The Chrysippus Semiotic Square of Oppositions

Before understanding our reconstruction of the Chrysippus semiotic square, we need to know a bit about semiotics , or at least, our version of it.

The author’s first acquaintance with the semiotic square came from following the courses of Greimas back in Paris, many years ago. The term “semiotic square” is nowadays generally associated with his name. The big weakness in the Greimas approach was his failure to come to terms with the subject. His semiotics is sans sujet. We will sketch out here a more fundamental approach to semiotics and the semiotic square that does include the subject.
To begin with, there are two kinds of semiotics, one associated with Ferdinand de Saussure (dyadic, arbitrariness of the sign etc.) and one associated with Charles Sanders Peirce (triadic). In our view, the approach of de Saussure is not semiotics
, but General Linguistics. Like Greimas, the approach of de Saussure is sans sujet. If there is a subject, it is part of the Spectacle, not the Spectator. It is merely what Hegel referred to as the empirical ego. In this perspective, the de Saussure approach is like that of the traditional sciences and mathematics. All of these sciences are sans sujet. We call all of these traditional science left side sciences. Left side sciences claim to be objective, which is another way of saying that they only concerned with a reality of objects where any reference to the subject has been excluded. They are all sans sujet. As such these sciences look at the world from a very specific point of view. This point of view has been described as the “view from nowhere” or the “God’s eye view”. This is a general characteristic of science sans sujet. It is a general characteristic of all the sciences and mathematics of today.
The other possible scientific paradigm goes in the opposite direction. It demands that the subject is always present. In other words, if there is a spectacle there must also be an accompanying spectator. You can’t have one without the other. We call the science based on this paradigm, right side science. The right side science becomes, in fact, the dialectic of the Spectator and the Spectacle, the Subject and its kingdom.
Unlike the many left side sciences, there is only one right side science. This is because its focus is on the science of the subject and this is quite different to the science of objects. It is the science of the Self. For a Stoic logician like Chrysippus, it is the science of the Logos. This generic entity, the Self, the Logos, the Ego, has a generic form. This form can be worked out from pure reason.
Now Charles Sanders Peirce was more inclined to the right side paradigm, but he didn’t make much headway. He also despised the Stoics, which didn’t help. Thus we have to start from scratch. Starting from scratch means that we start with a subject and its kingdom. Alternatively we start with a kingdom and its subject, the same thing. Both spectator and spectacle must be present in the same moment.
This is where we have to put our thinking caps on. The relationship between the Subject and its Other is a very particular kind of relationship. They each determine one another. The Hindus sometimes see this as a coital relationship. The subject corresponds to the masculine and the mysterious other is feminine where gender gets interpreted as sex, poetic licence oblige. The Stoics saw the relationship as that between the Active Principle and the Passive Principle. Vedanta philosophy often refers to the Active principle as the Principle of Individualization, the Spiritual Principle, or simply the masculine principle. We have here the building block for right side science. It’s getting a bit steamy so here is one way to arrive at a dispassionate view. It involves the gender construct.
The main role of the subject in this right side science, is that it does provide a determined point of view. As such it is a pure singularity. What is non-subject is non-singularity. This can be formalised with the concept of gender. The gender concept is very ancient, both in the West and the East. First there is the unqualified substance totally devoid of any determined specificity. Such an entity is typed as the pure feminine. One might say that the pure feminine is devoid of specificity and so has no attribute. This is not the case. It is only devoid of a determined specificity. It has an undetermined specificity. That is its attribute. This attribute, using the argument of First Classness, must be an entity in its own right. (Note that the Stoics always claimed that the property of an entity is an entity in its own right). This attribute entity will be said to be of masculine gender. Two entities, one has an attribute, the other is the attribute. The first entity corresponds to the feminine, the second to the masculine. These two entities provide the building blocks for the right side science paradigm.
The first thing to construct is the semiotic square. One way of understanding this square is as the architecture of a whole. Totality can only be understood from a determining point of view of the subject. Instead of comprehending the totality in any moment, which is impossible, it is understood as a whole. A whole is totality looked at from a particular point view. There are as many wholes as there are points of view. This requires that the subject must be present in the whole. Right side science always understands things in terms of wholes.
Thus the semiotic square, as a generic understanding of a whole, is a map of the subjects conscious understanding of the whole, any whole. The first moment of understanding is “Wow, here I am, this is me and the rest is not me.” We thus draw a square, cut it down the middle and adopt the convention that the right side corresponds to subject and the left side to what is not subject. The right side is masculine typed and the left side is feminine typed.
However, the subject in this particular configuration is not you or I. It represents the impersonal subject. In fact, it is this subject that corresponds to the “view from nowhere”, the “God’s eyes view” of the traditional sciences. These sciences, in their quest for objectivity, remove all reference to subject from consideration. They even remove this impersonal subject from consideration as they have no need for it. They demand a godless science, a pure science sans sujet. Thus the semiotic square for the left side sciences is the same as for the right side science, except that the right side is blacked out. Left side sciences thus suffer from a symptom well known to the psychiatrist. It is called hemi-neglect. Right side science knows about the left side, left side science wings it alone, content with half a brain, so to speak. Curiously, in passing, the human brain exhibits exactly this same bi-lateral specialisation. The right hemisphere does not exhibit hemi-neglect and sees a whole world. Only the left side exhibits hemi-neglect.

This is now where left side and right side science part company. Not content with just the presence of the impersonal subject, right side science must find a way of introducing a more determined subject, the personal subject. This is constructed by applying the first feminine masculine opposition to itself, an opposition of two oppositions. It might sound complicated but is easily visualised with the semiotic square. The second opposition is orthogonal to the first and so instead of a left right dichotomy, the dichotomy is front back. We use the convention of masculine in front, feminine at the back. It appears that we am not the only ones to adopt this polarity convention..

The end result is that we end up with a square shaped kind of placeholder for dealing with knowledge. The first kind of knowledge involves an elementary consciousness of self, a knowledge of what is and what is not. This is expressed logically in our reconstruction of the Chrysippus square. For the moment, note that the four parts of the semiotic square have been binary typed with gender. For example, the left front part is typed as MF. This reads that, from the impersonal subject perspective, it is typed as feminine. From the personal subject perspective it is typed as masculine. Thus the first letter in the binary gender typing is that of the personal subject, the second letter is that of the impersonal.

Figure 1 The generic semiotic square is constructed from the feminine masculine opposition applied to itself.


The semiotic square is a placeholder, the architecture of the generic mind, so to speak. The semiotic square is static and unique, for the purposes of the science. You only need one brain, it can be said.
In addition to the placeholder, there are values relative to it. These values are mobile. There are the four kinds of elementary substance that can be binary typed by the four binary gender types. The binary typed substance correspond to MF, FF, FM and MM. The ancients called them air, earth, water and fire respectively.

Stoic Qualia
Pure Gender Algebra
Element
masculine active
MM
Fire
masculine passive
MF
Air
feminine active
FM
Water
feminine passive
FF
Earth
Figure 2 The ancient four elements can be can be understood in terms of gender.

We now come to the semiotic square constructed with four of the Chrysippus undemonstratables. Note that one diagonal is constructed from the conjunctive syllogisms. These are known to logicians as Modus Ponens and Modus Tollens. The other diagonal is constructed from the two forms of the disjunctive. The diagram can be gender typed by matching the is copula with the masculine and the is not with the feminine, as shown. This matches perfectly with the semiotic square gendering shown above.
What is interesting, is that the logic of Chrysippus has introduced yet another dimension into the semiotics, a vertical axis. The square becomes the “Chrysippus cube”! We have used the convention of the implication arrows in the diagram going left to right to signal the upwards direction, and the downwards for the right to left. Talking intuitively, this indicates that the top two entities have an “upward flow” and the bottom two entries have a “downward flow”.
Chrysyppus Logical Semiotic Square
One should note that the gender coding of the top two elements correspond to the “elements” of air and fire. These are the “light” elements, being predominantly masculine and less substantial than the feminine bottom two elements of earth and water. Such reasoning is not very rigorous as we are not talking about the same kind of elements as in the left side, traditional science. The logic of Chrysippus however adds a different complexion to the matter.
These principles must have been part of core Stoic teaching, as Marcus Aurelius wrote in Meditations.
Your aerial part and all the fiery parts which are mingled in you, though by nature they have an upward tendency, still in obedience to the disposition of the universe they are overpowered here in the compound mass. And also the whole of the earthy part in you and the watery, though their tendency is downward,

The Stoics claimed that theirs was a unifying science that integrated logic, physics, and morality. Some people are attracted to Stoic values whilst thinking that their science has been completely eclipsed by the modern day sciences. However, how antiquated is the science of antiquity? Consider the following.
In our diagram we have added in the four letters CAUG matching up with the gender typings MM, MF, FF and FM respectively. This is part of another story in this book. These are the four letters of what we call the generic code. We’ve taken them from the RNA version of the genetic code. The genetic code is a standard code which codes all living beings, without exception. This is a known fact. The generic code is impervious to evolution and has remained unchanged since the year dot. By extending the notion of the living to that of the universe, itself considered as living by the Stoics, this same code takes on a generic vocation. In this book we explore its application to understanding elementary particle physics from a new angle (see Appendix). We use the generic code to code quarks and leptons. These claims may test our short term credibility. However, in the longer term that is the way it will pan out once we have properly digested this new science, a science with such ancient roots.
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The Logic of Relativity

The science of the ancient Stoics was naïve and erroneous. Modern science has come up with all the answers. The universe is not based on any life principle but, as “natural science” will have it, is just the ashy aftermath of a great dirty explosion. The end result is that, despite all of Becker’s the creativity of attempts to revamp a new Stoicism compatible with current science, he necessarily ends sliding into the Epicurean paradigm diametrically opposed to his original intention. Current science is atomistic, dualist and a philosophy espoused by Bertrand Russel, Peter F. Strawson, and so many others of modern times, the same position espoused by the ancient Epicureans.

