The Stoic Five Undemonstratables
There are two kinds of logic, logic with infrastructure and logic that can be carried out with the bare brain, the terra nullus logic. We first consider the bare brained version. This variety of logic is virtually infrastructure free. The logic is abstract and makes extensive use of symbols that do not mean anything. It is often referred to as symbolic logic. At the base of symbolic logic is the propositional calculus and its second order extension, the predicate calculus. The other kind of reasoning requiring infrastructure will be a terra plenus logic. In accordance with our two-hemisphere brain metaphor we refer to terra nullus logic as left side logic and terra plenus Stoic style logic as right side.
What is interesting about the Stoic logic developed by Chrysippus is that it can be interpreted as a left side symbolic logic as well as a right side logic, all decked out with dialectical infrastructure. Thus, Chrysippus’ logic has both a terra nullus as well as a terra plenus interpretation.
The kernel of the logic is articulated in the form of the “five undemonstratables”. The undemonstratables can be stated as five three step syllogisms as follows (Chénique, 1974):
If one has the first quality one has the second
one has the first
thus, one has the second
2 Contraposition of the conditional
If one has the first quality one has the second
one has not the second
thus, one has not the first
One has not at the same time both the first and the second quality
one has the first
thus, one has not the second
4. ‘OR exclusive’ or alternative
One has either the first quality or the second quality
One has the first
hence, one has not the second
5. ‘OR non-exclusive’ or disjunction
One has either the first quality or the second quality
one has not the second
Hence, one has the first
All of these syllogisms can be interpreted from the symbolic logic perspective of propositional calculus. As such, it can be said that Chrysippus was the first to discover the propositional calculus. In addition, the first and second syllogisms can be interpreted as definitions of modus ponens and modus tollens respectively. This is all familiar ground for traditional logic.
The third syllogism deals with the incompatibly paradigm. In the propositional calculus context, this corresponds to the Sheffer stroke. In this context, the syllogism loses its explicit temporal nature and flattens down to the simple formula:
NOT (a AND b) is true
Note that the “at the same time” part of the formula has been dropped. Traditional modern logic has no notion of time. To entertain a notion of time, one needs a brain. The brain of the logician does not count, because that is not a formal part of the logic. Modern logic has no such infrastructure. It has virtually no infrastructure at all. Brainless, this is truly the logic of the terra nullus.
Building the Logical Brain
Logic combined with integrated cognitive structure goes from being logical to being ontological. In other words, it starts to become a science of being. Integral to a science of being is the science of the generic subject. The formal presence of the generic subject in the science provides a fundamental point of reference. All propositions become relative, relative to the subject. As we have said before, the subject, any subject, is the centre of the Cosmos. This means that you are located at the centre of the universe. Since you could be anybody located anyewhere, the centre of the can be literaly anywhaere. This identity of the generic centre of the universe and the individual centre of the universe is a most important principle. (In my book to appear, I show that any spatial reality with this property is equivalent to the Special Theory of Relativity. It is not verycomplicated)
As we have seen, the generic subject is endowed with a particular brain architecture. First, the impersonal, undetermined subject is based on a left-right dichotomy, with the subject on one side and its kingdom of objects on the other. The usual polarity convention is right and left sides respectively, but this does not have to be the case.
The above paragraph has a certain apparently outrageous dimension. It is probably enough to make some readers choke on their crumpet. However, it just takes time to become comfortable with the generic viewpoint. The situation can get untenable when we move on to the next paragraph. Written in italics in an effort to ease the reader’s pain, it reads something like this:
The brain architecture of the personal subject, in addition to the left right dichotomy of the impersonal, has a front back determination with the polarity, subject in front and kingdom in the back. These left right, and front back determinations can be explained in terms of gender, where the singular Oneness of the subject corresponds with the masculine and the non-singular wild card Otherness corresponds to the feminine. The configuration at this stage is that of a square divided into four quarters. Reading from left to right, starting from the front, the quarters are gender typed MF, MM, FF and FM respectively. Any subject whatsoever will have this configuration.
Perhaps one redeeming point is that we are not the only ones to have ever argued along these lines. Apparently, the ancients, going back thousands of years, have passed by here many times before. One thing to keep in mind is that we have not yet distinguished between the form of the world and the cognitive structure needed to comprehend it. Our basic thesis on this matter is that:
- The form of the world and the cognitive structure are different,
- The form of the world and the cognitive structure are indistinguishable.
