traced back to Aristotle who developed his mantra that everything can be rationally understood as instances of classifications. Particulars were considered as instances of species, which in their turn ended up being instances of genera. Aristotle argued that any traditional scientific discipline was limited to the study of entities that were under the umbrella of a determined genus. In so doing, he provided a useful definition of what we are referring to as left side sciences. What interested Aristotle in Metaphysics was how he could classify something that had no determined genus. He needed some sort of meta genus. He referred to it as Being qua (as) Being but left few precise details of what he meant. The study of beings without determined genera, the study of Being qua Being, he called metaphysics, a science with a decidedly ontological vocation. Aristotle’s metaphysics can be thought of as the first explicit and coherent reference to right side science and its distinction from the traditional left side sciences. Developing the foundations of such a science is the task of this paper. However, our inspiration will not come from Aristotle but from those that followed him; the little understood Stoics.
Another example of FC can be found in a modern particle physics where the mantra is “everything is a particle.” The particle paradigm attempts to resolve the dichotomy between particle and field. The effect at a distance explained by force fields is replaced by a new breed of particle, the gauge boson, which acts as a carrier of force. However, particle physics is a left side science and so can only approximate FC. The reason is that FC is irretrievably violated at the very foundational level where the dichotomy between entity and attribute is not resolved but ignored by only considering the attribute side of the equation. In particle physics this violation of FC reappears in the form of the irresolvable formless, point like elementary particles floating around in a void; the particle/void dichotomy. What can be measured is particle, what is without measure is void. We will not attempt to discern any Three-plus-One structure in Particle Physics, as there is probably little point in the exercise at this stage.
These examples show that FC is a very powerful and widely applicable principle. Central to the principle is that it abhors rigid dichotomies. However, even more fundamentally and quite surprisingly, as we shall see, the principle abhors symmetries preferring instead asymmetries in the form of Heraclitus style oppositions. In fact, practically everything taken for granted in the traditional left side sciences is torn inside out for right side science,
If particle physics is founded on the doctrine that the only things that exist are pinpoint particles in the void, right side science upholds the antithetical position that the only things that can exist are bodies. Voids have no role in the science. This is the world of bodies. Only material bodies exist. It is by rejecting the particle principle and the inevitable void of left side science and replacing it with bodies, the particle-void dichotomy is avoided, and FC not violated. This mantra dates back to the ancient Stoics as David E. Hahm writes, “According to the Stoics the only things that really exist are material bodies.” (Hahm, 1977) He also remarks that “For half a millennium Stoicism was very likely the most widely accepted world view in the Western world.” Thus, the concept has some pedigree behind it. This doctrine goes part of the way for ensuring the purity of a deeper doctrine. If left side sciences are fundamentally dualist, right side science must be fundamentally monist.
The Difference Dogma of Traditional Sciences
The central dogma of the traditional left side sciences concerns difference. According to the dogma, two entities are determined to be different from each other according to a difference in their attributes. For the physical sciences the attributes may be perceptible or measurable qualities such as, for example, mass, colour, position or velocity. In the case of mathematics, the properties are assigned via the definitional framework, or derived in some way. Of central importance to the dogma is that an entity is an entity and that an attribute is simply not an entity, it is an attribute. The dichotomy between the world of entities and the world of attributes is central in establishing the fundamental dualist nature of this kind of science. We will call this central dogma of left side sciences, the Difference Dogma.
Associated with the notion of difference, is that of distinguishability. In this paper, we will define that two entities are distinguishable if they have different attributes. From this definition it follows that if the Difference Dogma holds, and so difference is determined by attribute comparison, then the same applies for distinguishability. Thus for a science satisfying the Difference Dogma, difference and distinguishability are synonymous. This is understandable as the distinguishability notion begs the question: “Distinguishable by whom”? The whom referred to here is the subject. Left side sciences, because of their objective epistemology, are devoid of any determined subject. The perspective is that of the “view from nowhere,” the viewpoint of non-determined subject, the viewpoint of what can be called, the impersonal subject. From this “God’s eye” point of view, it is no surprise that difference and distinguishability are synonymous.
Difference Without Attributes
The Difference Dogma appears so obvious and familiar, that few people of modern times seem to question it. However, there is an alternative viewpoint, the monist viewpoint. Monism totally negates the Difference Dogma. For a want of a better name, we will call it the Anti-Difference Dogma. This dogma effectively declares that there is no determined difference between entities whatsoever. Clearly, this is what is required in order to establish a truly monist worldview.
At first sight, the Anti-Difference Dogma, and the implied monism philosophy, appears counter intuitive and diametrically opposed to common sense let alone any kind of scientific enterprise. Even Hegel’s tortuous attempt at such a science has done more to reinforce this assessment than achieve the original intention. How can one construct a science based on the premise that there is no ultimate difference between entities?
