1.Epistemology.

T Hello, A beautiful weather today, isn't it? Are you sure you want to discuss philosophy, instead of hiking and swimming?

STo tell the truth, I am not. I came here from curiosity, but I am not sure at all that we will not waste our time. Let us start. I reserve the right to say at any moment: that is enough, I am out.

T All right. I understand you very well. I also find many discussions on- and near - philosophy unproductive. Usually people simply do not understand each other; they speak different languages. There are many philosophical languages, and they change as time goes. As you know, I am not a professional philosopher, and to compare in detail the languages of various great philosophers is not within my competence. But I have always held the view that everyone must have his own philosophical language in which to answer the everlasting questions:

What is the world? What am I? (the subject of Ontology).

What is our knowledge of the world? How true is it? (the subject of Epistemology).

What is Good and what is Evil?

What are the supreme values and the meaning of life? (the subject of Ethics).

Having such a personal language, one should be able to translate into it the ideas expressed in other languages.

S But, surely, it is not always possible to translate from one language to another. Remember the complementarity principle in physics. You can describe a quantum-mechanical particle in terms of its coordinate, or in terms of momentum, but you cannot describe it in these two ways simultaneously. The more precisely you determine coordinate, the less you will know about momentum.

TI am afraid your example shows the opposite of what you intended to show. The incompatibility of the two descriptions holds only as long as you use the classical notions, and this was the point of Bohr's complementarity principle. To avoid problems, do not use classical notions where they are not applicable. In quantum mechanics the particle is described by its wave function. It can be written in the coordinate representation, or in the impulse representation, and it is easy to translate one into another by making the Fourier transform.

When we have two or more languages which partially describe a phenomenon, our goal should be to create a more complete theory which synthesizes and unifies the preexisting theories. This is what has been achieved with quantum mechanics. I see no reasons why this should not be a typical case. I am against invoking the complementarity principle as a justification for the absence of a unifying theory. Maybe we simply did not work hard enough. I do not see any logical reason why a useful unifying language and theory cannot always be found. In the simplest case, different languages give u different projection of the same phenomenon, and can be easily combined, as when we have three projections of a moving particle on three orthogonal axes.

The reason why we do not always want to combine philosophical texts and languages is more down-to-earth: it is not that we cannot do it because of some universal complementarity principle, but that we simply do not need it. A text, or the whole set of texts written in a certain language,may express the meaning that adds nothing new, because we already know this and have expressed it in a different language. Or it may have no meaning at all. To make a discussion meaningful, we must make it sure that we understand each other. This is why I propose that we start our discussion with epistemology, to which the problem of meaning belongs. For some time I have been looking for a kind of a universal semantics, some guiding principle to understand a text in every possible language, if it, indeed, has any meaning.

SDid you find one?

T I think I did - to some extent.And I think every philosophy,and science as well, must start with the discussion of this, or a similar, principle. We need some criterion of meaningfulness. Otherwise we will not be able to distinguish between the meaningful and the meaningless. We simply will not know what we are speaking about.

SI am eager to hear about the principle you discovered.

TWell, discover is too strong a word. My epistemology will not surprise anybody who is not unfamiliar with the modern philosophy. My semantic principle, briefly, is: the meaning of a linguistic object for me is in my ability to use this object as an instrument for making models of the world, in other words, in generating predictions about the world's processes. I come to this principle by arguing that whatever has meaning must, somehow, increase our knowledge, and the cybernetic idea of knowledge is that it is a model of reality.

Closely tied to this principle is the method in which I propose to develop philosophy: the method of progressive formalization [16].This is the method universally used in science. We first rely on an intuitive understanding of simple concepts, then on the basis of this understanding we convey the meaning of more formal and exact, but also more complex, concepts and ideas.

This statement itself is an illustration of my method. I used in it the words `understanding', Îmeaningâ, Îformal'. In due course, these notions should be analyzed and `more formal and exact' meanings should be given to them, in their turn. These new meanings, however, will not come to replace the original meanings, but to make an addition to them. 

Compare this with the situation in physics. We start this branch of science speaking about bodies and their masses, measuring distances in space by applying rulers, etc. Later, when we study the structure of matter, we find that those bodies and rulers, are nothing else but certain structures consisting ofhuge numbers of atoms. This concept of a ruler is, however, a new concept, even though it refers to the same thing. To come to the concept of a ruler as an atomic structure, we must pass a long path, at the beginning of which a ruler is a simple thing the usage of which is easy to explain.

In the Principia Cybernetica Project [5], we come to philosophy with the standards and methods of science. We try to define and explain such basic things as Îmeaningâ, Îunderstandingâ, Îknowledgeâ, Îtruthâ, Îobjectâ, Îprocessâ etc. But to explain, e.g., understanding, we must rely on understanding in its usual intuitive sense, because otherwise we will not know if we ourselves understand what we are saying; so, there will be little chance for our words to be meaningful.