As Becker well knows, the “doctrine that the universe should be understood as a purposive, rational being” is central to Stoicism. Throw it into the dustbin of history and Stoicism goes with it. Becker, or any of the moderns for that matter, has not even attempted a case against the ancient scientific doctrine. The only argument seems to be is that if it is ancient then it must be inferior to the science of us moderns. In those days, they did not even have internet shopping and motor cars. An alternative approach, and the one promoted here, is to resurrect the ancient science of antiquity and in particular the Stoic version.

The Stoics conceived a world free of anything or anybody behind the scene pulling the strings. There can be no outside organiser. This world is totally unconstrained. There are no pre-ordained rules. The only principle constraining the world is that it be totally unconstrained. Thus, the central principle is of a rational kind. The system is constrained by its own Logos. This principle applies to the cosmos, and equally to any being of the Cosmos.It is important to note a key subtlety here that distinguishes the Stoic mode of thinking to that of Aristotle. The principle doesn’t apply to Everything as Everything is not a thing. It applies to Anything. The Stoics never proposed a TOE (Theory of Everything). Instead, they proposed a TOA (Theory of Anything). This subtlety rests on the difference between thinking abstractly and thinking generically. The Stoics were not abstract thinkers like so most other thinkers. They were not generalists, they were generic thinkers, they were generitists.

One modern way of describing the principle of such a system is that it is bound by the iron laws of First Classness (FC), a term borrowed from Computer Science. FC is a fiendishly difficult concept to formalise and even more difficult to make iron like. Many examples of FC abound in Computer Science but won’t be mentioned here. Remember though that asking your local guru on the matter will only result in a partial answer. The only thing we will say about FC is that it leads to the common perception that developing systems that do not violate FC is considered Good. Whenever a software developer violates the principle in his work, he knows deep down that he is committing a sin which one day will come back to haunt him. Thus, in the field of software development, the FC concept provides a moral compass to software engineers. It is perhaps, the only moral compass.

Returning to the Stoics, a basic expression of FC in Stoic physics is that the property of an entity must be considered an entity in its own right. If this were not the case, an entity would be ontologically more important than its property, or perhaps vice versa. FC demands a dictator free zone: no one definitively calls the tune.

Now Becker argue as that in the centuries following the Renaissance the advancement of science put Stoicism on the defensive. This is certainly the case in the emergence of classical physics. Classical physics violates the Stoic FC requirement concerning entities and their properties. Classical physics opted for Second Classness constituted of two modes of being, particles and force fields between particles. The force fields were not particles in their own right but a kind of something else. Stoic physics was dead in the water. Physics had become an Epicurean atomistic, dualism.

But then, in the twentieth century came the rise of quantum mechanics. The tables were turned. There were no force fields, just particles. The forces between particles could be explained by an exchange of other particles called gauge bosons, particles in their own right. The movement back towards the original Stoic FC doctrine had started. However, quantum mechanics is still only an empirical “suck it and see” science. None of its findings can be derived from first principles. The source of any such principles of course can only be from the dictates of FC, a slippery beast but not an impossible one.

FC is a principle and has no explicit structure. However, structure, a certain kind of structure, is necessary in order not to violate FC. Some of the ancients knew this going right back to Empedocles. A reverse engineered version of the reasoning will appear in a book I am writing, but we all know what it looked like. Empedocles called them the four Roots. Others have called them the four Letters. The Stoics saw it as the theory of the four Elements. In my book, I argue that the four Letters can be interpreted as a unifying science that includes the four-lettered genetic code as a special case. I call it the God Code.

That any entity in reality can be coded by a four letter, generic code has stupendous implications. That every cell of an organism must contain a copy of the same code for the whole organism is incredible enough. What is even more stupendous is that that this genetic code should be more generic than just for the animate, applying right across the board, applying to anything. None of this would have surprised the Stoics. This was the way too that they saw the world. Present day traditional sciences might be devoid of any “grand teleological explanations” as Becker states, however things will be different for the resurgent new unifying science based on the ancient Stoic doctrine.

The naivety of the theory of the four Elements lies more in the naivety of the eyes of the modern beholder than in the ancient theory. The naivety of modern science lies in its belief that the only source of scientific knowledge is because of empirical measurement. This naturally leads to a dualistic way of seeing the world: The world is populated by material entities, which possess sensual properties. The sensual properties are not material and are not even entities. This is a valid and useful way of conceiving the world. It is particularly useful as it is free of any costly overheads that may come with a more elaborate conceptual schema. All that really matters are the data. However, it is not the only way, and certainly not the most fundamental way of conceiving the world.

The empirical view of the world violates FC because of its dualism between entity and property. Ignoring attempts by quantum mechanics to buck the trend, modern science is based on Second Classness.
This acceptance of a Second Classness view of the world can be traced back to Aristotle. Aristotle interpreted the four Elements of antiquity in a way that would be somewhat similar to the moderns. The four elements were the elementary constituents of matter. Matter was a simple mixture of these four elements.

Aristotle retained some of the ancient form of reasoning in terms of oppositions, but otherwise his approach resembled the moderns. For him each of the Elements possessed particular, plain and ordinary properties. Thus, according to Aristotle:

• Water is primarily cold and secondarily wet.
• Earth is primarily dry and secondarily cold.
• Air is primarily wet and secondarily hot.
• Fire is primarily hot and secondarily dry.
 
The Elements were material, their properties were not. Aristotle’s system was definitely incompatible with FC. The science of the moderns replaces the four Elements with a much more extensive list with more elaborate properties. However, the underling acceptance of the Second Classness paradigm which accords with Aristotle is the same. In this sense, modern science can trace its lineage right back to Aristotle.


Chrysippus and Ground Zero

By Ground Zero, we mean the centre of the Cosmos. Ground Zero has a certain shape, the shape of the entity located at the centre of the Cosmos. As we know, this entity is none other than any subject whatsover that takes the pain to contemplate on its particular spot in the universe. Without fail, this subject, like any other subject, sees itslef as being located at the aforsaid location, notably the centre of the Cosmos, the centre of its Cosmos, at least.
As for the shape of this entity, the generic subject, it has a left and a right side and also a front and a back. This is the structure we have been referring to as the semiotic square. It is a structure that can be interpreted in many ways, as a blueprint for epistemological organistion of knowledge, for example. There are also ontological, and of course many biological interpretations. On the biological front, this structures can be thought of as the structure of a whole, as coded by a chromsomal codon. Any biological organism is organisaed as an entity viewed as a whole from a myriad of points of views. To each codon there corresponds a holistic point of view. The genetic cum generic code is the language that articulates the geometric algebra of this exhaustive but holistic view of the organism. Another intepretation of this highly generic semiotic square is that it offers a schematic for elementary cognitive structure.

Chrysippus Square of Oppositions reconstructed, based on four of his undemonstratables

So prodigiously generic is this structure that it can make the head spin. To top it off, we now have Chrysippus joining the fray. Now Chrysippus was consided by the ancients to be the equal of Aristotle, so he cannot be dismissed as a lightweight. In the diagram below, we have organised four of his five fundamental syllogisms into a form which falls quite naturally into the elementary structure of the generic semiotic square. As can be seen, the premises of the first and the second hypothetical conjunctive syllogisms make one diagonal of the square and the two disjunctive forms mark out the other diagonal. It is becoming clear that we have here, a structure which has a resembalnce to the Square of Oppositions of Aristotle. The Scholastics added the AEOI four lettered labelling to Aristotle’s system and spent over a milenium probing into its delights. Not to be outdone, we have added our lettering to out reconstructed version of the Chrysippus Square in the hope of preparing it for its reinvigorasted role in the present millenium. Suffering from a lack of creativity, we have borrowed the RNA version of the biologist’s genetic code. Why invent when you can steal, is our motto. It took the author a little while to get the right fit, but he is reasonably confident that the his allocation of the CAUG lettering, is the spot on. He would be very miffed if this was not the case.

Chrysippus and the Grand Unification
The ancient Stoics have been the historic mentors for the material presented in this work. They developed the most succesful and diverse form of monistic philosophy that the Western world has ever seen. Zeno provided the intuitive and informal core elements of the doctrine. Chrysippus’s logic marked the first tentaitve steps towards the formalisation of a unifying science. The full significance of Chrysippus’s contribution has been little understood by the moderns, blinded as they are, by the achievements of the current day sciences. Despite these achievements, the present day sciences are lacking in any kind of cohesive unifying discipline. The unifying science started by the Stoics, will provide such a unification.
Of critical importance is to learn how to reason in a different way than is customarily taught in modern schools and universities. The moderns only have a partial grasp on rationality. Modern science and mathematics only understand the notion of the true and the false. What lacks, is the understanding of truth. However, the very mention of this word, truth, can seem off puting. After all, probably more people have been burned at the stake because of an alledged incorrect understanding of truth, than for any other reason. However, buried amongst the historic debris of lost causes lurks indeed the rusted hulk of truth.