Unlike the left side sciences, the object of right side science is devoid of any determined attributes. Such an object of enquiry is quite familiar territory in philosophy. Kant called it the thing in itself. The Stoics referred to it as unqualified substance. We will refer to it as an entity characterised as being devoid of any determined attribute whatsoever. We then make the observation that being devoid of any determined attribute does not imply that the entity is attribute free. The contrary even, it implies that the entity has a very specific attribute, that of the attribute of being free of determination.
Apparently, this primordial starting point entity is not alone. The entity is in the company of its attribute, the attribute of being free of any determination, qualification, and specificity whatsoever. It is at this conjuncture that the principle of FC most be invoked, FC abhors the rigid dichotomy. In order not to violate FC, there must be no dichotomy between objects and their attributes. The attribute of this primordial starting point entity must be an entity in its own right.
Thus, this generic starting point for the new science is not a lonely “thing in itself,” as Kant imagined it, but necessarily two different entities. These entities are of a different kind. We will formalise this difference in kind by recycling some ancient terminology, the terminology of ontological gender. The starting point entity, which has the specificity of being absolutely devoid of specificity, we will say, is an entity of feminine gender. This entity has an attribute, that of non-specificity. In order not to violate FC, the attribute must be an entity in its own right. The attribute will be said to be an entity of masculine gender. Thus, the feminine entity has an attribute; the masculine entity is this attribute. Here resides the object of the right side science. From here on, the science at its most fundamental becomes the scientific dialectic of to be and to have, the dialectic of gender. The central task of right side science will be to develop a new calculus, the gender calculus. It is via this calculus that one will be able to describe and proscribe any entity whatsoever, any world whatsoever, as long as FC is respected. In the process of developing the gender calculus, we will make a remarkable discovery. We will realise that we are in fact reverse engineering a calculus that already is apparent in Nature, the four-letter genetic code. We are discovering the underlying generic structure of Nature.
Note that these two entities are formally different as they differ by gender. However, they are indistinguishable to a third party. Distinguishability requires a difference in attributes; however, in this case the two entities have only one attribute between them: One entity has it the other is it. Unlike the left side sciences, right side science does not rely on distinguishability to determine difference. Right side science is a monism where maintaining in distinguishability is paramount. Rather than attribute comparison to determine difference, right side science is totally based on the relative typing scheme provided by ontological gender.
Right side science is the science of the oneness of monism. The first question concerns the compatibility of the unified oneness demanded by the doctrine with a differentiated reality seemingly dominated by multiplicity. The science must provide an account of such differentiation. There are two approaches one objective and one subjective. In this section, we recount the objective approach.
Unlike left side sciences, right side science accounts a reality where the subject is always present. The subject can be present in two ways, either implicitly or explicitly. In the implicit scenario, the subject becomes the Spectator. In the explicit scenario, the subject becomes Spectacle. Traditional left side science and left side philosophy, such as analytic philosophy, only consider the first scenario and ignore the second, as indeed they must in order to remain true to the objectivity paradigm. After all, the whole thrust of traditional science is to be objective and this demands elimination of the subject from consideration. This objectivist prise de position of the left side sciences has obvious advantages as witnessed by the spectacular success of the objective sciences over the past few centuries. However, it comes at a cost.
The downside can be illustrated by what appears to be a similar prise de position underpinning the organisation of the biological brain. In the biological case, subjects acting with only a functional left hemisphere exhibit hemi-neglect. where they only identify with the right half of their body and even may only be conscious of the right half of a clock. The subject may only eat the food on the right side of their plate and still complain to be hungry. They may only shave the right side of their face and wash only the right half of their body and so on. (Berlucchi G, 1997) (McGilchrist, 2009). Acting with only the left-brain, they are only conscious of half a world. In the converse case, a subject operating with only a functional right brain does not exhibit hemi-neglect but is conscious of a whole world. One could say that the left-brain only has a body, in fact only half a body at best. In contrast, if the right brain operates under the sway of the monistic paradigm then it must conceive itself as part and parcel of body. In this scenario, the right brain would not be conscious to having a body, but conscious that it is body, all body, all of body.
The traditional left side sciences suffer from a similar form of hemi-neglect. This fact does not have to be proven because, as remarked above, hemi-neglect forms the core of the objectivist stance of the traditional sciences. To be objective, one must eliminate any subjectivity pollution that may be introduced by the subject. The traditional left side sciences and mathematics adopt their own form of hemi-neglect, based on the neglect or refusal to allow the subject into their epistemology.
The hemi-neglect syndrome is most easily observed in axiomatic mathematics where mathematicians even boast about it. Axiomatic mathematics is abstract left side mathematics par excellence. Such mathematics necessarily produces a symmetric view of the world where every mathematical theorem, every mathematical object, every mathematical space possesses a symmetric dual, without exception. Any theorems proven valid in one side of this reality will automatically be valid in the dual reality. Pure mathematicians see this as a godsend, often boasting to their students that they get “Two for the price of one!” This must be one of the most popular clichés of abstract mathematics. It gives mathematicians a perfect excuse to practice hemi-neglect and always only work on one-sided realities. Most still eat food on both sides of their plate though.