Or take the concept of an object. In Principia Cybernetica we have a conceptual node devoted to it. But we cannot do without speaking about objects long before we come to that node -- in a close analogy with the two concepts of a ruler in physics.

Relations between things in this world are very often circular, so we are often at a loss when trying to start and finish definitions. Using various levels of formalization allows us to avoid vicious circles in definitions.Suppose we use informally some concept A to define a concept B. Let us represent the fact that A conceptually precedes B or B relies on A as A < B. Then we want to make A more exact: Aâ. We define it, and discover that it now depends on the already defined B. Hence if we were to require thatin a formal definition. of a concept all the concepts on which it relies are formally defined, we would either have to limit ourselves to strictly hierarchical subsets of concepts, or never finish the job, moving in a vicious circle. Instead, we recognize that there are various levels of formalization of essentially the same concept, and we allow them to coexist. Thus after defining B with the use of A, we define Aâ using the informal concept B; since B relies on A, the old, informal version of A is not discarded, but stays in the system of concepts. Now we could make the definition of B more formal, basing it on A' instead of A; on the next turn of this spiral, we may wish to define even more formal concept A'', etc.:

A < B < A' < B' < A'' < B'' · etc. 

Whenever we want to understand a definition, we start unwinding the chain of dependent definitions from right to left, until we come to basic intuitive notions about which there should be no disagreements.

SYou define your primitive concepts using the concept of modelling. But this concept itself is far from primitive.It relies on the same primitive concepts which your are defining.

TYes. This is the process of progressive formalization. I define modeling by appealing to your understanding of the basic method of science. After that I start defining various concepts of philosophy referring to something you already understand: modelling. I define the place of these concepts in modelling. It gives you a way to decide if in a given context these concepts are used properly. This means that my definitions are more formal than if the concepts were not defined, but simply described and announced primitive. 

S But the concept of modeling is quite advanced. Why should you take it as the beginning? I may not believe in the model epistemology, but agree with your ontology that actions are primary reality, and accept the idea of progressive formalization. Starting from such primitives, I would come to formal definition of modeling. But you insist on accepting epistemology first. Thisonly makes things more difficult for me.

T You are free to start from any point in the spiral of progressive formalization. But if this point is not what I take for the beginning, you have to rely on the intuitive understanding of abstract philosophical concepts. With different people it may be different; only the words used are the same. I do not know how to compare intuitive meanings. But I know how to check that a person uses the idea of modeling correctly. Therefore, the explanation of abstract concepts in terms of the concept of modelling becomes, for me, acceptable. This is why I start with epistemology. But I repeat that you can start the discourse from any point. If you wish, start it with ontological primitives. I start with epistemological primitives.

SI expect that you will now explain, or, as you say, make more formal, what is a model, and what does it mean that it is formal or informal.

TExactly. First, about modeling. It is a kind of activity of a cybernetic system, in particular, a human being.

SAnd what is a cybernetic system?

T No comment. I believe that whatever notion of a cybernetic system you have, it will do. In due time, in this dialogue, or elsewhere in the course of the Principia Cybernetica Project, we shall give an answer to this question. But not now. This is the method of progressive, gradual, formalization.

SA convenient method, indeed! I could go on insisting that you give a definition now.

TAnd block any further discussion. This is easy to achieve by various means. To your irony I answer: yes, it is convenient. It allows to have things started. 

We can construct models of various systems. Let me call the system we are modeling simply `the world', meaning by that some part or aspect of the world as we see it. The system that constructs the models, to which I have been referring until now as `we' or `I', will be, in the third person, called the subject of knowledge. The model we discuss is a subsystem of the subject of knowledge.

The most immediate kind of a model is a system that implements the concept known in mathematics as homomorphism. This system can be described as follows (see Fig.1).

Let W₁be a state of the world as reflected in the primary sense organs of the subject of knowledge. Let R₁be the representation of the state W₁. By this I mean the existence of some procedure M (mapping) which produces R₁whenW₁is given:M(W₁) = R₁. Suppose further that the subject of knowledge takes an action a. As a result, the state W₁ changes into W₂.(Among possible actions of a cybernetic system there is the action of doing nothing: just waiting for a period of time).To be a model, the system must be able to perform one more procedure, let us call it F_a. It mimics in the model the effect of the system's action a in the world, so that F_a(R₁) = M(W₂). Thus by applying F_ato R₁ the system can predict, to some extent, the development of events if it takes action a. Then it can choose an action which helps it survive. Modeling is a powerful instrument of survival, and this is how it emerged in the course of evolution. 

SI must note that your concept of a model is not the only one. For example, if your mapping procedure, which implements a function, is replaced by a general relation, that will be again qualifying as a model, and you will find such a definition in some books.