Nevertheless, as any philosopher knows well, truth of this kind must be self justifying. For many, such as Karl Popper, the notion of a self justifying truth is synonomous with the blind faith of religious zealots and doctrinaire extremists, something anathema to science. Popper is content with the kind of knowledge where each proposition is forever condemed to the judgment that it might be false. Even worse. at the same time the proposition must accomodate to the stark reality that this judgment might indeed be true. But then again, it mightn’t. Modern scientists are a brave lot.

Sidenote: Popper did eventually nuance his views on this matter in the light of the self justifying biological organsim notion. In so doing he imlicitly admits that the bilogical organism is obsessed with self justifying its continual existence in the world. As such, biological organsims seem to have ontologically more in common with the logic of religious zealots and political fanatics, than with the cool, dry head of the analytic philosopher. 


The stark truth about truth is that it must be relative. and never absolute. It is only in this way can it become an absolute truth. In other words, it becomes an absolute truth relative to itself. This is the essence of monistic philosophy: It is the rationality of the self justifying Self. Relative to this subject, there is only one truth.

We have already made inroads into the science of the subject.. Unlike the analytic rhetorical type reasoning of the analytic philosophy, the reasoning of this right side, monist philosophy is expressed in terms of oppositions and oppositions between oppositions. It is in this way that the readoning becomes a relativisdtic form of reasoning. Rather than rhetorical, it becomes dialectical. The nuts and bolts of the reasoning deals with the dialect of two entities, one which has and the other that is. These entities differ by gender, the first corresponding to the feminine gender, the second to the masculine. The dialectic of to have and to be, constitues the core essence of the monistic, right side form of reasoning.
This is the dialectic of the subject minamally conscious of itself. It leads to a particular kind of knowledge. It leads to the generic truth that reality, viewed from any particular perspective, is the reality viewed from the the point of view of the generic subject, the any subject whatsoever kind of subject,
The elementary form that arose from our investigations was the semiotic square. This structure arose from the opposition between what the subject is and what the subject is not, that is to say, what it has. This opposition was formalised in terms of the gender construct. This leads to the four distinct parts of the square being gender typed MF, FF, FM and MM.
This very generic quadtuple structure is highly lacking in determination. The edifice is so undertemined that it is not even clear whether it corresponds to the semiotic structure of knowledge of the world, or the stucture of the world itslef. Is this epistemology or is it physics? Is this the structure of Mind or is it the structure of Body? Is it structure of a generic language or that of a generic world?
Finding an answer to these kinds of questions is key. It is here that we find the great enigma of this science. Unlike the analytical thinkers who want to understand the realtionship between Mind and Body in terms analogous to that between horse and cart, the synthetic monist thinker must take a different tack. The horse will not be seperated from the cart but treated as an organic whole. One cannot have one without the other. We cam across the very essence of the monist solution in the form of the gender construct. Rahter than plucking attributes from a predefined definitional framework or harvested from emperical measurments, we constructed the one single fundamental attribute from which stem all other attributes of our science. This was the attribute possessed by the pure feminine entity. The attribute, an entity in its own right, was the masculine entity. These two entities are different. They differ by gender. However, they are absolutely indistinguishable. Two entities are distinguishable if they have different asttributes. Here there might be two entities but there is only one attribute between them: Two entities; one has an attribute, the other is the attribute.
This gender construct provides the generic formula for all of the science that follows. The dialectic of the masculine and the feminine provides the generic base for all other seemingly dyadic stuctures such as the popular Mind Body duality of the analytic philosophers. The relationship between the pure feminine and masculine is a generic form of the same relationship between Mind and Body.
Not everyone will agree with this assertion. Certainly, an analytic philosopher or anyone reasoning from a Cartesian viewpoint, would take the abstract road, abstractly arguing that Body is like a machine and Mind is an intelligence that drives the machine. The two are linked together by some kind of “bridging laws”, perhaps, There is no dialectic here as the notion of a bodyless mind and mindless body, is considered quite respectable. They can conceivably go their separate ways: Put the brain in the bottle and the brain dead body on life support, should do the trick.
Such a surgical seperation is impossible for an organism constructed from the gender construct. The organism is constructed according to a four-lettered code. According to out gender calculus version of this code. Each letter is made up of one of the four binary gender typings, MF, FF, FM and MM. On the face of it, the organism might be just a highly complex essemblage of hydro-carbon based compounds. However, from an organisational point of view, it is a seething mass of intertwined, gendered entities. It is this gender typing of content and form of the organsim that ensures systemic coherence. It is in this way that the One can be constructed from the inseperable and indistiguishable Two.
The Stoics saw this dynamic systemic organ

isation of the organism in terms of the tensions and tenos of a fifth kind of substance they called pneuma.

The pneuma is in constant motion. It is a process into itself, and from itself. The inward process produces unity and substance, the outward process dimensions and qualities. The pneuma is a disposition (hexis) in process. As a disposition, the pneuma holds the cosmos together, and accounts for the cohesions of each individual entity. The pneuma is the cause of the entity’s being qualified: For the bodies are bound together by these. [Chrysippus views on the pneuma (Reesor, 1989)]

The coherence, the very being of an organism is synomous with it maintaining Oneness. The mechanism for achieving and maintaining Oneness is through the establishment and maintenance of gender typing. The oranism must know, without a shadow of doubt, what it has and has not and what it is and is not. In all cases. These are the key determinants of consciousness. Also, the determinations are purely relative. They are purely subject-ive. This, one must admit, is trully a beautiful, self referring system.

Beautiful indeed, but how does it work? With profound beauty one would expect an accompanying simplicity, a profound but simple principle. Seeing that everything involved in this kind of self organising organism is relativistic, there should be some some fundamental relativistic principle at play. In the tradional sciences of our day, the only reltivistic principle known is in physics. There is no known equivalent in biology. In physics, we see relativty theory expressed as demanding that the laws of physics remain invariant from one reference frame to another. Perhaps more pointedly, as shown by Zeeman, the principle of relativty is intimetely bound up with the non violation of the causality principle. It is here that one can grasp the simplicity and elgeance of the theory. System coherence demands the coherence of causality. The claim of generic science is that this is not enough. A much more demanding form of relativity is required, what we call generic ralativity.

If the work presented in this book is to be more than the usual exposition of inconclusive philosophical prose, then we should be able to advance an equally simple and elgeant formulation concerning the essence of generic relativity, the cornerstone of the generic science we are trying to develop. Fortualely, we don’t have to look far. The principle is located at Ground Zero and there is noone who knew this spot in the Cosmos better than Chrysippus, the Stoic logician par excellence. Ground Zero is the location of the Logos, the reasoning faculty of any subject whatsoever. The form of the Logos can be understood in terms of the dialectic of having and being which leads to the semiotic square. Chrysippus provided tha logical framework of the Logos semiotic square in the form of four of his five undemonstratables. We have ressurected this structurte as an alternative to Aristotle’s Square of Oppositions as already shown in Figure 30. We have named this Chrysippus’ Square of Oppositions. The fit between this strucute and the four undemonstrables is confortable and reasonably self evident. Thes stucure effectivel provides an additional logical impetus to the thrust of our argument. The four undemonstratbles provide a logical dimension to the interpretation of the four element theory and the corresponding four letters.

Absolute Incompatibility

Five undemonstrables minus four leaves one. The missing syllogism is the third undemonstrable, the incompatibility syllogism: One can’t have one quality and the other at the same time. We now come to the fundamental tenant of generic science. It is founded on the premise that there is noting more incompatible in this world than the masculine and the feminine. This premise does have some intuitive appeal and so we will stick with it. This is not a bad idea as it appears that the whole cosmos hinges on the concept. It is this incompatibility principle that holds not only the cosmos together, but any being whatsoever that exists,

In the case of biological organisms, the concept should be relatively easy to grasp. A stumbling block might be in accepting the fact that the genetic code is more than a mere transcription language which curiously somehow accidently became a convention adopted by all living organisms since the year dot, without exception. Accidents do happen, but this accident does seem a little bigger than most. Life might be subject to evolution, but the language of life seems absolutely impervious to change. Nature seemed to have got it absolutely spot on, right from the start.
The reader may rest with that interesting accident hypothesis or move on to considering that the code may be based on a generic semantic and ontological structure. According to our take on the question, this structure is based on the dialetics of being and its naturally orthogonal counterpart, that of having. This can be formalised in terms of the gender construct and leads to a four letter code based on the four possible binary combinations of the two genders. It is generally accepted that all biological processes are coded by the genetic code, what we claim to be the genric code. Moreover, in multi-clled creature, the same code is repeated for each cell. We say that this code expresses a relative typing on all aspects of the organism. At the very ground roots level, the typing is in terms of complex combinations of gender typing. We claim that the organism relies on this form of organisation in order to arrive at knowledge and consciousness of itslef. It is via this absolutely relativistic gender typing that the entity knows what pertains to it or what does not. This is the most elementary and most essential feature of life.

Morevoder, the basic health of the organism will be placed in peril if this typing mechansim starts breaking down. The cohesian of the system demands the constant maintenance of the integrity of gender typing through the organism. The Stoic picture of a pneuma permeating every aspect of the organism is very helpful The penuma is constantly attracting and reppeling, constantly maintaining the equilibrium of the organsim.

The Stoics claim that there are two primary principles working through the pneuma, the active principle and the passive principle. This terminology is also helpful, as long as we recognise that the active and passive ultimately refer to the masculine and feminine, in a particular configuration. For example we refer to the feminine as active by the mixed gender term FM. The masculine as active becomes MM and so on for the passive MF and FF variants.