In contrast, right side mathematics, due to the ever-present subject, will be seen to produce a fundamentally asymmetric world. The structure of right side mathematics, although complementary to the left side version, is so antithetical that in Part 2 of this paper, we will call it anti-mathematics.
Hopefully, the biological split-brain allegory helps to illustrate an essential difference between traditional left side sciences and the embryonic right side science introduced here. The right side science is based on the monism paradigm. This makes it immune from hemi-neglect and demands that it not only considers reality as a whole but must continuously embrace reality as a whole. From the standpoint of monism, both sides of the equation are always present. The subject cannot be separated from its object kingdom. They form an inseparable whole. This said the monistic paradigm must come to terms with the same world of objects that the left side sciences so adeptly study. However, it must avoid the half world mentality of left side science. Thus, there are two worlds of objects, that viewed by left side science and that viewed from the monistic perspective of right side science. Left side sciences completely discard the implicit subject and has no need for it. Right side science must retain the implicit subject at all times and exploits it to the full as the reference point for development of its unique kind of knowledge of reality. In the process, it comes up with its own science of matter, for example. Our aim here is to show that such a science will be a more modern version of the four-element theory of the ancients, dating back to Empedocles. The end results are deceptively simple. The reasoning leading to the results is tricky to explain but should be easy to understand. In this section, we only attempt the right side science version of the left side science of objects.
Left side sciences address a reality populated with composite entities ultimately made up of atomic or sub-atomic particles. All particles and their composites possess attributes that are measurable by a disinterested third party. To prove that the third party is disinterested, all results must be demonstrably reproducible. In contrast, the right side science version cannot employ attributes harvested from experiments. The attributes must be constructible from first principles. As for the disinterested third party, it becomes the subject and plays an integral role in the development of knowledge. We proceed as follows.
In this scenario, the subject is the same impersonal subject as for the traditional left side sciences. However, there is a difference. Rather than being dismissed as irrelevant, the subject is always present and in this scenario provides the reference point for the argument. Attributes are involved in the exercise but in every case, the attribute is determined relative to the subject. One could even say that the attributes are determined by the subject. There are no idle players in this game. Unlike left side science, there is no a priori notion of stand-alone attributes, which are indifferent to all subjects. The only attributes permissible in right side science are those calculable from the unique position of the subject. For the case in hand, the subject is any subject whatsoever, the undetermined subject, or what we call the generic subject in its totally undetermined guise. Any attributes calculable from the generic subject will be generic attributes. By an ironic twist in the argument, any subject whatsoever will experience the same generic attributes and so there will appear to be, in fact, “stand alone arguments” which are indifferent to any subject. However, they are not a priori to the subject. They are part and parcel of what determines subject as subject.
As anyone who has ever delved deeply into this area knows full well, this domain is a minefield. The dialectic of the Spectacle and the Spectator sometimes appears as a morass of hopeless self-referring contradictions. There are many ways of tackling the problem. One way, the one opted for here, is to see it as a problem of choice. The subject, in order to be such, must be capable of choice. It must be capable of choosing between this and that. The immediate problem is to determine what these choice alternatives are. In the left side science, this and that just appear willy-nilly. In contrast, right side science must ignore the accidental and employ an entirely different technology for creating and processing attributes. An integral part of this technology is the process of choice. In this highly relativistic game, the very act of choosing is intimately implicated with the ontological status of the object chosen.
We start where the generic Subject is called upon to engage in a thought experiment involving objective choice. We note in passing that this “thought experiment” may indeed be a “real life experiment.” At this stage of the development, there is no determined difference between the two. Confronted with Kant’s thing in itself, the Subject has already reasoned that it is confronted with two entities, not one, the entity which has an attribute and the entity which is that attribute. The Subject must now attempt to differentiate the one from the other.
Note that differentiation is not the same as distinguishing. Distinguishing is difference determination that is posterior to an already accomplished differentiation. Distinguishing can only take place when differentiation is already a fait accompli. Differentiation is an active process involving the Subject itself. It is the fait à acomplir.. Differentiation involves an act and the specificity of that act. The act is that of choosing, in this case choosing absolutely objectively. This brings us to the First Choice, the most objective choice of them all.
The First Choice, the most fundamental of all choices, involves two alternatives, one passive, and the other active. The passive alternative is to choose not to choose. This is the “Let the mountain come to Mohamed” type choice. The active alternative is to choose to choose. The active case is the easiest to understand, but like any choice, opting for one alternative at the expense of another always restricts the range of possibilities further down the track. In the case of the active choice, the Subject has opted to know the entity by its attribute. Knowing via attribute is the methodology of the traditional left side sciences. The choice involves opting for a masculinising view of the world. Such a world is perceived as being uniquely populated by attributes. What this means is that, viewed through this methodological eye, the two primordial entities, one feminine and the other masculine, will now both appear as attributes. In other words, they will both appear as masculine. This is a consequence of enacting the active choice alternative.
