The primordial part or share (which the Greek called Moira) can be equated with the ultimate unity. The term points to a status of nature, which is incomprehensible for men, a contradictio in terminus. In the ultimate unity or one-division is no transgression of frontiers, because there is no fragmentation to get things going.
The one-division is a division and not-a-division at the same time. This is hard to imagine. Our human mind is so geared toward division, that a thing, which is (visible), cannot not be there (invisible). We are not used to think and comprehend in an undivided environment. An infinity that crosses our intellectual path, either by chance or after a deliberate attempt to reach the boundaries of comprehension, has to be broken down to be understood. The very moment of division also means that infinity is lost.
It seems as if the Unimaginable One has to multiply to be understood. The scholar Kent PALMER (2000) called this level of deeper Being the Enigma and referred to Merleau-Ponty (Flesh, the Wild Being), Deleuze and Guattari (the Rhizome), Arkady Plotnitsky (Complementarity), and Cornelius Castoriadis (the Magma). They all made their own effort to designate the character of a world of pre-duality.
These researchers follow – as many did before them and certainly others will pursue in the future – a road that was ventured by the before-mentioned philosopher Leibniz (1646 – 1716). He ‘invented’ the monad: a foundation of reality with no material existence, no placement in time and space, no velocity or direction and no movement. In short: a one-division. If a (further) fragmentation takes place, then all the ‘parts’ will carry the imprint of the original division in them. As a result, a colony of monads (one-divisions-in-parts) is created. Each monad is a tiny mirroring of the entire cosmos and has the capacity or potential to express the fullness of the universe.
The position of God lies, in Leibniz’ view, outside the realm of monads and potential being. God is full being, characterized as the intellect of the universe. Leibniz used the principle of sufficient reason (which tells us that for every event or fact there is a sufficient reason, even though we may not know what it is) to prove the existence of God. There must be a sufficient reason for the universe and that is its creator.
The quadralectic world view accommodates for the position of God in a similar way, but determined the entity as the principle of division. Leibniz’ assumption as God being the intellect of the universe is transferred to the position of God as the principle of division. This condition refers to the process of division only and not the actual number. There is – within the state of Being – no preference for a particular form of division.
The problem of unity (and one-ness) surfaced again at the beginning of the twentieth century as the set theory. This theory was an attempt to unify all mathematics concepts into one single theory, which contains every theory and idea in mathematics. This was thought to be achieved by regarding every number as a set. Every set contains, in reverse, the same number of elements as the number of the set. This approach (to unity) resembles the position of the ‘division’ within the modern way of thinking: every number is a division, and every division is related back to a number.
Problems did arise in the form of the ‘Paradox of the Biggest Set Ever’. If a set is defined as a ‘collection of elements’ (like a division is a collection of parts) then the question will rise: what is the biggest set there is (or: what is the biggest part there is)? This query assumes knowledge of the biggest number (part), which, unfortunately, cannot be determined. Infinity leads, by definition, to nowhere.
This paradox finds its origin in the definition of a set. A set (and a part), as a unity, needs a plurality to be understood. A ‘set of all sets’ refers to circular thinking. In the end, the truth must be faced that the definition of a set is wrong. Consequently, the set theory lost its acceptation as a theory of ‘everything’. What remained were the seven axioms of the standard set theory which are intended to be sufficient for the deduction of all mathematics (extensionality, subsets, pairing, sum-set, infinity, power set and choice) (BARROW, 1991; p. 36). The set theory did serve, despite its disappointing outcome, the better understanding of unity and plurality.
The logical paradoxes of set theory and the weird properties of infinite sets, which were investigated by the German mathematician Georg Cantor (1845 – 1918), established a climate of uncertainty in which constructivism could flourish. This widely applicable ‘ism’ starts from the assumption that knowledge is in the heads of the persons and constructed from a personal experience. All kinds of cognition are essentially subjective and there is no way to prove that the experience of one person is the same as the attainments from another person. The rigors of deductions, which lead the argument into contradictions, is avoided in a constructivist environment.
The constructivists ideas are particular suitable to side-track the singularity theorems, leading to such creations as the Big Bang theory – the most popular appreciation of the birth of the universe at the moment (WEINBERG, 1977). ‘The important lesson that we learn here’ said Barrow (1991, p. 187), ‘is that the notion of what is ‘true’ about the Universe appears to depend upon our philosophy of mathematics.‘
The (theoretical) world of one-division is born in a logic necessity to create room for further division. People realized this from the early days of man-kind. The Great Unknown or Creating Nothingness got names all over the world. And we have to admit that the labeling of this place as the ‘First Quadrant’, as will be done in the context of this book, is just another name for an unimaginable universe of which we are a part.