Maintenance of the integrity of gender typing throughout the organism is paramoint. Since the system is changing and reacting to its environment, this integrity must be synchronised. This brings us back to the key logical ingredient that keeps guarentees such coherence. The coherence principle.

The Gender Coherence Principle

The organisational coherence of an organism is regulated through gender typing. The maintenance of organisational coherence is synonomous with maintaining the integrity of gender coherence. This can best be expressed in the form of Chrysippus’ third undemonstratable, the incompatibility syllogism. The premise can be restated in the form

In no singler moment can an entity be both masculine and feminine at the same time.

We will call this the gender coherence principle, the fundamental organisational principle of Nature.

Note in passing that an entity can have multiple gender typing. However, it cannot have two different gender typings at the same time. This raises interesting question regarding the degeneracy of the genetic code. Take the amino acid asparagine, for example. It can be coded by either the bases AAU or AUC. In gender terms, this translates to the gender typing MFMFFF or MFMFMM. According to the gender coherence principle, such an netity has two possible “quantum” gender states. At any time it can be functioning as either MFMFFF or MFMFMM, but not both at the same time. Remember that gender typing at any instant of time is not absolute and cannot be measured deterministically by a third party. Gender typing is relativisitic and dynamic and in coherence with the organism so typed.

Note that the so called superposition of states addressed by quantum mechanics dissapears if they are considered to be more like relativistic gender states. Any observer that tries to deterministically measure a relativistic gender state of an organism will encounter superposition. For the organism in question, there is no superposition whatsoever. Relative to its integrity system, the gender coherence principle demands that the very opposite apply at each and any instant.

As for the organism, in the life sciences the organism might be a cat on a slab in the lab. For the physicist, the organism might be a much smaller or much larger creature. However, it is stillan organism based on the same generic organisational principles.

Physics Interpretation

In an appendix attached to this work, elementary particle physics will be interpreted from a generic point of view. This realuts in elementary entities like quarks and leptons being gender typed in terms of codons, similar to in biology. In this way, any being in nature code itself in terms of the genric code based on gender typing. This includes the cosmos itslef, as a dynamic self organising being.

In traditional relativity theory one can discern an elementary organisational coherence which can be stated in a form comporable to the gender coherence principle. In this case it becomes the principle of causal integrity. The principle states the dialectic of cause and effect.

The cause event is always antecedant to the effect event.

This is the most fundamental organisational principle known to traditional physics. The law must not be violated in any context (i.e., in any reference frame) and so demands a system that obeys Einstein’s Special and General Theory of Relativity.

One can see that the form of Eistein’s relativity has a certain resemblance to the generic form expressed, not as a causality coherence, but as gender coherence. There is also a fundamental difference, Eistein’s relativity demands a coherence across time: Causes must preceed effects in time. In other words Eistein’s relativity is diachronic in nature. In contrast, the generic version of relativity demands a coherence at the same time. In orther words generic relativity is synchronic in nature, and up until now, has been totally ignored in physics.

Computer Science Interpretation

It is important to keep in mind at all times when dealing with the generic that it is not an abstract science. Generic science is capable of formalism but not as as an abstraction, which is necessarly dualist. Generic science is monist and non abstract. Some effort is required to become accustomed to this totally different paradigm. Interpreting some of the concepts in a Computer Science setting can help, in this regard, unlike axiomatic abstract mathematics, Computer Science is a constructive science and naturally synthetic in nature. It also leads to natural monisms where the theory of code can be expressed in code.

Generic science is a disciple which has for its vocation the task of articulating the structure and organisational principle of any living being. The science is naturally constructionist. This raises the question of how to construct an organism based on generic science principles. Such an organism would have to be based on gender typing and be organised on the gender coherence principle. In addition, the whole system must not violate the principle of First Classness. Is this possible?
This is a silly question as our very own presence on this globe is at least some kind of feasability proof of the concept, a living proof in fact.

What we wish to do in this section is to provide a very simple example of how Computer Science, unknowingly, has already started to go down the path of Generic Science. Our example is the very computer itself, the Von Neuman computer.
Before Von Neuman, there already existed programmable calculating devices. However, they all had one thing in common. They were based an an absolute dichotomy between data and program. For example, the program migh be hard wired into the device and the data fed in via paper tape. If we want to put some gender typing into the mix, we could say that the program was masculine stuff and the data feminine. With this arrangement, the gender coherence principle could be satisfied because at no time is any confusdion possible between what was program stuff and what was data stuff. Data was always on the paper, and program in the machine. The only problem was that such a device violates First Classness which is incompatible with such a blatant and absolute duality. First Classness cannot tolerate a world cut up into two, one made of paper and one made of the other stuff.

Von Neuman started the process of moving the calculating macjhine into the realm of a generically organised entity. He made two innovations. The first innovation was shared memory where there was no longer to be any absolute dichotomy between data stuff and program stuff. They were all loaded into shared memory in the same format as small chunks of information. Von Neuman was then faced with the problem of how the computer could tell the difference between program stuff and data stuff. It was here that Von Neuman decided to invoke his version of Chrysippus’s incomatibility principle. The principle was that:

No chunk of information in shared memory could be both data and program at the same time.

In order to implement this principle, he came up with his second innovation. It was called the Program Counter, The Program Counter is a pointer into the shared memory of the computer. The rule was that a program instruction was the chunk of memory pointed to by the Program Counter at a particular instance in time. All the rest of the chunks were considered data. Having executed that instruction, the Program Counter would be incremented to the next memory location, and that would then be considered a program chunk and no longer potential data. In the case of a JUMP instruction, the Program Counter would be moved to some other distant place in memory and the process continues. The computer was born.

Like practically every major advance in computer science, the Von Neuman’s computer was an exercise of eleiminating violations in First Classness, in this case, eliminating the fixed dichtomy between data and program. Hence forth, the distinction became relative to the dynamically changing Program Counter. What was program and what was data depended on contect.

However, such a deice is far from freeing itslef from violation of First Classness. The Program Counter itself, becomes a rigid priveledged memory location, totally estranged from the run of the mill informastion chunk in shared memory. That is yet another dichotomy to be eliminated by generic engineering principle. There is a long way to go.

The Von Neuman computer needed a fuew furth innovations in order to be operation. However, not many other innovations were needed. Add a stack, interrupts, and a few input/output ports and that’s about it.

 

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Dualism, Monism and the Stoics

The Double Articulation

Two birds living together, each the friend of the other, perch upon the same tree. Of these two, one eats the sweet fruit of the tree, but the other simply looks on without eating. The two birds are the Jiva and Isvara, both existing in an individual compared to a tree. [Mundaka Upanishad]

What interests us about Stoicism is the paradigm. The paradigm does not belong uniquely to the Stoics but stretches back from Heraclitus and Parmenides right through Leibnitz to Kant, Fichte, Hegel, Marx, and Yung and to some of the more recent moderns. The paradigm has been referred to as monism.

The natural opposite to monism can be seen in the present sciences of our day. These sciences are characterised by atomism, fundamental dualities and abstraction. These traditional sciences, which include axiomatic mathematics, are aligned on virtually the same epistemological axis as Epicurean. Charles Sander Peirce pointed this out likening the Epicureans to John Stuart Mill’s philosophy. Bertrand Russell and Karl Popper could be added to the list. As you know, the author characterises the Epicurean type paradigm as left side science, as this is this kind of thinking is privileged by the left hemisphere of the brain. Initially we used this as a metaphor but things have started to become a little more literal. A lot is known about the functioning of this side of the brain, its syntactic language capability, but semantic limitations, its attention, even obsession, to fine detail, its tendency to fabulate when in doubt. A general characteristic of left side thinking is the continuous attempt to meld the mind to the world.