Choosing to choose is the masculine choice, the active choice. Choosing not to choose is the feminine choice, the passive choice. In the feminine case, the two simply gendered primordial entities do not appear as attributes. Given that attributes are essential for any appearance, they do not appear as anything. In other words, no explicit knowledge can be garnished from these two entities viewed through the prism of the passive choice. This means that in this context the two entities must be considered as feminine. However, these two entities can be known, not explicitly, but implicitly. They can be known not be what there are, but by what they are not.
This is the land of the poets and there are many ways of explaining the self-referring reasoning involved here. In a nutshell, relative to the impersonal Subject, there are not two, but four types of elementary substance making up the generic substance, the original unqualified stuff, or thing in itself. In other words, relative to the ever-present impersonal subject there are four kinds of stuff.
- MM the masculine as masculine or masculine active
- MF the masculine as feminine or masculine passive
- FM the feminine as masculine or feminine active
- FF the feminine as feminine or feminine passive.
In Western culture, this construct dates back to Empedocles of the fifth century BCE. As Aristotle records:
Empedocles, then, in contrast with his predecessors, was the first to introduce the dividing of this cause, not positing one source of movement, but different and contrary sources. Again, he was the first to speak of four material elements; yet he does not use four, but treats them as two only; he treats fire by itself, and its opposite—earth, air, and water—as one kind of thing. We may learn this by study of his verses. (Aristotle)
Empedocles called the four classical elements roots, associating fire and air with male deities whilst water and earth were associated with female deities. We also note that Empedocles saw the four elements as a Three-plus-One kind of structure that we have associated with FC. In this case, Empedocles associates the One with Fire or Zeus, to which we have associated the binary gender MM.
Right side science dispenses with determined attributes and replaces them with self -determining attributes where system entities are determined relative to each other. At all times the subject is present, either explicitly or implicitly. In the present scenario leading to the four classical elements, the subject is implicitly present. Implicitly we are discussing the very substances that constitute this organism that we have being referring to as the Subject. This subject, any subject, is constituted along these lines according to the doctrine of the four elements. The coherence of this relativistic gender typing scheme is known to the subject in question. In fact, the very coherence of the organism depends on the relative coherence of its gender typing system.
The subject in question is none other than the impersonal subject. But the same argument can be applied to any subject whatsoever. Any such subject will be constituted from matter based on the organisational structure of ontological gender. The gendered structure is determined relative to that subject and is in coherence with that subject, and that subject only. To each subject, there is only one centre of the Cosmos, and that is itself. Right side science involves the ultimate in introspectively.
Differentiation is based on the right side version of objective reality. In that scenario, the subject is implicitly present where the explicit becomes a material presence. The gender argument leads to the classical four element constituents of material presence. Any substance present will itself be constituted from the four elements. Such an organisation just does not happen by chance but comes into being from a creative act, the creative choice process that endeavours to stay within the bounds of FC at all phases of the development.
The previous section considered the right side science version of the objective reality that underpins the traditional left side sciences. In the first instance, this leads back to the ancient doctrine of the four elements. In a nutshell, this can be summarised by enumerating all of the primordial choice alternatives confronting the generic subject. With impeccable precision, the science predicts that the outcome of any choice will be one of four possibilities. According to right side science, anything can be constructed from these four generic types of entity. This provides the basis for the right side version of composite structure, a certain kind of “monistic atomism.”
Right side science is a two faced coin. We now turn to the other side of the coin, where the subject moves out of the shadows onto full stage. The entity of study becomes the explicit subject. Unlike the case of objective reality considered in the previous section, there is no left side equivalent for this side of right side science. At best, it is covered by the hemi-neglect aspect of traditional science. Our focus now becomes that of subjective reality, considered by many, such as Karl Popper, as being the domain of the “unscientific.”
We have already seen that even with the right side epistemological version of left side science, the resulting knowledge is expressed in terms of oppositions. The primary opposition, of course, is that between entity and type. In order not to violate FC, the type of an entity must be considered as an entity in its own right. Thus, there are fundamentally two kinds of entities, according to the right side paradigm. This difference in kind can be formalised as a difference in gender, the ultimate and most generic expression of the ontological opposition.
In summary, left side science relies heavily on using labels that do not mean anything. Left side Science is also based on dualism and atomism. Right side science replaces labelling technology and dualism with ontological oppositions. If there are any labels or letters involved, they must be constructed and will necessarily mean something.
