The space of knowledge affords and demands a new logic, a logic of knowing, whereas traditional logic deals with truth, particularly with truth values, that means in general with true and false. These necessarily exclude one another: what is true cannot be false, and vice versa.
To knowledge, however, this does not apply in the same manner. Its embodiments, spanning a much broader spectrum of possible forms, can exist side by side, even if they partially contradict one another. This coexistence is crucial, it constitutes a field of tension, a network of relations indispensible for all kinds of knowing. So knowledge, in all its possible forms, is always extended and full of inner tension. Each such appearance, again, combines with others to keep on forming new figures of knowledge.
Conventional logic — and scientific systems based upon it — largely lack the ability to express dynamic contents adequately. They are too rigid, building on never changing conditions. New things are just added, not created by conversion of the old. Fundamental changes would destroy the foundations of the whole system.
To avoid this, the basics were more and more abstracted and miniaturized, down to smallest building blocks and most general rules. Of these all sorts of things may be constructed. Meanwhile, however, the road from the most elementary preconditions to the real outcome has become unmanageably long and complex.
In practice, nobody goes the whole way. Single purposes are covered by specific models. Although these should, in principle, be reducible to those generally accepted foundations, this is actually not practicable at all. That what ultimately counts is to find and to establish the methods fitting for a particular purpose.
The problem is that this common — and, besides, the only realistic — practice misses well-founded theoretical reasons. So there is no common ground for communicating about it. There exists no certain plan covering larger areas.
Knowledge puts various things together — and makes them be one thing.
Knowledge determines how the things act and interact. That they behave according to certain rules, expressing constant relationship. It is this regular behavior, recurring always in the same manner, that constitutes the new certain thing of knowledge, the fact. Thus crystallized, it becomes graspable and handy, making it a gain in knowledge.
So we just have described the key process of knowledge. We should frequently replay it before our mind’s eye, recapitulate it, internalize it. Only so we can really understand it.
In particular, it is most important to realize this to be actually a process; something is happening, a change. Activity takes place. Without that there were no realization, no understanding, no knowledge. For it is this activity that brings together what formerly seemed to be totally unrelated. A transition takes place. And only when this transition becomes an unalterable habit, the represented relation is firmly established. From now on it automatically replicates itself. Now it is clearly evident, without a doubt, that those things belong that way together — in this sense being one thing.
The act of knowing (as described before) is central and fundamental and has impacts on everything based upon it. It affects the structure of knowledge, making it fundamentally dynamic.
So, what does this mean? Is there no stable structure at all?
Well, initially it says that the elements of every structure emerge from activity and actually are activity, in their deepest inside, as one might say.
Yet, we have found out some more, namely that there is also always a spatial structural component, such as a net of relations and a field of tension. Thus we can redescribe the act of knowing so that a spatial structure concentrates and reduces to one thing.
This thing is a thing only because it represents a repeatedly observable regularity, that is, because it muliplies. So it constitutes a particular structure of its own, established by its appearances. Seen in this light, the central act of knowledge is the passing from one structure to another.
Hence, activity is not only enclosed in the elements that form the structures of knowledge, but the deformations and reorganisations of the structures themselves are in effect the same activity.
The very essential parts of knowledge-structures, their true elements, are their alterations!
The elements of knowledge-structures mentioned before are exactly the same as what we have elsewhere called the objects or bodies or particles of knowledge. Nowadays we may in the first think of data, but every other representation of knowledge (or information, as one might say sometimes) is also implied; it merely must be reproducible and somehow uniformly applicable so that it has kind of a constant meaning. Like a mathematical formula, for example. Or a description of a plant. That means that these elements or objects or things may have quite different forms, some of them very complex. Still, in a sense, each of them is one thing. “One” just means that it may be duplicated as a whole, One is the base of every plurality. And seen in this light every such thing is — in spite of all possible complexity — simple. This is no magic, but sheer logic.
The act of knowing always takes place in a non-empty space. Every search for knowledge tries to discover a stable pattern — in examining a pre-existing structure. Even the pattern itself is, in a sense, already existing.
Nevertheless something is created: exposing the new means changing the existent. The pattern becomes a thing that has not been so before. It solidifies, becomes concrete, graspable. So that something new arises, being more than simply a new arrangement. The crux is its creation, which does not happen once and for all, but ever anew, whenever the new thing appears. The fact that this happens habitually or automatically does not mean that no activity is needed.
Where there is knowledge, there is activity, too. Only so it can come into being. It manifests itself in activity. In doing so, it gives form to activity.