What is of interest here is the complementary mode of thinking, right side thinking. Much less is understood about this side of brain functioning. Here I am talking about the biological brain and also the “epistemological brain”. The latter brain contains, or should contain, two hemispheres of complementary knowledge.  In this right side case, rather than mould mind to the world, the task becomes that of moulding the world to fit the mind. In other words, if the traditional “left side” sciences are bottom up oriented, the right side science will be a top down science – non-empirical, all worked out from pure reason alone – the Kantian scenario.
In our view, the right side thinkers par excellence were the Stoics. It appears to us that the Stoics were more advanced in many ways than even Hegel, the most prominent right side monist Western thinker of modern times.
It might seem strange that we have difficulty talking about the Stoics without continuously considering them in oppositions with their opposite number, the Epicureans. Even worse, we keep spreading the discussion across a left side right side epistemological dichotomy, a dichotomy that has distinct biological reverberations. Not only is knowledge organised along these lines, not only the universe but the very architecture of our brains also has this shape – a left side, a right side and even a back side with frontal lobe front side. Everything surely is connected and intercalated, as the Stoics claimed. Maybe they were right.
The basic message we want to get across is that there are two basic philosophical paradigms. Now everyone knows that already. The Western philosophical tradition has been split right down the middle almost since the year dot. What interests me is the multi-paradigm paradigm. This has been a long interest even in the author’s professional work developing computer languages. To many in the IT community, computer languages are like religions. The author treated each of the four fundamental computer language paradigms as separate dogmas and integrated the dogmas. This gave him a lot of practical experience in integrating what appear to be totally conflicting dogmas. Single doctrine doctrines are just doctrines and dogmas. Multiple paradigm paradigms become systems.
And so we finally come to the main point. We believe that one cannot arrive at a deep fundamental understanding of Stoicism without simultaneously understanding the nature and way of thinking of its opposite, which in the occurrence, is incarned in the Epicurean dogma. In addition, this great epistemological divides should be looked at from higher perspective than merely this historic occurrence. These two doctrines are instances of a greater generic dichotomy that has further instances in Cosmology right across to brain architecture.
Right side thinking expresses itself in oppositions. Thus, even to promote a particular doctrine such as the basic paradigm of right side thought itself, that paradigm must be put in opposition against others. Perhaps one should note in passing that Chrysippus himself practiced this technique. As Diogenes Laërtius wrote, early on in his studies “he got the habit of arguing for and against a custom.” (LAERTIUS)Chrysippus was also known for his prolific and lengthy citations. This is an important aspect of the critical nature of right side thinking. The demise of a vibrant critical tradition in politics and the social sciences is a lamentable fact in present day society. In the case of the sciences, such a tradition is totally absent: the only critique is that of peer review. What we need is a totally different kind of science to put the cat amongst the pigeons.
At this present time, our Western culture and our education system place all the emphasis on left side thinking. This is particularly apparent in the sciences. There the fundamental left side paradigm goes right back to the first atomists, Leucippus and Democritus, forerunners to Epicurus. The present day traditional sciences and modern formal mathematics continue the development. Some of the key aspects of this tradition are:
·        Dualist and atomist – tolerates rigid dichotomies.
·        Abstraction
·        Languages
·        Bottom up methodology
·        Likes labelling things.
All of these characteristics are interrelated and are expressions of s single underlying paradigm. From a neuro-psychological perspective, these are also fundamental characteristics of left hemisphere brain function.
When it comes to right side thinking, it has its own tradition with the Stoics occupying a most prominent position. Some key characteristics of right side thinking are:
·        Monist – no rigid dichotomies, everything relative.
·        Generic (Non-abstract)
·        No Languages just bare meanings – semiotics and a semiotic code.
·        Top down methodology
·        Likes expressing knowledge in terms of oppositions, not labels.

Language Difference

On the biological front, a most dramatic differences between the two hemispheres for humans is that the left hemisphere can speak and the right hemisphere cannot. A subject with the left hemisphere immobilised will be mute. With the right hemisphere immobilised the subject will be able to generate syntactically correct speech, although it may be severely impaired with regard to its meaning.

Hemi-Neglect

Another dramatic difference between the two hemispheres is that the left hemisphere, on its own, suffers from hemi neglect. This means that the left hemisphere appears to be only conscious of one half of reality. It will only recognise and be conscious of one side of the body, the right side. It will not be conscious of its left side or of anyone or anything on its left side. It may even only be able to see the right side of a clock. The right hemisphere exhibits no hemi neglect, recognises both sides of the body as its own, and sees a whole world.

Biological versus Epistemological Brain

In brief, the left hemisphere can have languages whilst the right side is mute. The left hemisphere sees a half world; the right hemisphere sees a whole world. These are differences easily observable in the clinic. However, these are differences between the biological hemispheres. A persistent theme in this work is that the biological brain and the structure of knowledge, the “epistemological brain,” share a common generic structure. If indeed this were the case, then the phenomenon of hemi-neglect for the left hemisphere and language muteness for the right hemisphere should have some epistemological analogues.
It finally comes down to the fact that there are two distinctive modes of thinking, a left side and a right side. If we admit of a second dichotomy, as indeed we must, then we end up with four modes of thinking. This secondary dichotomy is the front back dichotomy that we have been talking about. We argue that this four-cornered playing field provides the common ground for organising knowledge. For right side science, all knowledge is defined relative to this playing field, relative to the generic subject.

Biochemistry and the Double Articulation

The architecture of the generic subject was worked out starting from the Parmenidean question: What is? Answer: Reality is. This entity that really is, this Parmenidean incarnation of the real that is the eternal now, this thing can be thought of as the impersonal subject. It is from the point of view of this subject that situates the God’s eye view, the view from nowhere of what is not Everything is relative of course. There are no absolutes. This Other, that is not (relative to the Subject), this other entity corresponds to the impersonal object. The impersonal subject and the impersonal object relate to each other in the most intimate and profound way. The Other, from the perspective of the science, is totally devoid of any specificity whatsoever. However, so pure and profound is this lack of specificity is that the lack of determined specificity becomes a characterising principle. This lack of attribute, this utmost purity can actually be thought of as an attribute. This Other has the attribute of such purity and lack of specificity.
We have already discussed this dialectic of to be and to have and cast it into a relative typing system called gender. The pure feminine was characterised as the entity having the pure attribute and the masculine, considered as an entity in its own right, becomes that attribute. The feminine has it, the masculine is it. What has the attribute can only be known via the attribute, via what is. This fundamental dichotomy between the feminine and the masculine is that between the object world and the singular subject, what we have been calling the left right dichotomy.
This is the dichotomy between reality and the impersonal subject, the result of the “view from nowhere.” In order to arrive at a tractable science, a tractable view of the world, a more determined purchase is necessary than the view of from nowhere. What is required is a view from somewhere.
The view from somewhere is the view you get when you are at this location, be it in time and space or whatever. In order for this to be the case, you must take on the determination commensurate with a subject sufficiently qualified to do the job. No longer are you an impersonal subject, but you become a personalised subject. The same gender qualification will do the job, but it is a qualification relative to you and not reality. The qualification must provide the singularity of you. This is the masculine side of the qualification. The feminine is the other side of the qualification. The side that is not a singularity in itself but has the singularity all the same – as an attribute, but not as its essence. The essence of the feminine remains a total mystery in this metaphysic: the mystery is its essence in fact. The feminine remains the wildcard at all times. It is the masculine, which is the open book.
The Indian Hindu thinkers, particularly the Advaita Vedanta school, understand this metaphysic very well and in detail. Many interpretations are of religious and spiritual nature, which illustrate these difficult the allusive ideas in vivid colourful detail. Sometimes the concepts are adorned with ancient mythical stories dating right back to Vedic times. At the more technical level, the absolutely unqualified entity, which even escapes any subject object dichotomy, is the Brahman. The Brahman is the cosmic self and is identical to atman, the self of all living beings. At the first level of qualification, the pure subject object dichotomy associated with the view from nowhere, corresponds to the Nirguna Brahman, the non-manifested form of the Brahman.
The next determination leads to Ishvara considered as both a transcendent and immanent entity. By coming into being, he creates the world and thus ends up living in it. In fact, he is the world in the sense that “this world is covered and filled with Ishvara”. After these two determinations, the world is divided up into four. This is ground zero, and like the North Pole, all roads from here lead in a single direction South. The interpretations of this original semiotic square abound. In all cases, there is the usual Three plus One form of the square. Since we know that the most generic labelling of the four elements of the square, we can consider different variants using the gender typing as a constant frame of reference. In other words, we use a gender-labelling scheme, noting that the labels are not arbitrary, as for left side methodologies, but ontologically constructed. One semiotic description of the Ishvara semiotic square consists of the triad Ishvara, all sentient entities and the World. The triad is complemented by the One, corresponds to the Brahman. Other accounts explain creation in gender terms resembling the Stoic version. The feminine is unqualified, formless substance. The masculine expresses the Individualisation Principle that fertilises the feminine, bringing about individualisation.
From all of this a universal structure emerges based on two oppositions and the mutual opposition between them. One opposition, the impersonal, is between Reality and its Oneness. The other, is the opposition between an individual being and its oneness. Oneness translates as the masculine, the Other as the feminine. We adopt the left right polarity convention for the first opposition and front back for the second. The masculine Oneness sides of the convention correspond to the right and front sides of the resulting semiotic square. This square becomes the generic reference frame for all that follows. An intuitive interpretation is to see this structure as the architectural layout for the generic mind. In terms of gender typing the four parts of the square are typed MF, FF, FM, and MM. These binary typed entities can be labelled with four single letters. We have chosen the convention of the four letters A, U, G, and C respectively, using RNA coding. A central tenant of this work is that these letters correspond to the four letters of the genetic code. We call it the generic code as we claim it can code any material being whatsoever, not just the biological.
From this generic Ground, the development must take into account the generic Figure. Ground, relative to itself, is obviously static, that is the nature of any ground, the nature of anything relative to itself for that matter. On the other hand, Figure, relative to Ground, is mobile. Figure itself can be understood in terms of a semiotic square structure. The structure of Ground is a Three plus One structure, where the Oneness part is typed MM and denoted by the letter C, the singular singular. The same applies for Figure. Figure can be determined relative to Ground where the AUG triad of quarters of Ground act as placeholders for the mobile quarters of Figure. So mobile are the quarters of Figure that for a determined Figure any triad of combinations are permissible including even repetitions and duplicates. This is like a dynamic Rubik Cube of prodigious complexity. Everything might appear jumbled and all over the place but there is a higher plan to produce an Oneness from this apparent chaos.
Figure and ground are the two moments of Self. Relative to Self, both Ground and Figure are mobile. Ground determines where, Figure what. Ground determines angle of point of view, Figure the view.
This kind of discussion can easily lapse into either poetry or abstraction. In an attempt to escape from this temptation, we provide the following easily understood example from biology as illustrated in the diagram below. The diagram is a schematic, not a detailed functional diagram. It shows schematically the relationship between the genetic code and the biological body that it is coding. The body is coded in a sequence of triads called codons. Each codon will consist of three letters from the alphabet A, U, G, and C. To each codon there is an implicit semiotic square where the fourth element corresponds to the body being encoded, looked at as a whole. The first codon is AUG and is the start codon. It determines the body to be coded as ground, the initial reference frame for all that follows. Each succeeding codon articulates a succession of holistic prescriptions for biological synthesis. Although lacking in determination and qualification to begin with, this sequence of holistic views increases in qualification. The specification becomes increasingly more precise as requirement on requirement compound and stack up. However, this code is nothing like the recipe for a cake, the sort of thinking characteristic of left side science. By continually viewing and recognising the organism as a whole, no matter from what viewpoint as the specification progresses, the wholeness of the whole becomes an invariant in this kind of language.
This generic language is hardly the kind of language that you would want to use to order your lunch. For that problem environment, a left side language is adequate. However if the objective is to create an autonomous unity of Oneness, you need a code whose very essence is abse3d on Oneness. For that you need the generic code, the genetic code, and as some call it even in its genetic version, the G Code.
Now the important point to note in the diagram below is that this biological body language of the genetic code illustrates what some French linguists call, the double articulation. The first articulation is what the biochemists see. This is the same view as the pastry cook. The recipe says, “Add an egg”, the pastry cook adds an egg. In the example below, the second codon says “UCC.” Looking up a table, we see that UCC codes the amino acid serine. We would thus expect to see, via the standard biochemistry mechanism, the synthesis of a component of the amino acid serine. Biochemists confirm that this is indeed the case: The organism is being constructed along pastry cook lines.
Biochemists can then write detailed memoirs of the role of the amino acid serine in the body chemistry of living organisms. Any mention or reference to the code that inspired its necessity in the scheme of things has been long forgotten. The genetic code only has one articulation. It is little more than a mere transcription language.
However, looking at the diagram we see that there is an implicit second articulation at work. The opaque four-letter code harbours an underlying generic structure based on ontological gender. Rather than
Rather than three letters per synthesis event, the diagram implicitly refers to six as each letter is double gendered. Rather than a dumb sequence of three opaque letters, we see revealed the seeds for a kind of generic geometry. This code is no longer just transcribing, it is building a highly elaborate structure of generic interiors and exteriors and so forth that make a Klein bottle look like child’s play.
The big challenge before us is to understand this second articulation. Until we make important inroads along this direction, we will have to downgrade the incredible achievements of the biochemists. They need provocation. Our finger points to the moon and the biochemist only sees the finger.
In the next section, we look at the generic logic behind the generic code. In a later section we will look at generic geometry.
Figure 25 A schematic illustrating the two articulations of the genetic code when encoding a biological body. The first articulation is biochemical transcription. The second articulates the specification in terms of a sequence of wholes. The genetic code becomes the generic code.