As Kant observed, these kinds of oppositions are, in effect, antinomies. Thus right side science describes and cognizes its reality in terms of two faced coins. The coin itself is a whole, but always has two sides to it. In this way, right side science must express itself dialectically. Plato expounded the practice of dialectical argument in the form of the dialog between two antagonists. Here we see that monism based thinking is monist on the outside but dualist and antinomic on the inside. Such is the nature of dialectic reasoning. This contrasts with the left side sciences to which the dialectic is totally foreign. Left side thinking is rhetorical, speaks with a single voice, and so expresses its non-duality in that way. Nevertheless, it always remains totally dualist in regards to its subject matter. The left side sciences are thus dualistic on the outside and monistic on the inside, so to speak.
Instead of dealing with objective reality, we are now dealing with subjective reality. Our attention is drawn to the generic specificity of the subject. What is this specificity and by what mechanism does the subject – any subject – maintain its coherence and integrity? By what mechanism does the subject know what it is and what it is not? According to the monist doctrine of right side science, the coherence of such an organism can be articulated in terms of a relativistic typing system. However, such a typing system is only a means to an end. The end is the organisational coherence of the subject itself. This involves a process of unification. Once again, four binary typed entities come into play but this time there is no multiplicity and the entities are no longer mobile. Rather than values, we are dealing with placeholders. The placeholder par excellence for value is the subject.
Relative to object, the subject is active. It is an innovator, a source of creativity and, embarrassingly, a wildcard when it comes to prediction. Subject can be seen as a causal factor of certain events, of certain effects. A subject thus enters into the causal chain and, in so doing, upsets the deterministic applecart. Epicurus was perhaps the first to recognise this problem and find a suitable remedy. Implacable determinist that he was, he had to find a way of admitting the subject into the realm of causes whilst at the same time salvaging a deterministic concept of causality. His was a left side science viewpoint advocating a dualist, atomistic and deterministic world, His solution to admitting some slack into a brutally deterministic system was in the form of the Swerve. All atoms behaved deterministically, but he added a caveat. Atoms behaved deterministically most of the time. Occasionally they experienced an unexplainable, imperceptible Swerve. According to Epicurus, it is via this mysterious Swerve mechanism that the universe micro swerves from its primordial state into the highly structured reality we know today. Remnants of Epicurean Swerve theory can still be discerned in modern science, resurfacing in the form of Heisenberg’s Uncertainty Principle and Darwin’s Theory of Evolution, for example.
Our topic is how to construct a science without attributes, not to explain causality. Nevertheless, when it comes to science of the subject, causality cannot be ignored.
Causality and the Subject
In physics, the Principle of Causality is very much related to the Theory of Relativity. Erik Christopher Zeeman sheds some light on the situation by effectively showing that the fundamental invariant behind the Special Theory was causation itself (Zeeman, 1964). The principle of causation demands that any cause event must be antecedent in time to any consequent effect event. Zeeman showed that in order for this principle not be violated in any reference frame, the mappings between reference frames must be the same mathematics as for maintaining the speed of light as a constant. In other words, the transformations must be Lorentz transformations. Zeeman’s causality interpretation is a weaker, more generic version of relativity than the Special Theory. The constancy of the speed of light could be seen as just an implementation detail for assuring the non-violation of the causality principle in physics.
The causality principle can be thought of as a polarity condition: Causes come first; effects come second, not the other way around. Any violation of Relativity Theory is a violation of the causality principle, which in turn is a violation of the causality polarity condition. Relativity Theory guarantees the coherence of causality. It can intuitively be thought of as guaranteeing the integrity of the Arrow of Time, which expresses the irreversibility of time. The Arrow of Time can be thought of as a polarity convention. It declares that, in our universe, time flows this way, not the other way. From the left side science perspective, this is difficult to formalise. Arthur Stanley Eddington introduced the Arrow of Time term stating:
Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past. That is the only distinction known to physics. This follows at once if our fundamental contention is admitted that the introduction of randomness is the only thing which cannot be undone. (Eddington, 1928)
The Arrow of Time points in the direction of increasing uncertainty. He then continues to a most important observation:
We shall use the phrase ‘time’s arrow’ to express this one-way property of time which has no analogue in space.
Eddington highlighted the familiarity of the arrow of time to consciousness and how this stood out in stark contrast with physics where all of the fundamental laws are essentially time symmetric. In desperation, he was forced to turn to entropy considerations to get a handle on the direction of temporality. He admitted that this was a poor solution, remarking:
I do not think he [the scientist] would say that the familiar moving on of time is really an entropy-gradient.
Eddington was writing in 1928 and since then little has changed to challenge his observations. Particle physics is dominated by Schrodinger’s Wave Equation, which is time symmetric and so completely catholic in regard to which way time flows. What is not time symmetric is the “collapse of the wave function” which is irreversible. Applied statistically we see this irreversible process just like all others leading off to increased entropy according to Eddington’s time arrow, hardly an illuminating observation.
