Knowledge and activity are essential parts or features of a greater whole, namely the logical system described here. Therefore they cannot be viewed in isolation. They get their meaning from the whole and from their relationship with each other and with other similarly fundamental terms.
Above all thing and space. These are, in a way, as diametrically facing one another as knowledge and activity. In the extreme, so to speak, space is the opposite of the thing, that what resides between the things, what separates them. But of course each thing occupies some space; and space may be treated as a thing — representing knowledge — arising through activity.
These concepts belong together, for they are four corners of one and the same figure.
Knowledge, activity, thing, and space form the basis of our system, a square. All the four corners are interconnected, so it arises from the crossing of the diagonals the shape of an X. This is a really graphic reason to call the system “X-Logic”.
The intersection of the diagonals, the centre of the quadrilateral, could be regarded as a symbol for unification, thus for the whole that gives the parts their ultimate meaning. It is connected to all the cornerpoints. However, it itself is not a corner, it has no contact to the outer world — and interrupts, in a sense, the direct relationship between diagonally facing vertices.
So, for expressing the whole, the oneness, it makes more sense to move out of the plane and to raise a pyramid. The original planar figure then can be seen as a two-dimensional projection. Which comes into usage mainly if there is only a flat surface available for presentation.
But the more expressive symbol is the pyramid. It is an illustrative model of the x-logic system described here.
A pyramid may quite generally symbolize unification: the set of points forming the base pass into the single point at the top, the apex. This kind of transformation is fundamentally important for knowledge.
It is part of what we have called the “act of knowing”. A certain pattern crystallizes into one thing that multiplies as a whole — and so constitutes a new plane or space of knowledge.
This move into a new dimension is nicely depicted by the pyramid shape, too.
Knowledge comprehends relations between things. For this, these things have to be, in a sense, synchronously present, side by side, closely arranged. This holds even if the things are in reality separated by large distances, yes, even for events taking place at different times. All this cannot stop knowledge. It overcomes times as well as distances, it compacts, omits superfluous details and gets to the point.
This process, often called “abstraction”, appears to lead into areas lying beyond any physical reality. However, this idea itself is merely an abstraction, a picture that may depict a certain process by highlighting and strikingly illustrating one particular feature held to be essential. So here, in this case, the idea of absolute immateriality is derived from the freedom that inheres in every knowledge because of being not the hard and heavy matter itself, but its image, so to speak.
Yet, finally, every image, every representation, every form of knowledge is itself again subject to restrictions that are not less real than those of the represented thing, simply different — and therefore many of the original ones disappear.
Something, however, has to remain, a certain identicalness must exist. Image and original must allow to treat them as one and the same. The picture of a house must have enough in common with the depicted object to be itself called “house” (as in phrases like “This is our house”). Insofar it must be house.