T Yes. But I have serious reasons to choose my definition. I will discuss this later, when we come to the evolutionary origins of knowledge. 

The concept of modeling as I have defined it can be generalized by declaring a model any tool which produces predictions. My definition of a prediction is: a statement that a certain process is finite, meaning by being finite Predictions are, in principal that it comes to a certain, specified in advance, stage. In particular, the prediction supplied by the above-described model, namely F_a (M(W₁))=M(W₂)is nothing else but the `finiteness' of the process which we shall denote as Pand which can be described as follows. ApplyMto W₁then apply F_ato the result, and call X₁ the result of that. Let the cybernetic system that carriesthe model make action a. Let the resulting state of the world be W₂. ApplyM to W₂with the result X_1. Apply the comparison process to X₁and X₂. We define comparison as a process which stops when (and if) the identity (or equivalence) of X₁and X₂is established. Thus a successful end of this process means a successful end of the whole process P. Therefore, the statementF_a(M(W₁)) = M(W₂) is a prediction thatPis finite.

Predictions are, in principle, verifiable. You only have to initiate the process that it is about and wait until it comes to the final state.

As you remember, I started by tying up meaning to the cybernetic concept of knowledge. A model, or a generator of predictions, does certainly represent knowledge. However, we must not limit the whole concept of knowledge to a generator of predictions. Pieces of our knowledge (propositions) do not necessarily produce verifiable predictions, but may produce something which will produce predictions. Moreover, they may produce objects which produce objects which produce predictions, and so forth to any height of the hierarchy of knowledge objects. I will often refer to this process as hierarchical production of predictions. A simple example from mathematics: the equation x + y = y + x is not immediately verifiable, but it produces such an equation as 7 + 4 = 4 + 7. This statement, in its turn, is still too abstract for a direct verification. We can, however, verify the prediction that four apples and seven apples can be added in either order with the same result. If we take something even more abstract, like Maxwell's equations, we shall see even a longer hierarchy of specification before we come to observable facts.

I propose, therefore, the definition: a piece of knowledge is an object which we can use for hierarchical production (or generation of predictions. In a more formal way: a piece of knowledge is a generator of predictions or other pieces of knowledge. This recursive definition allows a piece of knowledge to produce a hierarchy of objects before it starts producing predictions. Note that according to my definition a thing may never start producing predictions, and still qualify as knowledge: call it empty knowledge. The reason for the inclusion of this case is that with a recursive definition of generating procedures we cannot always tell in advance if a given generator will produce a single object.

Now I have come to the point where a more formal definition offormal is due. A statement or a language is formal if its usage relies only on the `form' of linguistic objects, and not their intuitive meanings. 

SBut whose usage it is?

TA good question. My next step in making this definition more formal and precise is to specify a set of perceptions and actions which are registered and performed in the same way by all members of the society whom the languages serve. Let us refer to these perceptions and actions asuniversally defined. A language is formal if the processes involved in its usage, namely the representation function M(W) and the modeling function F_a(R),are expressed in terms of universally defined perceptions and actions. The notion of universally defined, though, cannot be formally defined. Thus, the difference between formal and informal always remains informal. 

We usually assume that universally defined perceptions and actions can be relegated to a machine. The question is still open whether this is a realistic assumption. We accept it with a qualification that if there is a doubt about a specific abstraction or action, it must be excluded from the universally defined set. Then a formal language is a language usable by a properly constructed machine. A machine of that kind becomes an objective model of reality, independent of the human brain which created it. Science is construction of such machines.

SI understand, this is the reason for your program of progressive formalization.

TExactly. We create formal versions of our common notions in order to understand better how our language and mind work, and to create artificial languages and minds, which will imitate our mental processes, and one day, perhaps, go beyond what is possible for us. By a series of consecutive formalizations, philosophy becomes science. 

Thus let us continue on this path. Our definition of knowledge allows me to further define what is meaning and what is truth. When we state something we, presumably,express our knowledge,even though it may be hypothetical or false. Thus to be meaningful, a proposition must conform to the same requirement as a piece of knowledge:we must know how to be able to produce predictions from it, or produce tools which will produce predictions, or produce tools to produce such tools, etc. If we can characterize the path from the statement to predictions in exact terms, the meaning of the statement is exact.If we visualize this path only vaguely, the meaning is vague. If we can see no path from a statement to predictions, this statement is meaningless.

SYou cannot say just ãmeaninglessä. It may be meaningless for us, but will it forever remain meaningless for everybody?

TTrue enough. This is why I said ãifwe can see no pathä. What I want to emphasize is not the subjective side of all knowledge (about which there is a general concensus nowadays), but the specific mechanics of acquiring a meaning: production of verifiable predictions. A piece of knowledgeis true if the predictions made by theuser of knowledge on the basis of this knowledge come true. Since there is no general method to determine if a recursive generator produces a result of a given kind, there is no generally applicable method to establish truths. Since sets of predictions,like multidimensional vectors, are hard to compare, there is no universal evaluation of truths. 