This constitutes the basis of generic science and is why it is only necessary to study cognitive structures. Just put yourself into the position of that electron over there, the one that’s peering at you. It is a subject just like you. It might surprise you to know that, in this context, it has a cognitive structure indistinguishable from yours.
In the final analysis, the two points above apply perfectly to the two basic building blocks of generic science. These were the pure feminine entity and the pure masculine entity. They are both different whilst being indistinguishable. The masculine, in this sense, is the ultimate embryonic cognitive structure; the feminine corresponds to the ultimate embryonic world.
Bridging Laws of Consciousness
David Chalmers characterised what he called the Hard Problem (Chalmers, 1995) as the problem of explaining the relationship between a physical account of reality and conscious experience. As he saw it, solving this Hard Problem required determining the “bridging laws” that related physical reality and conscious experience.
The “bridging laws” solution to the consciousness question is a natural response of traditional left side scientific thinking. Such thinking is naturally dualistic where dichotomies abound between Mind and Body, the abstract and the real, and in this case, between the realms of the physical and the conscious. The solution to the problem seems like after the fall: How do you put Humpty Dumpty back together again? How do you bridge the broken? Chalmers is looking for an abstract solution to a problem that is a direct consequence of abstract thinking itself. Explaining abstractly how to bridge the abstract with the real is definitely a very Hard Problem, reserved only for the most courageous of abstract thinkers. For the less courageous, an alternative approach is to avoid abstraction and think generically.
From the monist right side viewpoint of the generic, there is never any need for a bridge as nothing was ever broken apart in the first case. At the ontological foundations of the generic, the very first spark of consciousness stirs with the pure unqualified feminine that has the pure attribute of Oneness. The masculine entity is this attribute. The embryonic physical unites with embryonic consciousness: One has an attribute; the other is this attribute. The bridging here is more like how some of the Hindus describe it, as a coital embrace. This couple have no need for a prosthesis, bridging or otherwise.
According to our embryonic Generic Science based on the generic algebra of gender, any being is coded and organised through this generic code. In the case of the biological, the generic code becomes the genetic code. The four-letter code is really based on binary valued gender. Any life form is coded in this gender algebra and organised through it. The original gender construct of the masculine and feminine now becomes a massive complex entwinement of gendered entities. The overall coherence and survival of the organism absolutely depends on maintenance of the coherence of the gender typing that runs throughout every nook and cranny of the organism. If there is failure of coherence then no bridging Band-Aid will ever bring this organism back into consciousness. The organism would be well and truly dead by now.
When viewing the healthy gender typed organism from the perspective of a third party, everything appears to be in ambiguous and chaotic superposition. Gender states are dynamic and something like quantum states, except that they are relative to each other and the organism, not absolute. Unlike quantum states, the subject sees its states quite differently from any third party. Viewed from the perspective of the organism, these states are in coherence with its own being and articulate its being. There must be no ambiguity whatsoever in gender typing.
We propose that the formal mechanism of gender regulation can be articulated in the form of Chrysippus’ third undemonstratable, that of incompatibility.The premise of the syllogism states:
One has not at the same time both the first and the second quality.
In the context of the generic coded organism, this becomes
One has not at the same time both the masculine and the feminine gender.
It is by the implementation and maintenance of this principle that any living being maintains its Self. This solution demands a dynamically gendered system with a global mechanism for the maintenance of gender coherence.
For a cosmological system, the mechanism is that of pure rational coherence, including the non-violation of the causality principle. As a science, it will present as a much more generic version of present day relativity theories. The geometric aspect of the mathematics (or anti-mathematics) will however need a substantial overhaul. In fact, a new geometry is needed. It will be a more generic version of what is now called geometric algebra.
In biological systems, the genetic code, although material, is a different substance from the proteins it codes. In the realm of pure physics, the code and the substance entities are possibly the one and the same. However, the same generic principle is at work in any realm.
Chrysippus and The Square of Oppositions
Chrysippus’ remarkable logical system can be naively interpreted as a simple left side version of the propositional calculus. There the incompatibility paradigm can play a pivotal role as the key operator from which all other logical constructs can be constructed.
