The CF-graph provides a unique guide in the complexity of reality. The widening of thoughts displays the difference between visibility in a dualistic environment and in a tetradic territory. A dual frame of reference is used in the first case, reducing differences to oppositions. There are still differences in the second case, but the aim is now to search for similarities and resemblances. The active role of the observer in the communication process is acknowledged.
It is necessary to widen the scope of the dualistic frame of mind if the quadralectic mood will be understood. The nature of duality prescribes a widening in the ‘visible area’, because there is no gradation in the invisible area. The dualistic frame of reference gets confused when a quadralectic mind talks of ‘invisible visibility’. A concordance of quadralectic and dialectic thinking is only possible in the Third Quadrant (of a quadralectic division), which is governed by a ‘visible visibility’.
The Part, as a visible proof of division, is the vital link between the lower and higher stages of division thinking. The highest understanding is found in the pinnacle of lower division imagination, the material, when the Third Quadrant opens with the CF-value of 11.
The definition of visibility is part and parcel of the third step in the Second Quadrant (II, 3), i.e. even before the actual visibility of the Third Quadrant (III) has shown itself. The creation and notion of (visible) visibility is a monumental event and the crown on the inquiry into the nature of communication. The CF-graph, as the product of a conceptual exercise (of shifting four-divisions), holds the key to a genuine representation of the interchange between the communication partners.
The rigid approach to visibility, in a dualistic environment, demands an exact figure (of the CF-value) in order to participate in the understanding of the CF-graph from its own (limited-oppositional) point of view. A subjective interpretation of the graph-as-a-whole is required in order to bridge the gap of comprehension. This necessity has led to the proposal to put the boundary of empirical visibility in a quadralectic communication cycle at the value of CF = 11.
The arguments for this choice are, first and for of all, the noticeable beginning (and end) of the Third Quadrant with this particular CF-value. The Third Quadrant embodies the (visible) Part in the quadralectic view, although CF-values within the quadrant vary considerably. Two ‘highs’ (CF = 13) and one ‘low’ (CF = 10) are characteristic of the Third Quadrant. A quadralectic mind perceives this setting of subdivisions as a repetition of the major four-partition on a smaller scale. The dualistic mind only sees a part or not a part, without any intermediate stages.
The second consideration to put the (visible) visibility boundary at CF = 11 is provided by the horizontal lines in the second part of the Second and the third part of the Fourth Quadrant. The CF-graph reached at those particular moments/places some sort of equilibrium at the value of CF = 11. They represent the only events on the CF-graph were a continuation of the communication is not associated with changes in intensio or remissio. This typical capacity provides a boundary in its own right. The start of the visible visibility (at the CF-value of 11) is visualized in fig. 48.
Fig. 48 – The various important moments at the start of a quadralectic communication. The theoretical-empirical visibility on the CF-graph starts at the beginning of the second quarter of the Second Quadrant, where the CF-values reach the value 11 for the first time. This identification implies that every quadralectic communication, which makes itself known and has a certain extension, is preceded by an invisible period (of 5/16 V), called the proto-communication.
The (subjective) choice of the CF-value 11 as the beginning of an empirical visibility makes this value of special importance within a quadralectic setting. The correct interpretation of this point – which is only possible in a tetradic environment – is exactly the moment where the two-fold and the four-fold, quadralectic interpretation diverges.
It is possible, on the one hand (in lower division thinking), to see the value (of CF = 11) as an absolute measure for visibility. However, it is also conceivable, on the other hand (in higher division thinking), that such a value is a typical boundary in a quadralectic setting. The visibility of CF = 11 becomes, in the latter case, a value within a dynamic framework of nearing and drifting apart. The objective visibility (of an empirical entity) is stationed in the Third Quadrant. This part offers, by its very (dualistic) nature, two possibilities:
- The absolute way is keeping to the letter of the law (or definition).
This means: under CF = 11 visible, over CF = 11 invisible. This con-ceptual position has to be placed in the third quarter of the Third Quadrant (III, 3). If we apply this strict rule to the Third Quadrant as a whole, it turns out that the visibility (of the Part) is not very prominent. In other words, the part does not have a good view of itself, in terms of its own definition. Most CF-values in the Third Quadrant are higher than the (arbitrary) ‘visibility-boundary’ CF = 11 and only the area around the CF-value of 10 qualifies for a ‘real’ visibility in an empirical sense. The greater visibility in terms of intensio are reached in the Second and Fourth Quadrant, when the CF-values reach their lowest points (CF = 6).
Fig. 49 gives a comparison between the ‘absolute’ (CF<11) visibility in a dualistic and quadralectic environment.
- The multitude way is anticipating the dynamic visibility of the higher division thinking. The cognitive position dwells in the fourth quarter of the Third Quadrant (III, 4). Polarity, as an oppositional rigidity, is left behind and a quadralectic setting of the CF = 11 value can now be envisaged in a different way.
A perceptive plurality with unlimited imaginative possibilities enters a communication at the very moment that polarity has lost its grip on the human mind. Opposition can be seen as a phase in a wider setting, rather than being characteristic for the communication-as-a-whole. The conscious use of four different types of visibility – in every stage of the communication – puts the empirical visibility in its proper place. It is just a static moment in time, with limited boundaries, in a sequence of other types of observances. The multitude way (of thinking) opens a gateway to the world of the Fourth Quadrant, with the (Smutsian) ‘whole’ as a new unit of measurement. A full (tetradic) communication includes the previous stages of division thinking.
Fig. 49 – A graphic expression shows the comparison between the areas of empirical visibility in a dualistic and quadralectic environment. The CF-value 11 is used here in an ‘absolute’ sense to indicate the boundary of (visible) visibility. The upper box with the dualistic vision has the dividing line between the visible and invisible right in the middle of the total communication. The lower box shows four areas of invisibility (dark) and three of visibility (light), representing the quadralectic perception.
The definition of visibility in the form of a single CF-value is the ultimate crown on an intellectual voyage, which had no beginning and no end. Visible visibility (including our own presence in this world) is the result of a special interaction between communication partners, in which the choice of a (primary) division is of the utmost importance. The human being, as the Great Observer, stands in a universe of unimaginable dimensions and is only equipped with its own ability to order the observations in a comprehensive way. CF=11 looks like the Philosophers Stone in an alchemists’ dream.
Visions of Four Notions 