Eddington pointed out that there was no satisfactory “this way” arrow for time in the four dimensional Murkowski space necessary for Special Relativity. The same applies to Riemann space for General Relativity. An extra dimension has been added for time, but it is just like the other spatial dimensions, totally lacking in orientation.
Eddington’s plea for a physics that somehow included consciousness has been revisited in more recent times. Roger Penrose writes:
A scientific world-view which does not profoundly come to terms with the problem of conscious minds can have no serious pretensions of completeness. Consciousness is part of our universe, so any physical theory which makes no proper place for it falls fundamentally short of providing a genuine description of the world. I would maintain that there is yet no physical, biological, or computational theory that comes very close to explaining our consciousness. (Penrose, 1994)
Nobel laureate Brian D. Josephson also joins the fray with his Mind-Matter Unification Project (Josephson) in his quest to find a physics that embraces mind as well as matter.
In effect, all of these writers are lamenting about an incurable condition of the traditional left side sciences: All sciences that operate under the left side epistemological paradigm are conde mended to suffer from hemi-neglect. Such sciences can never accommodate a role for consciousness due to their wired in antagonism to a science of the subject. After all, how can a science sans sujet, ever produce a non-trivial science de sujet?
The right side scientific paradigm must not only render a science that makes embracing consciousness possible but fundamentally necessary. The right side scientific paradigm moves the subject into the explicit realm of study. The subject becomes the fulcrum for all subsequent knowledge which follows and as such, provides the answers to the “which side up” type of questions posed by Eddington. There are no absolute, context free answers. All answers must be relative to the subject. By proceeding along these lines, we will be able to eventually arrive at a fundamental notion of the Arrow of Time. In this kind of scenario, not only does time become asymmetric, but also so does spatiality. The Cartesian spatiality of the left side sciences treats any orientation, any frame of reference as being equally valid. There is no preferential reference frame in Cartesian geometry and so one could argue that this is a good example of FC. The fact that no reference frame is privileged over any other is an example of FC, but a very second rate example. Cartesian geometry violates FC because it is based on a dualism, a dichotomy between reference frames and geometric objects situated in these reference frames. FC demands that these geometric objects should be treatable as reference frames in their own right. This form of FC is impossible in Cartesian style geometry. However, in the geometry of the right side scientific paradigm, the converse applies. This science of the subject treats the subject as the origin and reference frame for any spatio-temporal geometry that might be involved. Such a geometry, dictated by the specificity of the subject, loses its time symmetry and its spatial symmetry. What is on the left and what is on the right, the front and the back, the up and the down, all becomes absolutely determined and not interchangeable. A new form of absolutism enters the scene. The only caveat is that the absolutism only applies to a specific subject. As far as this subject is concerned, it knows with absolute precision, what is on its left and right and any other relative position to it. In this right side scientific paradigm, the subject becomes the privileged entity in the system. As such, one might think that this violates FC, as FC is anathema to absolutely privileged entities. The way out of this apparent conundrum is the fact that, in this science, the subject under investigation is any subject whatsoever, the generic subject. The generic subject is not an abstraction. Understanding the difference between the abstract and the generic, is synonymous with understanding the difference between the left side and right side scientific paradigms. Abstractions cannot exist. This cannot be said of the generic.
In effect, all of these writers are lamenting about an incurable condition of the traditional left side sciences: All sciences that operate under the left side epistemological paradigm are condemned to suffer from hemi-neglect. Such sciences can never accommodate a role for consciousness due to their wired in antagonism to a science of the subject. After all, how can a science sans sujet, ever produce a non-trivial science de sujet?
Shape of the Generic Subject
A classical problem for traditional schools of thought such as Analytic Philosophy is the Mind Body problem. Viewed from the left side perspective, this presents as a problem to be tackled. It is however, a fruitless quest as the very problem is a mere immediate consequence of the explicit dualism of the left side paradigm itself. The best that can be achieved is some kind of psychological neuro-science brain theory. Nevertheless, left side philosophy has bravely pushed ahead and come up with a philosophy of Mind. However, this philosophy essentially consists of systematically cataloguing all of the known possible (left side) approaches to the philosophy of Mind. This is like presenting a nineteenth century theory of flight by cataloguing of all of the brave would be aviators who jumped of cliffs with a flight contraption strapped to their backs.