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Genetic Code and Gender

The traditional science and mathematics all rely on a priori knowledge. We call these sciences left side sciences. What interests us is the science on the other side of the epistemological brain – right side science. In this section we move from the One Many opposition to gender opposition. This is treated very simplistically here. However, the gender construct, so present in all the sciences of antiquity, is more profound and will be explored in greater depth later.

The author claims that the four letter generic code can be more fundamentally expressed in the binary terms of gender. This section gets as far as the start codon which starts to take on a familiar geometric meaning known in physics; Our story is starting to get very intriguing … and daring.

Introducing Elementary Gender

Left side reasoning relies on a linear, sequential, punctual form of rationality. This has become the standard and universally accepted form of reasoning in science and mathematics. Nowadays, few professionally educated people would countenance the possibility of a science based on a completely different form of reasoning. Indeed, if such a science were to be proposed, the common belief is that it would be characterised by the epitaphs fuzzy, woolly, bleeding heart, mystical, irrational and New Age. The author does propose an alternative form of reasoning which is quite “orthogonal” to left side reasoning and he intends to rebuff any such characterisations. He claims that ultimately, at its core new the science will be more rigorous that left side science. This is because the science will not rely on the vagaries of measurement, only the reason applied to reason.

So far we have illustrated elementary forms of right side reasoning by getting acquainted with thinking in terms of oppositions rather than just labelling things and then manipulating the resulting symbols. It is now time to step the reasoning up a rung. So, right side reasoning deals in wholes. The left side deals in fine detail. Let us now look at the semiotic square more closely. Our simple way of understanding the square is in the form of the One Multiple oppositions as figure 3

The alternative to left side reasoning is naturally called right side reasoning and it is inferred that this is the dominant form of rationality of right hemisphere biological brain function. However, linking the alternative form of rationality to the biological brain may be considered as an ambit claim at this stage of development. The veracity of the argument does not rely on such an association. However, the argument would gain such potency if this were to turn out to be the case, and for reasons that will become apparent with time, we will assume that the ambit claim is valid anyway. If we have to stick our neck out, then we may as well do it courageously.

The author has argued that traditional left side rationality is based on only one fundamental opposition, that between abstraction and the real. This naturally culminates in the “view from nowhere,” God’s eye view form of objectivity popularly called the Scientific Method. The Scientific Method excludes one-half of reality, the subject side, and only considers the half world of objects.

Right side rationality goes the other way. Rather than excluding the subject, the subject must be present at all times. It keeps both subject and object present at all times. However, the subject of the Scientific Method is only the impersonal subject, the formalisation of the view from nowhere. In addition to embracing the impersonal subject as partnered with the impersonal ‘objective” object, the right side demands that the personal subject also be present. This means that, instead of just being based on just one opposition like left side science, right side science needs a second opposition. The second opposition is orthogonal to the first and is intuitively formalised in the form of the semiotic square discussed earlier. The result is fascinating.

The right side presents two kinds of subject, the personal and impersonal and defines the real as that which coincides with the personal and the impersonal, the conjuncture between the classical science “view from nowhere” of the impersonal subject and the “my view” of the personal subject. This gives one “real” slot and three “non-real” slots that we refer to as imaginary. The real can only be properly known via its three imaginary partners. The front right lobe of the resulting square provides the slot for the conscious subject entity and there are three imaginary entities. This is yet another version of Jung’s One-plus-Three structure that can be discernable in all the important theological configurations. We have also seen an instance of it in Freud’s version of the semiotic square for the human psyche. Many more versions will become apparent as our incredible story unfolds.
So far, our gentle introduction to right side science has been a very intuitive and qualitative affair. On the left side of the classroom, the student has already been introduced to some elementary symbolic logic. It’s time to catch up. On the right side we can teach about symbols too, different kinds of symbols of course, and we don’t need as many as those that travel in the left lane.

Elementary Gender and its Simple Compounds

Figure 7 Semiotic square with the four generic types of structure in terms of elementary compound gender, MF, FF, FM and MM.

It is now time for the first introduction to the most fundamental and profound concept of right side science. It is a binary construct called gender. Gender has two sides to it, a masculine and a feminine side. Here, we only consider gender from an elementary point of view. After all, the students on the left side have only started learning about elementary symbolic logic. Later we will work towards a more fundamental understanding and will call it ontological gender. However, for the moment we are only going to consider it from a rather Pythagorean point of view, the point of view of cardinality

Side Note:

s will be discussed later, the fundamental approach to gender starts with the notion of the totally unqualified, completely lacking in any specificity whatsoever. Such an entity is defined as being of feminine gender. The entity of pure feminine gender possesses the attribute of being totally devoid of determined specificity. This attribute must be an entity in its own right. It will be considered to be of masculine gender. Thus, two entities with only one attribute between them. The feminine has an attribute. The masculine is that attribute. This is a very profound concept and takes some time to get one’s head around. It is for this reason we make the simplification of assimilating the gender dichotomy to the easily understood, simplistic One Many opposition. Unspecific cardinality is not an attribute, whilst the cardinality One is. The Many has the attribute of oneness, the One is that attribute. The feminine has, the masculine is.

Gender comes into play in the relationship between what can be considered a singularity and hence have cardinality One, and that which is not a singularity and hence has cardinality Many. The first kind of entity will be considered to be of masculine gender, the second of feminine gender. In introducing the cardinality interpretation, it must be stressed that we are not talking about absolute quantification. The cardinalities are relative. An entity is One, and hence masculine, relative to something which is not One and hence the feminine Many. A crude example would be a container and its content. The container would be One and hence masculine, relative to the Many contained by it, which would be feminine. However, relative to something else, the masculine container entity may be part of an ensemble, which would be feminine.

From now on, rather than talk about the One and the Many, we will talk about the masculine and the feminine. An entity that is of masculine gender will be labelled M and the feminine labelled F. A more correct statement would be to say that the entity of masculine gender can be used as the masculine label and the entity of feminine gender can be used as the feminine label. In this game labels are not only made of the same stuff they label, but they are what they label. I am my name. My name is I. We will not labour over this point, but it should be kept in mind that there is no arbitrary relationship between the signified and the signifier in this domain. Such arbitrariness is only permitted in the sciences of the left side.The interesting thing about right side science is that that’s it. Two symbols is all that you require to construct a code capable of describing and specifying any entity whatsoever in a rational universe. More complicated things than the elementary One and Many can be described by concatenations of M and F letters.

The first compound entities are made up of binary combinations of M and F. There are of course four of them and lead to the semiotic square shown in Figure 7.

The Four Letters of the Generic Code

Figure 7 shows the four possible generic structures that are necessary to describe and/or construct a coherently rational reality. Figure 8 provides a more iconic representation of the same thing. Like all of right side science, the idea is simple, simplifying but subtly profound.

When Figure 7 is looked at from a left side viewpoint, it leads to simplistic and misleading interpretations. A predicable response of left side reasoning would be to interpret the structures from a reductionist perspective as being atomic building block of nature.

