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Back to the ancients to find the future of science

Dialectics, Theology, and Opposition Based Reason

Right Side Reasoning is based on Oppositions

Left side reasoning is what we associate with the traditional sciences, including mathematics. The reasoning flows sequentially from premise to conclusion via intermediary steps. Every step in the process involves a proposition of some kind, be it simple, modal, a predicate or whatever. The reasoning involves a flow of logical steps. A mathematical proof, for example, presents itself as such a flow.
In the West, we have becomes so accustomed to this way of thinking that we refuse to countenance the possibility of any other kind of formalism of reason. Our task is to demonstrate the contrary. Orthogonal to sequential reasoning of left side thinking is a non-sequential form of reasoning. We call it right side reason. Instead of thinking in terms of sequences of single units of rationality, right side reasoning takes the path of Heraclitus and expresses itself in terms of binary oppositions. 
The atomism of left side logic can involve complex propositions being formed from the sequential concatenation of simple propositions.  On the right side, the equivalent to the compound proposition is the compound opposition. There we find oppositions between oppositions. The simplest such compound structure is the semiotic square.

Non trivial aspects of left side reasoning can be taught at an elementary age. The student can be introduced to the propositional calculus including the concept of negation, disjunction and conjunction, for example. Venn diagrams can also be used as an aid to an intuitive understanding. Right side reasoning should also provide its own gentle introduction. The semiotic square is the first artifice along the road to understanding. Understanding this artifice requires many practical examples. At all times, it must be stressed that right side reasoning cannot be an abstraction. Abstractions always leave something out of the picture. In right side reasoning, the entity is investigated as a whole. The semiotic square, composed of two opposing oppositions encapsulates the whole. The whole can be thought of as Totality viewed from a particular perspective. The perspective forms an integral part of the resulting whole. The semiotic square and its dialectic is a simple tool for understanding these concepts.

The Dialectic of the One and the Many

The semiotic square can be used to analyse a particular kind of whole. In this case, the basic oppositions are deconstructed from the whole. Deconstruction is the right side equivalent of analysis. The approach can also be constructive, starting from a primary opposition; a generic whole can be constructed. This latter approach will be illustrated here. First, we look for a fundamental opposition to work with.
There are many fundamental oppositions. The most fundamental of all oppositions is the masculine-feminine gender principle of ancient pre-Socratic times. This will be considered in later chapters. Here we choose a rather more tangible opposition, that between the Many and the One. We remark, in passing, that this Many-One opposition can be thought of as a simplistic version of the masculine-feminine opposition, and so paves the way towards understanding the more advanced concept.The cardinality Many-One opposition can be considered as a dichotomy that divides reality into two. On the left side, there are the Many, on the right side there is the One. These two different realities can also be seen as the one and the same. The two realms are a consequence of the two possible takes on reality, the left side atomist take and the right side monist take. One sees an exploding multiplicity; the other sees an all-embracing unity.
This Many-One opposition provides the left-right cut for our semiotic square. The next cut is the split into the front and back. Cutting a long story short, this cut can be made by reapplying the same Many-One opposition to itself. The One side goes on the front and the Many takes up the rear. The reasoning here is that any One can be many, any Many one and there can be many Many. Last of all, there must be one One. Having exhausted all possibilities, we end up with the semiotic square in Figure 3. This is the semiotic square of the Cosmos as a whole when viewed from the perspective of its cardinalities.
The end result is that this semiotic square demonstrates not two different takes on reality, but four. There are four completely different ways to conceive reality. Such a mind-boggling vision has not gone unnoticed across the ages. Corralled by the emergence of the written word, formalised in canonised texts, different ethnic and geographical regions have coalesced around one or the other of these great doctrinal viewpoints. Each gave birth to its own world religion. There are four such world religions

Godhead Semiotics

Left side sciences rely on abstraction, the “view from nowhere”, the God’s eye view. It could be said that right side science takes the “godhead view.” It sees the world from four different vantage points. What interests us now is that each of the four different takes elaborated in the Many-One semiotic square spells out the central tenant of a world religion.
The fundamental question of theology can be asked. What is the relationship between the One and the Multiple? As can be seen from the semiotic square, there are four answers. Each is discussed below.

Figure 3 The Theological Brain. A semiotic square for the four takes on reality based on cardinality oppositions.