From the right side perspective, the problem vanishes as the monistic paradigm, due to FC, does not allow any rigid dichotomies at all, let alone any Mind Matter kind of split. At first encounter, this concept can be annoyingly difficult to fully grasp. In what follows, we will be constructing the “shape” of the generic subject. In so doing, the subject becomes endowed with a determined form. Now it may be all very well for us to say that this is the generic “shape of the subject,” but the nagging anxiety arises as to what constitutes the subject. Is this a subject confronting Nature? Alternatively, is this subject really Nature looking back the other way? As for the specificity of the shape, is this the shape of Mind or is it the generic shape of Matter or of Nature herself? Perhaps annoyingly, right side science does not even attempt to answer any of these questions, as they do not make sense in the monist framework. The difficulty can be traced to the difference between abstraction, which is a left side science technology, and the generic, the right side sibling. Abstraction is naturally dualist. On one side, there is the abstract understanding of the thing in the form of a theory, opinion or whatever. On the other side is the thing pure and simple. There is no mix. This is a harsh dichotomy.
The dualist epistemology of left side science is easy to understand. Going from the abstraction formalism of left side science to the generic formalism of right side science is much more delicate. The existence even of such an alternative formalism has long been contested. Suffice to say at this point, is that the dominant characteristic of right side epistemology is the absolute intolerance to rigid dichotomies as dictated by the demands of FC.
Even though the absolute dichotomy is anathema to right side science epistemology, the generic structures from which generic knowledge is constructed are built on what appears to be absolute dichotomies. This is only an apparent absolute contradiction as all dichotomies are relative to the subject. The subject needs to know its reality in terms of absolute dichotomies. It needs to know what it is and what it is not and know so absolutely and even urgently. However, viewed by a third party, such dichotomies, such determinations, so vivid to the subject, will be virtually undiscernible. After all, the third party has its own boat to row.
Other than expressing structure and knowledge in terms of oppositions, the second cardinal characteristic of right side science is that knowledge is expressed in wholes where, at no time, can any aspect of the whole claim autonomous and separate existence. Any aspect of the whole is necessary for the existential coherence of any other aspect.
The third characteristic is that the subject is always present.
The totality of reality cannot be conceived or perceived. Reality can only be known in the form of a whole. Each whole is reality considered from a particular pint of view. There are as many wholes as there are points of view.
Any whole must include the subject. Thus, due to the presence of the omnipresent subject, any whole can naturally be considered as a dichotomy, the subject on one side and what is not subject on the other. We will adopt the convention that the subject is on the right side of the dichotomy and the other on the left. Certain subjects may be based on the opposite polarity convention, but that does not affect the argument. To each its own polarity convention, as long as it lives by it.
Any subject is characterised by its own specificity. In the case of the left right dichotomy, the subject involved enjoys the specificity of being totally devoid of any determined specificity. Such a subject is customarily referred to as the impersonal subject. The impersonal subject is what it is, nothing more and nothing less. It inevitably finds itself in the company, of what it is not. We will informally refer to this Other of the subject as its kingdom. However, we keep in mind that there is no construct that determines in any way that the kingdom may be of a mental or physical nature, or of any other kind. Relative to the totally undetermined impersonal subject, there is the presence of the equally undetermined kingdom.
As we have already remarked, left side science also is involved with this kind of dichotomy. However, the left side science ends up dispensing with the impersonal subject and concentrating on getting to know the great unknown kingdom via various forms of pragmatic techniques, the details of which we are more than familiar.
At this point right side science definitively splits from its suck it and see sibling and starts its own distinctively dialectical journey. The step in the quest for the conscious subject was based on the realisation that “I am not alone.” The second step involves being conscious of this realisation. This is achieved by the presence of a more determined subject than the first. Entering into this reality, already split asunder by the presence of the impersonal subject, is the personal subject. This subject is neither on the side of the impersonal subject nor of its kingdom. It must straddle both and in doing effectively produces a dividing incision orthogonal to the first, resulting in the whole being cut into four quarters
One might argue that the notion of an orthogonal incision does not make much sense here, as there is no a priori notion of orthogonality in the first place. This objection has some merit; however, the objection comes too late. In the wake of this dichotomous operation, a primordial form of orthogonality becomes a fait accompli. Having achieved this tautological operation of effectively applying the first opposition to itself, we will adopt the convention that the personal subject is located at the front lobes of the resulting four part square and its kingdom is located at the back. We retain in mind that the primordial rapport between the front back axis and the left right axis is some equally primordial kid of orthogonality.
Keeping in mind that both the personal and impersonal subjects are singular relative to their kingdoms, we can say the both subjects are of masculine gender relative to their respective kingdoms. The kingdoms themselves are of totally unknown specificity and hence of feminine gender. What we now have constructed is relative typed form of a generic whole as illustrated in Figure Ap 1.. This corresponds to the generic form of the subject as a generic placeholder of value. There are four placeholder positions, each binary gender typed. The gender typing relative to the personal subject is defined by the first letter whilst the second letter conveys the gender typing relative to the impersonal subject.
The Semiotic Square
There are two fundamental ways of organising knowledge, the left side and the right side way. The left side technique is the easiest to understand as it is based on a taxonomic hierarchical form of organisation involving different levels of species and genera. This kind of structure can usually be represented in tree diagrams. For example, Chomsky’s transformational grammar for representing the syntax of natural languages is based on tree diagrams and transformations between tree diagrams. The essence of the left side tree-diagram approach is that entities, and knowledge of them, can be broken down into increasingly smaller and refined components.