Right side science must take the other interpretation and advocate a monism instead of the atomistic outlook. The monist interpretation is shown in Figure 8. Once again, we have a semiotic square representing a whole. It represents any whole. The whole can understood from a general, a particular, and a universal viewpoint. We have already investigated some examples. The overall entity is the singular self the only “real» entity. It can be understood in terms of its three “imaginary” qualifications, the general, particular and universal qualifications. These qualifications are not absolute but determined relative to each other.The Figure 9 also indicates an embryonic algebra. At the finest level, the qualifications are all in terms of gender, a relative typing system. The general corresponds to MF, the particular to FF, the universal to FM and the singular to MM. There is no need for external, traditional style empirical attributes.

The author has introduced a shorthand terminology where the four binary compound gender terms have been replaced by four single letters. It is at this point that it might appear that the author has lost his mind. Rather than invent his own lettering scheme, he has borrowed that of another general, universal, particular algebraic four-letter scheme for describing and organising singular entities. The four letters, of course, are A, U, G, and C used to denote the four bases of the genetic code. At this point, the reader can merely assume that any structural resemblances with the genetic code would be shear co-incidence.
Figure 8 Iconic representation of the four bases and compound binary gender.

The Start Codon

Left side science and left side thinking has obvious and well-known proven strengths. One role of this book is to point out some of its terrible failings and how a radically alternative right side science can remedy the situation. However, right side thinking also has its peculiar traits and limitations. Some have said that to work in this domain of Kant and Hegel, the first thing to go out the window is common sense. It certainly takes some getting used to. However, one of the uncanny aspects that are particularly hard to accommodate is the absence of scale. Even in our little examples with the semiotic square has brought this absence of scale to the fore. One minute we are looking at a semiotic square of how to get rich, and then it’s looking at the Cosmos as a whole, followed by the Freudian Psych and Parliamentary Democracy in the one breath. It seemed that we didn’t even have to change tablecloth. It was all done with the one semiotic square.

The semiotic square representing the whole provided a common rational ground, a common launching pad for the analysis. The structure of the common launching pad can be sketched out as shown in the semiotic square shown below. The square represents a generic whole and illustrates that any whole can simultaneously be looked at from a general, a particular, a universal and a singular viewpoint. The square does not represent a spectacle. That would be a left side way of interpreting the representation, the spectacle without spectator, the object without subject. Right side reasoning demands that the subject is always present
Relative to the one spectator, there is only one spectacle. In the One-plus-Three structure, the spectator, the subject is the One. The One is the real part. The “three” is composed of the three relative attributes. That forms the imaginary part, the subjective part. Time and time again, example after practical example yields the same result. Three attributes labelled A, U, G form the ground attributes for the whole. This applies to religions like the Christian Trinity as Carl Jung consistently observed – AUG, the general, particular and universal aspects of the whole. It applies to Freud’s Ego, Id and Super Ego triad making up the human Self. Readers can construct their own versions of this semiotic launching pad for analysing their favourite wholes. Each time the iniquitous three modes A, U, G keeps raising its head.

Here, we have the embryonic beginnings of a code, a code for coding anything whatsoever, as long as it forms a holistic aspect of a holistic rational system.Finally, we turn for Nature’s code for any singular animate subject, the generic code. In genetics, the three bases AUG form the start codon that, on amessenger RNA molecule, marks where protein synthesis begins. In positions other than at the start, the AUG codon codes an amino acid just like other codons. AUG in this case will code methionine, but the biochemistry is not of central interest as it is purely the implementation technology and does little to explain genetic code semantics. Only semiotic structure can do that.

A central plank of right side science is that it is not limited to scale, it is also unlimited by application domain. Generic structure is generic structure no matter what the problem domain and what the implementation substrate… The illustrative semiotic analysis cases considered so far do not prove this assertion. The rationalisation comes from overall systemic coherency of reality in its ensemble, something that we have barely touched on so far.

In order to get some kind of handle of the role of AUG as the start codon in the generic code, we should try to look at other problem domains. Anyone with some background in physics would find that the semiotic diagram in Figure 7 looks a bit familiar. The cone of arrows for MF is evocative. Could this be interpreted as a cone of time-like arrows used in the customary explanation of relativistic space-time? In addition, the arrows in the FM cone, are they space-like lines? In addition, what about the bundle of parallel lines? Are these optical lines? Maybe such an interpretation may lead to a deeper understanding of something here.

The author has been privately carrying out semiotic analysis exercises over the past twenty years or more, both in his profession and in philosophical and linguistic interests. He has carried over a thousand such analyses. His basic conclusion is that there is a common language that is generic spanning across the board of the semiotic right side world of reasoning. Later, we will come back to the cones and lines illustrated in Figure 7 and add some life into them.

Figure 10 One interpretation of the semiotic square is that of four generic types, the general, particular, universal and singular.. The types can be designated by four letters. The four letter A,U,G, and C habe been chosen as shorthand for Mf, FF, FM and MM respectively.

Key Phrases: semiotics of gender, ontological gender, gender and sex, Semiotic square, genetic code, generic code, DNA, start codon, left right hemispheres, the divided brain, epistemology, anti-mathematics, masculine, feminine, gender differentiation, Generic Science, Semiotic structure
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Parmenides, Ontology and the Stoics

There are two takes on reality, two kinds of knowledge, two kinds of science. In this work the traditional sciences, traditional knowledge we call left side. This kind of knowledge relies on a priori knowledge. Right side knowledge is unconditioned by any a priori and must be developed using pure reason alone. The two kinds of knowledge sit on opposite sides of a great divide. A deep understanding requires a deep understanding of this great divide. The ancients had their say on the matter. Consider, for example Parmenides who came after Heraclitus but before Empedocles.

Parmenides

Parmenides was one of the first to put forward a clear view of the structure of reality from a reasoned perspective. The philosophy of Being, ontology, starts with him. His poem, On Nature, recounts the epic voyage of the young man on his quest for knowledge.

The tone is dramatic and urgent. Despite only disparate fragments of the text remaining, one can almost hear the pounding hooves and see the sparks flying as the wise chariot steeds gallop at a furious pace through the black darkness on the renowned way of the Goddess. Streaking towards where Dark meets Day, maidens show the way. There is no room for dilly-dallying here. This is not the time for fine-spun arguments. It is time to confront the truth. The goddess, with her own hands unerringly conducts this man who knows through things. Wheels swirling, the chariot axle glows red in the socket and gives forth the sound of a pipe as they approach the gates. The daughters of the Sun hasting to convey him to the light, take back their veils. Having arrived at the gates of the ways of Night and Day, after much persuasion they pass through the gates. The young man is greeted kindly by the goddess. She welcomes him to her abode, far from the beaten tracks of mortal men.

She invites him to have an open and critical mind, to learn all things, but above all the unshaken heart of persuasive truth. There are two takes on reality. On the one side there is that taken by mortal men as they blindly stumble about in a world of opinions. On the other hand, away from the world of fickle beliefs, there is another world that harbours unshakable truth, a world where reason holds sway. At the epicentre of this world of reason is the simple truth that there are two possibilities. The goddess declares:

“The first, namely, that It is, and that it is impossible for anything not to be. This is the way of conviction.”

She then recounts the other possibility:

“The other, namely, that It is not, and that something must needs not be.” She then explains, “That, I tell thee, is a wholly untrustworthy path. For you cannot know what is not – that is impossible – nor utter it.”

The Parmenidean Paradigm

An epic journey is always a good ploy to get the reader into the right frame of mind. Excuse the pun. Parmenides’ allegory like any allegory can be read in many ways. One could see the tale as taking place on two levels, a logical foreground a gender background. The background imagery displays the feminine in all its plurality, culminating in the abode of the goddess. There the ethereal feminine welcomes the singular masculine, he who knows through things. However, he is but a youth still in quest of knowledge. Nevertheless, he knows he has been conducted here for a purpose.

Across the unsaid background tapestry, spreads the ephemeral abode of goddess and teaming maidens. It is far from the world of mortals and untainted by their bumbling subjectivity. This is the pure feminine, so pure that it is totally devoid of attribute. It is completely unknowable. She is not even real. The goddess, the feminine incarnate, explains that “you cannot know what is not.” You can only know what is. It looks as if the goddess has negated herself out of existence.

This is Ground Zero of rationality. Many thinkers have come here over the ages, each making their own interpretation. Parmenides paints his picture in great clarity. On one side, we have the land of mortals enmeshed in opinions. On the other side is the immortal land of Truth. This other side is what we have been referring to as the right side take on reality. It is in this domain that Parmenides must construct his version of monism philosophy. He must explain Oneness. Like all who have toiled in this domain, he must tackle the dialectic of the One and its other. His reasoning is stark, even brutal: The One is, the Other is not.

As we have seen in previous sections, right side reasoning is expressed in oppositions and oppositions applied to oppositions, a dialectical, semiotic form of thinking. Left side reasoning starts from given preconditions such as opinions, traditions, rumours, gossip, innuendos, measurements, experiences, sensations, axioms, stabs in the dark, fabulation, and sometimes wicked self-serving deception, just as the good goddess explained: This is the natural lot of mortals. Right side reasoning has no preconditions. It must start from the primary opposition. It is here that we find the primordial form of Ground Zero. The task for the philosopher, the ontological scientist, is to provide an explanation of Ground Zero in terms of the primary opposition. The understanding of this primary opposition varies, depending on the thinker. In the case of Parmenides, his position can be summarised as follows.