On this basis, the probably most general definition of knowledge may be given, as counterpart of activity, so to speak. Thus, while activity stands for change, knowledge means sameness and steadiness.
The preceding definition of knowledge is in accordance with the common tacit assumption that the laws of nature, for example, hold timelessly universally. And not only the laws, but also the involved terms or rather the notions or ideas referred by them. A proposition accepted as true may proove false, but the concept of truth as such always remains unaffected. The value of a certain quantity may change, but not the respective number itself, such as the three, or that what it stands for, its meaning, the idea of three.
And so we may realize a constancy we always rely on, the constancy of certain elements of our theories and sciences, mental entities that serve as foundations of all our systems, even those of mathematics and logic. Viewed is this light, our definition does nothing but making that constancy obvious, giving it a name. We now call it “knowledge” — which is certainly not all-too farfetched.
Although each of us has to learn the laws of nature before knowing them — and maybe forgetting them again — these themselves are wholly timeless. They exist, in a manner of speaking, irrespective of whether we know and see them or not. They may come into focus — and disappear from it again. Still, this does not alter them in any way.
And so are all those things that exist only in our mind or psyche or so, that means all notions, conceptions and so on. They are not bound to any restrictions of time or the like, being so typical for physically real things. This freedom makes them everlasting and untouchable, on the one hand, but also, on the other hand, pure fiction without any substance. What they are lacking is definitely the interaction with the real material world; this leaves them unverifiable.
At least, that is how they are frequently viewed.
But here we say that this world, seemingly existing idependently (and therefore seemingly not really existing), this world of knowledge is, in fact, permanently connected with acivity — and thus to all the other things, through mutual influence. Because even knowledge can never be without activity. And this is true not in spite of its immovability, but rather because of it. Activity is the complement of knowledge, a logical necessity. We cannot have one without the other.
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 the shape an X from the crossing of the diagonals. This is a really graphic reason to call the system “X-Logic”.
The intersection point of the diagonals, the centre of the quadrilateral, could be regarded as a symbol for unification, the whole that provides the parts with their actual meaning. This point is connected to all the cornerpoints. It itself, however, 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, too, is nicely depicted by the pyramid shape.
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, all images, all representations, all forms of knowledge, are themselves 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 also rightly called “house” (as in phrases like “This is our house”). Insofar it must be house.
After all, our exploration of the concept of abstraction simply shed some light from a different angle on exactly that what we previously called “act of knowing”. All knowledge is, in some ways, abstraction. Or, more generally, representation. It is always about some extraction of what is deemed essential, and its projection onto another plane, into another space, into another dimension. What, as previously shown, can be illustrated as a pyramid.
Another way of achieving knowledge is called “perception”. And this too can perfectly be described with almost the same words, so that the same pattern becomes recognizable — the principal figure of knowledge, so to speak.
This X-Logic cannot be the ultimate system comprising everything — not even in principle; quite simply because such a thing does not exist. Every image, every model, every system is partial or one-sided.
When we apply a certain model, we try to realize it under the actual conditions. So the outcome should be always the same; we multiply it.
Still, this is what happens only if seen from outside, so to speak. From inside, while using it, the model itself cannot be recognized. There is effectively no way to become aware of it, because it is everywhere, stamping everything. What can be observed — through the model — is rather a diversity of things and their interrelations.
There are always different points of view. Seen from another one, a certain thing may appear completely different. So much that it can no longer be called the same thing (or an instance or a copy of it). Ultimately, there does not have to be any correspondence at all, no regularity integrating towards a thing or so. Maybe there is apparently nothing.
Even the smallest point still allows to be spread open, unfolds into a whole world.
And, the other way round, from the proper perspective the whole wide space with all the trimmings shrink to a single point — if anything of that is still to be seen at all.
Even matter is subject to the laws of logic. But this does not at all mean that real-world events could be deduced from logic alone. Not even theoretically. Because the theory of X-Logic knows neither absolutely elementary building blocks nor absolute all-embracing plans. So there is not the one system for everything; nor do closed partial systems without intervention from outside exist.
After all, exactly this knowledge can help making our systems more robust and more practicable. For, on the one hand, we no longer rely on the illusory security of absolute reasons, while, on the other hand, we avoid getting lost in endless chains of them.
There is always more. No representation, no image, no model, no theory will ever be able to cover everything. This principle is basic to such a degree that it is to be called “logical”.