The right side organisational approach is the converse to the atomist and atomising left side approach. In this scenario, any entity, viewed from a particular point of view, can be known in terms of a whole. The innovation comes from the fact that a whole, any whole, has a generic form consisting of four gender typed parts as shown in Figure Ap 1.. We will call this generic form, the semiotic square.
The semiotic square conveys that in any whole there are always four players. Each of these players has an attribute that distinguishes one from the other. This attribute is not of the empirical kind but of the ontological kind, being based on ontological gender. With the semiotic square, no labelling is necessary, only the polarity conventions. The semiotic square can be thought of as a generic cognitive structure, one of its roles is to type a player in reality views as a whole.
The semantics behind the gender typing formalism can be grasped more intuitively by using natural language; The semiotic square shown in Figure Ap 2. replaces the gender typing with natural language generic attributes. In this way, we start to see that our science with attributes starts to take attributes on board by actually constructing them.
The taxonomic, tree structure classification systems of the left side sciences are simple to understand and apply. For the right side version, it is the semiotic square that first springs to the fore. By applying a simple semiotic analysis to practical scenarios viewed as a whole, one can start to comprehend the semiotic square and its extremely generic nature.
Algirdas Julien Greimas developed his version of the semiotic square, inspired by Aristotle’s Square of Oppositions as will be discussed later, He applied semiotic analysis based on the semiotic square to many different areas, one of them being, the semiotic analysis of text. (Greimas, 1991).
The semiotic square provides an intuitive approach to formalising the Three-plus-One structure we mentioned in the introduction. The One is the Singular MM typed player with the triad making up of the rest. This singular MM typed entity corresponds to that which is simultaneously impersonal and personal subject, a singular singularity. Over the ages, many minds, from different cultures have mused over the nature of this being.
The Theological Semiotic Square
Semiotic analysis based on the semiotic square has been applied to many different areas by practitioners of semiotics. It can even be used in advertising to settle such questions as “How many fundamental ways are there to advertise underarm deodorants? It is not an abstract way of thinking, but a generic way of thinking. There are, of course, four strategies to advertise underarm deodorant, the singular, the general, the particular, or the universal approach. It is left to the reader to fill in the details.
On a higher note, the generic nature of the semiotic square is well illustrated by applying it in the theological domain in order to study generic theology. There are of course four generic religions and it is interesting to see where they fit into the semiotic square and relate to each other.
The four generic religions make up a whole. The whole can be informally constructed as follows. The generic structure of a whole is constructed from one single opposition applied to itself, leading to the semiotic square structure. For the generic semiotic square, the primary opposition is between the subject, necessarily masculine and its feminine gendered other. A simpler to understand version of this opposition is to talk of the masculine subject as the One and the feminine as the Other. The primary opposition thus becomes that between the One and the Multiple. Such an opposition can qualify as an opposition satisfying the Socratic Uncertainty Principle, as defined previously.
When the opposition is applied to itself this leads to four kinds of entity as shown in Figure Ap 3. This semiotic square illustrates the four fundamental answers to the theologically impregnated question, “What is the relationship between the One and the Multiple? Each answer corresponds to a fundamental generic paradigm that can be interpreted in theological terms. Each paradigm corresponds to one of the four world religions. The Providence paradigm of Christianity declares the rather individualistic stance that the One is Multiple. Islam takes the converse position declaring that the Multiple is One, where the collectively is decidable under the hammer of the One. Hinduism, according to the Advaita doctrine of Non-Duality declares that the One is One, and to add a phrase of Shankara, “Everything else is illusion.” All three of these religions incorporate the masculine subject into the paradigm in one way or another. The exception is the fourth paradigm that we associate with Buddhism. Buddhism, according to its doctrine of Non Self, declares that the Multiple is Multiple. There is no One. This doctrine is subjectless, pure FF.
Here is not the place to attempt an exhaustive semiotic account of theology, however it the importance of religion studies cannot be underestimated. Before moving on, we note that each of the world religions themselves can be viewed as a whole. As such, each will be characterised by its own semiotic square. For example, the semiotic square for Christianity will be based on the Trinity and have God in the singular position, God the Father in the general, Christ in the particular and the Holy Ghost in the universal slot. The Three-plus-One structure for each of the world religions is shown in Figure Ap 4.. In this way, one ends up with a semiotic square of semiotic squares.
In the diagram, no details are provided for the Buddhist Multiple is Multiple paradigm but it would probably be based on the Four Noble Truths. However, one must tread carefully as this paradigm is devoid of any explicit subject.
This is a long paper…only the first part has been included here.
I think it is getting too long for publication as well.
©Copyright Douglas J Huntington Moore 2011
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