Kant’s Semiotic Square

An easy way to construct a semiotic square is with two dichotomies. The hard part is choosing the pertinent fundamental dichotomies. We adapt the convention that the first and primary dichotomy provides the left side, right side dichotomy of the square. The secondary dichotomy provides what we will call the front side, back side of the square. Drawn on a piece of paper the secondary dichotomy will correspond to the two halves defined by a horizontal dividing line of the square.
In previous sections we developed a fundamental semiotic square based on the oppositions between the One and the Multiple. This opposition was applied twice, once as a left right side dichotomy and once for the other axis. In the first case the One involves the impersonal One. The second case involves the personal One. This was repeated in another interpretation as the opposition between subject and object. The first opposition involved the impersonal subject and the objects that it subjectifies. The second opposition involved the personal subject and its corresponding kingdom.
It was argued that the most fundamental of these kinds of dichotomies was based on gender where the masculine expressed the attribute of pure singularity free of any other particularity. The masculine was an entity in its own right. The only particularity possessed by the feminine was that it had this attribute. In other words, the primary opposition was between two entities of different gender. The only specificity of the feminine entity is that it has an attribute. The specificity of the masculine entity was that it is this attribute: One has it, one is it. The first gender opposition is between the impersonal feminine and masculine, the left right dichotomy. The second gender opposition has the personal feminine and masculine for its two poles, the front back dichotomy. The gender construct underlies the fundamental typing mechanism underlying all of the unifying science presented in this work and helps explain the ancient theory of the four “letters” or the four elements. Exploiting this hyper-generic gender construct, a universal typing mechanism can be constructed where any entity whatsoever can be described in terms of such generic types. The four binary combinations of the two gender types provide the alphabet for such a system. In a previous section, we made a preliminary interpretation of the genetic code as being such a typing mechanism. We even tentatively linked the four letters A, U, G, and C of the genetic code with their corresponding four binary gender types MF, FF, FM and MM respectively.
How this material should be taught and at what age the various concepts should be introduced, the author has no firm opinion on such matters. The author has found that even mature can have problems coming to terms with the concepts. Some, the highly trained academic for example, find the ideas threatening.
It’s time now to look at Kant’s version of the semiotic square.
In the Critique (Kant, 1738) and particularly more clearly in Prolegomena to any Future Metaphysic (Kant, 1783) Kant effectively outlined two superimposed dichotomies. The primary dichotomy was between knowledge founded on a priori judgments and that founded on a posteriori judgments. A priori judgments are based upon reason alone, independently of all sensory experience, whilst a posteriori judgments require real world experience.
In addition to the primary dichotomy between a posteriori and a priori judgments, Kant superimposed a second very important dichotomy. This was the dichotomy between analytic and synthetic judgments. Analytic judgments are where the predicate is wholly contained in the subject. Synthetic judgments are where the subject is completely distinct from the predicate and so must be related to some outside principle.
We can visualise Kant’s secondary dichotomy by complementing the left-right side primary dichotomy with a front-back side secondary dichotomy where the synthetic is on the front side and analytic is at the back side as shown in Figure 15.
Superimposing the two fundamental knowledge dichotomies leads to visualising the overall architecture of knowledge as a kind of semiotic square with left and right side specialisations each with its own analytic “frontal lobes.” In effect, this is Kant’s version of the semiotic square. The artifice provides a way of visualising the epistemological structure of knowledge, the layout of the epistemological brain, so to speak. In our more rash moments, we claim that this also provides a sketch of the architectural and functional layout of the biological brain. In later sections we will investigate the role that this structure plays in the science of spatio-temporality. In the broader picture, our we intend to demonstrate the science behind Kant’s claim that all perception and cognition takes place within a spatio-temporal framework. The first informal, intuitive acquaintance with this framework is via the semiotic square.
This artifice is not presented here as a theory of the brain, but merely as a pedagogic aid to visualisation.

As can be seen from the diagram, we end up with four different kinds of science. Kant homed into the front right side of the diagram, that of synthetic a priori judgments that, in theory, should synthesise new knowledge that was necessarily true. This is the domain where the Kantian question, addressed by this book, is located. How do we produce right hand, front side knowledge?

Figure15 Kant’s two fundamental dichotomies can be superimposed to construct a semiotic square of knowledge. Solving the Kantian question requires knowledge of the right hand front corner kind.

Polysynthetic Knowledge

The knowledge that we seek is based on Kant’s synthetic a priori judgments and is, in effect, doubly synthetic knowledge. Using a term borrowed from linguistics, we will call it polysynthetic knowledge.
In linguistics an important language classification is between analytic and synthetic languages. The difference between the two classifications is not very precise but, in general, analytic languages tend to have simpler words consisting of a smaller average number of morphemes. Also, the grammatical structure of the language is expressed more in terms of syntax based on word order rather than inflexion and affixing and prefixing of grammatical markers on individual words. Overall the analytic language will be synchronic in structure rather than spatio=geometric. Thus the analytic language speaks by the intricate sequential flow of single notes of a melody. On the other hand, the synthetic language expresses its message in terms of dense, rich chords, each articulating a beautifully vivid spatio-geometric image. It does this by using words with a larger number of morphemes per word. Also word order is of less importance or, in some cases, of no importance.
It is interesting to note that proto Indo-European was highly synthetic; this is the reconstructed common mother language of all Indo-European languages including Latin, Sanskrit, Hindi, and most European languages. Since then most Indo-European derivatives, of which English is a good example, have become increasingly analytic with the passage of time.
At the extreme end of the synthetic scale are situated the polysynthetic languages. Examples of these hyper-synthetic languages seem to be closer to the deeper natural order of things. Examples of polysynthetic languages include languages of North America, Siberia, and Australia.
The polysynthetic nature of Australian Pama-Nyungan languages is illustrated by the example:
“…the words meaning man (ergative) + see (past tense) + you (accusative) + big (ergative) can be placed in any word order whatever; they will be understood to mean ‘(A/The) big man saw you.’” (Heath)
At the other end of the spectrum would be the doubly analytic forms of knowledge located on the front, left side of the Kantian square, a posteriori knowledge expressed in analytic judgments; the analytic as analytic. We will call this polyanalytic knowledge. This classificatory term doesn’t seem to be used in linguistics and so we will refrain from rashly endeavouring to discern polyanalytic language groups. However, we can get a good grasp of what the polyanalytic entails as far as a philosophical classification is concerned. There probably would not be much objection to saying that a good example of a polyanalytic philosophy would be none other than Anglophone oriented analytic philosophy.

If we admit polyanalytic philosophy into the fray then, to be fair, we should also admit its totally opposite number, polysynthetic philosophy, yet to be born. Whilst analytic philosophy delights itself by listening to the tinkle of meanings flowing from natural language, usually English, on the other polysynthetic side, a different language is spoken where single words can be so large and the chords struck so vibrant that the music can last for a lifetime.

Key Phrases: semiotics square, genetic code, generic code, DNA, start codon, left right hemispheres, the divided brain, epistemology, anti-mathematics, masculine, feminine, gender differentiation,  Generic Science, Semiotics structure

D. J. H. Moore
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