Accordingly, no system, of whatever few axioms and simplest rules it may be constructed, can start with absolutely nothing. Instead, it must rely on endless amounts of given things. What these are in detail can never be specified.
Every so-called emptiness must be produced and maintained; protective walls, taking isolation to the extreme, are real and have fundamental impact on all that is happening behind them — othwerwise they would not be needed.
Even the mental world does not stand totally apart, but rather all over interwoven with material life.
All which is seemingly not present — though somehow active — does not exist as distinct thing. It is somewhere in between, between the things. It is the space between, its substance. It is that what makes up space.
As such it is ungraspable — unless it does become something, a thing. In this way many things may emerge out of space. At last, space is totally made of things, nothing else. They just cannot be seen — in the moment. Maybe they are too small, too big, too far away, too close, too well-known, too strange, too many …
Still, somehow they are there, and they have some influence on those things that can be seen. So we give them a name, as a whole. Here, in this context, we call it “space”.*(1)
Science is not only theory, but also practice; and, as such, it always stays close to reality and experiences. Its theoretical part, however, is permanently in danger of losing contact.
So, for example, while trying to realize the idea of one single all-embracing system constructed from few simple building blocks: sooner or later its complexity must get out of hand. Endless chains of deduction lead to no concrete results. The truth that should be granted by them gets lost on the way to realization. For it cannot enter the scene but from the other side, from reality, through experience.
Existence need not be justified. It appears. Beyond any reasoning and description. But, certainly, not without reason and the proper circumstances. Not outside its space, as we will say.
Every thing has its own space — although there is only one space, space, for it is endless. Everything that exists is part of it, a thing in it.
Things may sometimes be regarded as the opposite of space — since space is open and boundless, while the things are rather bounded and closed. As such they separate a region of space. And that is exactly how, after all, space is somehow bounded: by the things. Through them it can be left — and another one can be entered.
It is the space of the thing that is entered in this way. But, once entered, the space that initially appears to be the closed interior of the thing turns out to be space itself, the endless one, the universe. Because from inside no bounds are to be recognized.
So, where do they go? — Well, quite easy: again they are incorporated in the things of (this) space; and so they are perfectly integrated, yes, they are the ultimate substance of space.
At latest since the discoveries of mechanics, it is generally accepted in physics (and other sciences) that everything happens because of internal forces. The observable things embody all causes of whichever effects.
More modern developments, as for example the theory(s) of relativity, may be interpreted in a way that they abandon this view, putting the focus much more on so-called “fields” and the like. This may go so far as to consider physical objects to be nothing but special states of a kind of space.
Logically, however, this makes no principal difference to us. For whatever replaces the traditional physical things: it has to be, in the sense of X-Logic, things, no matter whether we call them “spaces”, “fields”, or likewise. Even if all material interpretations are set aside and only mathematical objects, such as “tensors”, are talked about. Yes, even the physical laws themselves are things of this type. With their respective spaces.
Previously we have already adumbrated a kind of motion which may be described as penetrating or analyzing a thing. In getting closer and closer to a thing, we probably become aware of something like an internal structure or even a regular inner life full of activity. Maybe we discover certain regularities, a plan according to which the whole is constructed, or a program controlling everything.
But the bigger we blow everything up, that is, the deeper we penetrate, the more we lose sight of the big picture. Instead, we find ourselves right in the middle of infinite space, surrounded by an endless variety of things, interacting with them.
Starting from here, we can now take the reverse direction, so to speak: we can recognize certain patterns in the buzz of activity around us, regularities, maybe even laws. Perhaps a plan becomes visible, the program and blueprint of everything. Still, in comprehending the whole as a whole, we finally understand that it is is just one among many, a thing.
X-Logic is about very simple basic principles of thinking and knowing. We consider them elementary. They are to be found everywhere, in every area of life and matter and so.
This may be explained by the fact that all we can know about the world is exactly this: known. Even experience, however direct, is somehow interiorized and so might have passed some sort of filter.
On the other hand, however, it might also be possible that the principles of X-Logic can be found in the mental for the reason that it inherited them, so to speak, from its material roots. These may be searched in structures and functions of the brain, or even deeper, maybe on a so-called “quantum scale”.
But after all, generally applicable logical principles do not really have to be based on whatever reasons. Instead, these principles can serve as a basis, for describing and explaining material as well as mental phenomena, for instance.
The X-Logic describes how different things melt into one that multiplies. This is a principle that could have been taken from biology, for it is perhaps most clearly realized in the propagation of life, especially in sexual reproduction. But it finds itself everywhere, even in the core of matter. It may be named the principle of two, of pairing.
