The Chrysippus Semiotic Square of Oppositions

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.

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.