The incompatibility paradigm, as Clark Kent, steps into the phone box and remerges as a virtual superman, ready to bring order and life into a chaotic world. Dumb left side logic transforms into the right side logic of the generic.
Having situated one of Chrysippus’ five paradigms into the generic scheme of things, we now have four left. There is no mystery where these fit in. The diagram below shows how they fit together to form a new kind of square of oppositions. Moreover, each of the four undemonstratables fits in snugly with our gender typing. This naturally leads to associating each of the four syllogisms with the corresponding four letters of the generic-cum-genetic code based on the AUGC alphabet. This is quite important, as the four letters now take on more semantic baggage than that of being a mere transcription language.
It is not clear how much of this was known to Chrysippus. Nevertheless, he does follow in the footsteps of Aristotle and his Organon. Here we have our version of Chrysippus’ Logos, the forerunner to the semantic cracking of the genetic code.
Figure 30 Author’s Reconstitution of Chrysippus’ Square of Oppositions.
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 whatsoever that takes the pain to reflect on its particular spot in the universe. Without fail, this subject, like any other subject, sees itself as being located at the aforesaid 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, a right side, 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 organisation of knowledge, for example.. The same semiotic structure might be taken as a good framework for brain architecture, but we will avoid that topic here. There are also ontological, and of course many biological interpretations. On the biological front, this structure can be thought of as the structure of a whole, as coded by a chromosomal codon. Any biological organism is organised 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 interpretation of this highly generic semiotic square is that it offers a schematic for elementary cognitive structure.
So prodigiously generic is a structure that it can make the head spin. To top it off, we now have Chrysippus joining the fray. Now Chrysippus was conceded by the ancients to be the equal of Aristotle, so he cannot be dismissed as a lightweight. In above, we have organised four of his five fundamental syllogisms into a form that 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 that resembles the Square of Oppositions of Aristotle. The Scholastics added the AEOI four lettered labelling to Aristotle’s system and spent over a millennium probing into its delights. Not to be outdone, we have added our lettering to our reconstructed version of the Chrysippus Square in the hope of preparing it for its reinvigorated role in the present millennium. 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 his allocation of the CAUG lettering is 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 successful 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 logic marked the first tentative steps towards the formalisation of a unifying science. The full significance of Chrysippus’ 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 pioneered by the Stoics, will provide such a unification.
Of critical importance is to learn how to reason in a different way from what 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 putting. After all, probably more people have been burned at the stake because of an allegedly 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 synonymous 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 condemned to the judgment that it might be false. Even worse, at the same time the proposition must accommodate the stark reality that this judgment might indeed be true. Then again, it might not. Modern scientists are a brave lot.
Popper did eventually nuance his views on this matter in the light of the self-justifying biological organism notion. In so doing he implicitly admits that the biological organism is obsessed with self-justifying its continual existence in the world. As such, biological organisms 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. 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 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 reasoning becomes a relativistic 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 minimally 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 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 quadruple structure is highly lacking in determination. The edifice is so undetermined that it is not even clear whether it corresponds to the semiotic structure of knowledge of the world, or the structure of the world itself. Is this epistemology or is it physics? Is this the structure of Mind or is it the structure of Body? Is it the 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 relationship 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 separated from the cart, but treated as an organic whole. One cannot have one without the other. We came across the very essence of the monist solution in the form of the gender construct. Rather than plucking attributes from a predefined definitional framework or harvested from empirical measurements, 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 attributes. 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 structures 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 bodiless 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 separation is impossible for an organism constructed from the gender construct. The organism is constructed according to a four-lettered code. According to our 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 assemblage of hydrocarbon-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 organism that ensures systemic coherence. It is in this way that the One can be constructed from the inseparable and indistinguishable Two.
The Stoics saw this dynamic systemic organisation 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 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 synonymous with it maintaining Oneness. The mechanism for achieving and maintaining Oneness is through the establishment and maintenance of gender typing. The organism 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. In addition, the determinations are purely relative. They are purely subject-ive. This, one must admit, is truly 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 fundamental relativistic principle at play. In the traditional sciences of our day, the only relativistic principle known is in physics. There is no known equivalent in biology. In physics, we see relativity 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 relativity is intimately bound up with the non-violation of the causality principle. It is here that one can grasp the simplicity and elegance 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 we call generic relativity.