  • What is the primal entity?
    Answer: It.
  • What is its specificity?
    Answer: It is.
  • What is the primary opposition?
    Answer: The opposition between what is and what is not.
  • What exists?
    Answer: Only what is exists, what is not does not and cannot exist.
    Comment: What is determines the knowable. Even more strongly, it determines the known. The deep essence of It is known. It is, end of story. What is not determines the inherently unknowable. The totally unknowable is tantamount to not existing.
  • Where is the origin of the primal entity located, i.e., where is Ground Zero?
    Answer: In the eternal present.

The above five points do not cover the complete ontological paradigm of Parmenides. Like any ontologist worth his salt, Parmenides must provide the enveloping rationale for why the above points are necessary.

David Furley has honed in on a passage from the narration that attempts to explain the noyau of the argument, the raison d’être of It:

The last section of the Way of Truth is particularly difficult. Parmenides repeats his assertion that there is no not-being and there are no different degrees of being; what exists is equal to itself everywhere and reaches its limits everywhere. From this he concludes that it is “perfect from every angle, equally matched from the middle in every way, like the mass of a well-rounded ball” (Furley)

We see here Parmenides’ attempt to explain First Classness, the central, all enveloping characteristic of rational reality. A world satisfying First Classness must be totally unconstrained in every way, the ultimate in perfection. It is here that resides the great challenge to ontology. This is the task confronting us. We have to understand such a world that is totally unconstrained with no one behind the scenes pulling strings, and no king pin calling the tune wether seated on high, low, in the middle, in or out of reality.

If there were to be hidden forces at work behind the scene, then a fundamental science of reality would be impossible. On the other hand however, if reality is left free to be dominated by the draconian requirement of the totally unconstrained system, then indeed it must be exactly that, a totally unconstrained system (the only constraint allowed) The iron laws of First Classness(FC) spring in to play, the laws of ontological fair play organise fair play. In this great riddle, there is only one answer and, as the goddess said, only one “unshaken heart of persuasive truth.”

Reconciling the coming into being, the genesis of reality, with FC is not easy. The very notion of a determined beginning violates FC as this privileges the starting point entity from all others. FC does not allow privileged entities and there is nothing more privileged than coming first. Parmenides resolved that violation by saying that an entity at the beginning does not exist, as it no longer is. He then argued that it never could have existed, finally ending up with the formula of the only thing real is the eternal present and nothing changes.

It is interesting to look at how the Stoics resolved the problem, as they too adopted a doctrine based on FC. For the Stoics, the only immortal was Zeus. They were pantheists so the universe was the body of Zeus. The body changes, is born and dies away in the conflagration but Zeus stays immortal throughout the process. The universe had a beginning and eventually ended up in the conflagration. In this more complex scenario, avoiding the violation of FC becomes more difficult. The beginning and the end of the Cosmos in the conflagration become privileged moments, one preceding all that will exists and one succeeding, thus violating FC. The Stoic solution was that time was circular with the whole story exactly repeating itself the next time around. In this way there are no privileged points in time and FC is not violated. This Eternal Return solution retained many aspects of the Parmenidean solution. Bodies in the past did not exist, nor did those in the future. The only bodies that exist are those in the present. By eternal repetition of the cycle, nothing really changed and no state of being was irreconcilably privileged over any other. FC was respected.

Parmenides’ allegory of the young man streaking across the heavens waved on by the veiled daughters of the Night, heading straight for the abode of the goddess evokes the image of a spermatozoid streaking to a rendezvous with the unfertilised egg. However Parmenides’ does not allow the union to be consummated.

There will be no masculine principle uniting with the feminine principle in this scenario, despite the atmospherics being full of it. The closest we get to any explicit such union is at the level of logic: one proposition in the affirmative and the other in the negative and never the two shall meets. Parmenides pitched his paradigm at the loftiest level and really could not embrace any explicit masculine feminine union as this would imply an explicit beginning and so violate FC. For a work around for this conundrum, we have to wait for Empedocles.

In the meantime we understand that there are two ways of understanding reality, one is the Way of Truth and the other is the Way of Opinion. For Parmenides, the only repository of truth was in the One, a pureness of eternal, ungenerated Oneness. It is that unique Being that “neither was nor will be, because it is in its wholeness now, and only now.” In truth only the One is.

For Parmenides “The only true reality is Eōn—pure, eternal, immutable, and indestructible Being, without any other qualification. Its characterizations can be only negative, expressions of exclusions, with no pretence of attributing some special quality to the reality of which one speaks” (Calogero, 2010) As for the Way of Opinion, this is the world of appearances, a misleading world of falsehood. It is this Being and only this Being that truly, objectively is. All else is illusory.

Parmenides provided a vivid image of how the very deepest reality could be comprehended. This image in useful to carry forward in one’s mind in the development to follow.

Ontological Calculus of Empedocles to the Stoics

This is not a scholarly work. In writing about Empedocles and the Stoics, for example, we imply that this is the way they thought and expressed their ideas. Clearly this is not the case. Rather than being scholarly, our approach is to fundamentally reverse engineer ancient thinkers’ concepts. As a consequence what we write is often more of what the ancients could have thought, and sometimes what they should have thought, if they remained true to their doctrines.

Keeping this in mind, we will now repeat the summary of Parmenides doctrine and adapt it to the next phase in the development of ancient physics. In order to develop the theory of the Four Elements, the initial structure of Parmenides must be pushed to the next stage. What follows is a brief summary of this next step, as seen from a modern perspective. The key idea is what we call ontological gender. It is this structure that explains how the fundamental starting point for our unifying science. The ancients got there first, but there is some cleaning up to do.

We have already considered these concepts in earlier sections, but here is yet another angle.

The Gender Paradigm

  • What is the primal entity?
    Answer: Any entity whatsoever.
  • What is its specificity?
    Answer: Entity has the attribute of absolute non-specificity.
    Comment: This attribute, that of absolute non-specificity, is an entity in its own right, in accordance with First Classness.
  • What is the primary opposition?
    Answer: The opposition between what has the attribute and what is the attribute.
    Comment: The entity that has the attribute determines feminine gender, the entity that is the attribute determines masculine gender. This is the definition of ontological gender. These two entities are different by gender but indistinguishable.
  • What exists?
    Answer: Only what is exists.
    Comment: This follows Parmenides but adds some detail: Only what It, that entity of pure masculine gender, fundamentally exists. The pure feminine entity has something (the attribute of total non-specificity) but when it comes to whether it is, clearly it is not. Having something differs from being something. However, the pure feminine entity, although different, is indistinguishable from the pure masculine. Parmenides glossed over that point.
  • Where is the origin of the primal entity located, i.e., where is Ground Zero?
    Answer: The location is that determined by the primal entity.
    Comment: The whole Cosmos gyrates around this location. Thus, Ground Zero can be thought of as any location whatsoever.

This summary has added in some innovations that don’r belong to the ancients. However, it is in keeping with a strictly generic approach that the Stoics were pioneering.. The summary represents where they were heading more than where they were at.

Traditional sciences, what we call left side sciences, express all knowledge in terms of attributes of things. This is quite reasonable because it is impossible to directly know the thing that has the attribute. The knowledge of things is always indirectly achieved via attributes of things. Note also that in pure left side science, an attribute is not a proper thing as it is in pure right side science.

In our work we are endeavouring to develop the right side science that does not rely on any preconditions whatsoever. Harvesting attributes as a precondition for theorising is a fundamental left science activity, but not so for right side science. Thus, all the empirical attributes that abound in left side sciences are forbidden on the right side. If right side science is to have any attributes then it has to reason them into existence, not measure them. This reasoning process leads to the attribute par excellence, that of masculine gender.

Then comes the incredible aspect of right side science. This is the only attribute we need! All other attributes can be constructed from it or with it. We enter into the web of gender intrigue. The only guiding principle at our disposal is that of FC. FC demands that an attribute must be capable of being considered as an entity in its own right: In this context it becomes the masculine qua feminine MF. What is good for the gander is also good for the goose. The feminine entity must also enjoy the possibility of being considered as an attribute in its own right: It becomes the feminine qua masculine FM. Here we are starting to get compound gendered entities, depending on roleplaying. The other two combinations are the pure gendered entities qua themselves, notably the masculine qua masculine MM and the feminine qua feminine FF.

In the process we have advanced from the primordial Parmenides paradigm through to the Doctrine of the Four Roots of Empedocles and later developed into the four-element doctrine of the Stoics.

There are four elements that have mixed gender MF, FF, FM, and MM entities, corresponding respectively to expansive air, water, converging water and fire.

These binary terms can be thought of as noun adjective pairs where F and M can play the role of noun or adjective, depending on their position in the pair. These terms are the elementary terms of the generic code. The genetic code is the biological instance of the generic code where the four letters, using RNA notation, are A, U, G and C respectively.

As a side note, it is interesting to look for traces of generic structure in natural languages. English, because of its huge vocabulary and penchant for labelling things does not offer fertile ground. However, French is a good place to look as it retains a strong version of gender typing. In fact it is rather pure in this regard as it even allocates gender to the names of countries. Ignoring gender constructs though and just considers the noun adjective example:

   une histoire vraie

which means a true story. Reversing the noun adjective order gives

   une vraie histoire

which means a made up story, providing a certain kind of negation of the first construct.

In the generic code, reversing MF to give FM produces an even more dramatic kind of negation, as will be seen. MF and FM, or air and water in the old book, are really like chalk and cheese.

D. J. H. Moore

[continue reading…]

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