The logic of knowledge is a logic of creative fusion. The central act of knowing is an act of love.
Things appear again and again. That’s it. We cannot give a deeper reason for that. Things simply could not be called things, there would not even be anything, if there were no such constancy and continuance in their appearances. Only so they can be identified in any way, as something. Thus repetitive appearance is a logical need.
We can also take it the other way round, just as well, and say that because we have repeating experiences we conclude that there must be something, some things we interact with.
Without a certain constancy in our perceptions and thoughts we would not perceive or know anything. There would be neither perception nor knowledge. There would be nothing — if ever…
To understand that repetition and propagation are fundamental moments of all being is decisively important. They mark the ground state, so to speak, from which all others can be deduced somehow, as special cases appearing under particular circumstances.
This is fairly opposite to the common approach, which generally presumes isolated static entities — without being concerned about how, for example, those objects might be subject to our perception and knowledge if they really were so inactive and closed.
The common dominant logic is crucially based on the presumption that a thing’s space is limited. Limits are set to its extension and propagation, namely by the existence of others.
Things abut one another, they collide, they displace one another.
That is the logic of solid bodies, of mechanics. It is the logic of delimited territories, of possessing, of conquering and defending, of fighting and making war — as well as, on the other hand, of meeting friendly and touching gently.
It is the logic of borderlines and separation. Either this or that; or nothing at all; but never both, in no case. The logic of NAND, of not-and. — Or of NOR, of not-or: we must decide, we have to take sides.
Conventional logic views the things from outside, so to speak. Hence they appear limited and closed. They become objects.
So this logic corresponds to the conventional ideal of science, the objectivity, always intended, but in the end remaining an idealization. For even science is persistently forced to immerse itself, to get into the thick of it, to be touched by the other, to take part, without a distance.
Actually, it is no problem to accept our own entanglement in reality as an essential condition for knowing. We merely have to factor the step towards objectivity into our computations by giving room for the spaces. They just belong to the things. The space stands for all that the thing cannot do without it. In particular the interactions, the outside contacts. It is space what mingles with others, what penetrates them and is penetrated by them.
In this way, by means of the space, the thing is able to leave itself behind it, to become another. While also remaining entirely itself, since only in permanent renewal it is. Seen in this light, its being is made exactly of this distancing from itself, of viewing itself through another’s eyes.
That is the core of every existence. And activity. It is what we sometimes call time. But before any standardization, without the artificial monotony of clocks. Lacking any coldness. It is life. And this life is knowledge. Reflection is elementary.
The X-Logic may be understood as a generalization of the hyperlink concept: every thing is linked to a space. Every thing is the door to a whole space of its own, it can be activated — and then pops up, so to speak.
The thing marks the passage between spaces. The passage is activity. All activity, every action, is ultimately a passage between spaces, nothing else.
The thing, however, is the unification of potential passages, so to speak. Every thing is an activity-node, it is target and source of various actions.
If we were able to define the basic terms of logic in a simple and unambiguous way — then the terms used in that definition would be the true basic terms.
The meaning of terms can only be learned — by doing. If these doings are clear and elementary, the terms may potentially be called logical.
Whether doings are clear and elementary depends crucially on where they take place, on the environs. On the available means. In the case of logic these are, above all, the means of expression and representation, now named the media.
These have definitely undergone — possibly crucial — changes.
Looking for knowledge mostly means to look for a suitable model of the real world that offers to us suggestions about the best course of actions, according to our needs and the given circumstances.
Such a model can be communicated and jointly developed, thus enabling us to gather our forces and act as a whole — albeit with a certain delay and usually with frictional losses.
That’s the way explicit knowledge works.
Every sign is the invitation to grasp its sense, to turn the key and enter the secret chamber. It intends to lead us to do the right things, to realize its message.
Every being bears such a secret.
Every thing is the door to a new world.
All that is perceivable and recognizable appears as a thing. Things gather and distribute. They are center and source of power and activity. Their pulsation keeps the world going. And together.
In order to be, things must renew themselves continually, they must arise again and again. Their potential wakes up, they become active, they appear. But then they vanish again. They give up themselves — for the sake of becoming, for the sake of being.
Space is a structured space of knowledge, knowledge expresses itself as activity, it bears things — and vanishes into space anew.
*(1) But we must not forget that it is what we call “knowledge”, too. And “activity”. And, of course, “thing(s)”.