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 elegant formulation concerning the essence of generic relativity, the cornerstone of the generic science we are trying to develop. Fortunately, we do not have to look very far. The principle is located at Ground Zero and there is no one 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, a form expressed by the semiotic square. Chrysippus provided the logical framework of the Logos semiotic square in the form of four of his five undemonstratables. We have resurrected this structure as an alternative to Aristotle’s Square of Oppositions, discussed previously. We have named this the Chrysippus’ Square of Oppositions. The fit between this structure and the four undemonstratables is comfortable and reasonably self-evident. The structure effectively provides an additional logical impetus to the thrust of our argument. The four undemonstratables provide a logical dimension to the interpretation of the four-element theory and the corresponding four letters.
Five undemonstratables minus four leaves one. The missing syllogism is the third undemonstrable, the incompatibility syllogism: One cannot have one quality and the other at the same time. We now come to the fundamental tenet of generic science. It is founded on the premise that there is nothing 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 the 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 that the genetic code is more than a mere transcription language. One should keep in mind that curiously, and apparently accidently, the code 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. The gamble of Nature seemed to have hit the jackpot 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 dialectics 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 generic code. Moreover, in multi-celled 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 itself. 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.
Moreover, the basic health of the organism will be placed in peril if this typing mechanism starts breaking down. The cohesion 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 pneuma is constantly attracting and repelling, constantly maintaining the equilibrium of the organism.
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 paramount. 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 guarantees 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 synonymous 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 single 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 the bases either AAU or AUC. In gender terms, this translates to the gender typing MFMFFF or MFMFMM. According to the gender coherence principle, such an entity 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 relativistic and dynamic and in coherence with the organism so typed.
Note that the so-called superposition of states addressed by quantum mechanics disappears if they are considered to be more like relativistic gender states. Any observer that deterministically tries to 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 still an organism based on the same generic organisational principles.
In an appendix attached to this work, elementary particle physics will be interpreted from a generic point of view. This leads to elementary entities like quarks and leptons being gender typed in terms of codons reminiscent of biology. In this way, any being in nature codes itself in terms of the generic code based on gender typing. This includes the cosmos itself, as a dynamic self-organising being.
In traditional relativity theory, one can discern an elementary organisational coherence that can be stated in a form comparable 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 antecedent 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 Einstein’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. Einstein’s relativity demands coherence across time: causes must precede effects in time. In other words, Einstein’s relativity is diachronic in nature. In contrast, the generic version of relativity demands coherence at the same time. In other 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 an abstraction, which is necessarily 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. The science also enjoys a natural tendency towards monism in the sense that the theory of code can be expressed in code.
Generic science is a discipline, 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 feasibility 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 Neumann computer.
Before Von Neumann, there already existed programmable calculating devices. However, they all had one thing in common. They were based on an absolute dichotomy between data and program. For example, the program might 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 confusion 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. First Classness 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 Neumann started the process of moving the calculating machine 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 Neumann 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 Neumann decided to invoke his version of Chrysippus’ incompatibility 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 Neumann’s computer was an exercise of eliminating violations in First Classness; in this case, eliminating the fixed dichotomy between data and program. Henceforth, the distinction became relative to the dynamically changing Program Counter. What was program and what was data depended on context.
However, such a device is far from freeing itself from violation of First Classness. The Program Counter itself becomes a rigid privileged memory location, totally estranged from the run of the mill information 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 Neumann computer needed a few further innovations in order to become operational. However, not many other innovations were needed. Add a stack, interrupts, and a few input/output ports and that is about it.
The Semiotic Logic of Chrysippus
Before reaching an understanding of our reconstruction of the Chrysippus semiotic square, we need to know a bit about semiotics, or at least, our version of it. We provide here a summary of our approach.
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 cannot 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 did not make much headway. He also despised the Stoics, which did not 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. The mysterious other is the 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 is getting a bit steamy, so here is one way to arrive at a dispassionate view. It involves the gender construct.
Figure 31 The generic semiotic square is constructed from the feminine masculine opposition applied to itself.
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, in both 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 are 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.
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 corresponds to MF, FF, FM and MM. The ancients called them air, earth, water and fire respectively.
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”.
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 have taken them from the RNA version of the genetic code. The genetic code is a standard code that codes all living beings, without exception. This is an established 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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