The One is Multiple (Judeo-Christianity)

The One is Multiple formula defines Providence, the giving, creator god. In the Judeo-Christianity, the individual roaming amongst the Multiple is showered on by the Benefactor on high. The loving god, the greatest giver, even sacrificed his own son for the redemption of the often egotistical individualists massing below. The One is Multiple doctrine emphasises free will and the temporality of the individual. Exercising free will is inexplicably concerned with temporality. The Judeo-Christian God is essentially temporal in nature. Christ is sometimes interpreted as the Lord of Universal History. The culture is very conscious of its history. God manifests through history. This is a temporal God.
Being a left side religion, the emphasis is on belief. The pious should believe in this god. It is possible, but not advisable, to disbelieve.

The Multiple is One (Islam)

In the Islamic take on reality, the tables are turned. God does not give to the masses; the masses must give to god. Islam is literally the doctrine of surrendering to god. The Judeo-Christian individual gives way to the collectivist convictions of the peoples of Islam. Gone are the historico-temporal preoccupations of the first paradigm. Enter spatiality. If Christ is the Lord of Universal History, Allah is the Emperor of Space. It is spatiality of Allah than unites the Multiple into Oneness. Allah is truly the Greatest because he is everywhere, with no exception. Mecca is the iconic centre of all spatiality dictating the spatial direction of the praying, emphasising the spatial unity of all and the spatial, all-embracing nature of Allah himself.
Islam is a right side religion and so is not based on a belief system. No Muslim believes in Allah. “There is no god”, declares the Koran. To believe in Allah would be to admit the possibility of not believing in him, a sacrilege. Situated on the right side of rationality, belief gives way to faith. Allah is the god that Muslims have faith in. “There is no god, except god,” states the Koran. Lose your faith and you lose your god. You cannot disbelieve something of which you do not have any inkling. The only way to have any inkling of Allah is to have faith in Allah. Allah walks the tautological line.

The Multiple is Multiple (Buddhism)

The Multiple is Multiple paradigm underlies Buddhism. The One has no place in this worldview soaked in Multiplicity. Each religion has its favourite icon. The iconic Buddha says many things. It radiates well-being, but what is so captivating is that famous ironic smile. The author’s strongest Buddhist image is of a lawn covered square in a Bangkok primary school. Each side of the square features a row of identical Buddhas, all looking across to the other side; multiple to multiple from left to right, multiple to multiple from front to back. Student desks were also arrayed under the awnings around the square. What an incredibly idyllic place to start school!
This Multiplicity doctrine is a left side religion, like the Judeo-Christian, and so is belief based. People believe in Buddhism. The problem is that, unlike its theist front side neighbour, there is not anything specific to believe in. All is multiplicity, there is no One. This is the belief. Working this into a tractable religion requires the work of someone of considerable intellectual agility. Hence, that ironic smile….

The One is One (Hinduism)

Advaita Vedanta is the core philosophical school of Hinduism and teaches the principle of non-duality. Ignoring the fine print, ultimately only the One is real. Apparent multiplicity is subjective and illusory. Advaita Vedanta articulates a non-compromising monism. The Western mind is reminded of Parmenides who took a similar monist position.

This Hindu doctrine is situated well and truly on the right side of the theological semiotic square and so, like Islam, is not belief based. According to Advaita Vedanta, the truth of the doctrine is obtainable via pure enlightenment. For Shankara, the founder of Advaita Vedanta, you do not believe in the oneness of the One. By enlightenment, you simply know.

The Theological Square of Squares

The theological semiotic square provides a way of understanding the four world religions and how they relate to each other. Every religion has its own semiotic square and so there are semiotic squares within the semiotic square. Take Hinduism for example. The One in the One-is-One doctrine is the Brahman, the impersonal god that cannot be worshipped directly. The Brahman can be comprehended in the form of a triad of personal gods consisting of Shiva, Vishnu, and Brahma. This leads to the semiotic square in Figure where Vishnu occupies the same front top slot as did the Christ god and Shiva occupying the same back left slot as Allah. Brahma, who is rarely worshiped takes up the Buddhist slot. Theologians warn that this is an error. The Christ god and Vishnu are quite different as are Shiva and Allah.
One way of formalising this difference is via a semiotic square of semiotic squares where each of the four squares is located in the respective slot of the first semiotic square. We will not pursue the details of such structure here. However, a good example of such structure can be found in the signs of the zodiac where there is interplay between figure and ground, the twelve signs and the twelve houses.
At this point the reader might be wondering what has become of the topic of conversation. Basically, we are exploring elementary cognitive or generic structures and their interplay with reality.
The theological semiotic square has provided a way of understanding a holistic view of reality and that are four fundamental “takes” on reality. These four worldview paradigms are mirrored in the four world religions

Key Phrases: 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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