Remember, you asked if I have found a universal semantic principle to decide on meanings, and I said `to some extent'. My reason for being cautious is that we usually expect from such a principle that it guarantees a definite answer with respect to any question. As I have just said, there is no such principle to decide on truth, even if the statement is formal. As for the meaning, the universal principle exists if we limit ourselves to formal languages. It requires that by our construction of the statement, it is a machine which produces only predictions. However, when we push forward the frontier of theoretical knowledge, we deal with informal statements which cause flows of ideas in our heads but are not (yet!) ready for formalization as machines. There is no formal principle to judge on the validity of such statements other than wait until they yield predictions. My semantic principle only indicates the goal, but cannot offer a universal algorithm.

But I believe that this semantic principle, nevertheless, can improve mutual understandability in philosophical and methodological arguments, because it indicates the direction in which to look for resolution of conflicts: it is how what we say translates or may translate into production of predictions. I am trying to show this in our present discussion. I formulate whatever I have to say either as a model of reality, or as a way leading to construction of models. Thus I see my own philosophy as definitely meaningful.

I propose this as a general guiding principle in human attempts to understand each other. If the other side in a dialogue produces chains of words the meaning of which you cannot grasp, ask it to explain how these words are relevant for construction of the world's models. I believe, optimistically, that if both sides hold to this method, the discussion will become more meaningful.

S What is the meaning, in your theory, of the statement: The distance from Boston to Portland is 107miles. Is it formal or informal?

TIt is the prediction that the following process comes to a successful end:set the odometer in your car at zero, drive from Boston to Portland, and compare the figure at the odometer with 107. I believe this instruction is completely within the universally defined perceptions and actions. So it's meaning is formal.

S But my statement is more abstract. It does not include a specific indication at the procedure of measuring. I could go from Boston to Portland by foot.

TIf you associate the concept of distance with more than one method of measurement, the statement of the equivalence of various methods is implicit.

SDo you seriously believe that in this way you can interpret the meaning of any statement which we can express in a natural language? Even, say, from Nursery Rhymes?

TYes.

SOK. ãMary had a little lambä.

TWell, sentences of natural human languages are burdened with many different implications, often conflicting. But I can sketch how your sentence can be interpreted in terms of prediction-making. First of all, we deal here with the past tense. Which means that our statement does not directly produce predictions, but adds to what can be called an internal picture of the world, which every person has.

SAre not you retreating from your original position that all that has meaning is prediction generation?

TNot in the least. The personal picture of the world is part of prediction generation, and has meaning to the extent it helps predict. Remember the modeling scheme? We viewed F_a (R₁) as a function of the current state of the world R₁ and the parameter a, the action the subject system could take. But this function depends also on our mental picture of the world as one more parameter.

SThen what you call the picture of the world is nothing but memory.

T Almost. It is that part of memory which is relevant for prediction making. Every experience adds something to your memory, but this additionmay or may not be meaningful. IfI say to you: ãAderti was compy stallous yesterdayä, the fact that I said this may stick in your memory, but the sentence itself will add nothing to your ability to make predictions. So I say that the sentence is meaningless.

Because of the human ability to have and construct mental pictures of the world -- the faculty of imagination, to which we shall return once again -- we can treat mental pictures the same way as we treat reality. In particular, we can make `predictions' about events in our pictures which, of course, will not be predictions proper but some constructions in those pictures. If Julius Caesar in our mental picture drops an apple, we assume that it falls down, and this becomes one more element in our picture of the world. If we know that Mary had a little lamb, we can assume that she gave it some food, and it was not hamburgers and beer. In this way we reduce the meaning of past-tense texts to the meaning of texts about the present.

So, ãMary has a little lambä. Now we face a problem that is known in computer science as knowledge representation. The standard method is to decompose a natural language statement into a formula of the predicate calculus using some primitive predicates. In our case this translation may be:

$x,y [Person(x)^ Called-Mary(x) ^ Little-lamb(y)^ Has(x,y)] 

To translate back into English: ãThere exist such objects x and y that x is a person called Mary, y is a little lamb, and x has y.

Primitive predicates are defined by appealing directly to our human perception, and the predicate is true if and only if our perception - which is a certain process of verification -- comes to a successful end. For example, in order to establish thatLittle-lamb (y) is true, i.e. some object y is a little lamb, and not a big bad wolf, we just observe y and confirm that we see a lamb. The meaning of the statement Little-lamb (y) is in the prediction that the verification process ends successfully. Existential quantification, i.e. the statement ãthere exists suchy that ... etc.ä is also understood as a prediction, namely the prediction that if you start examining all the objects in the Universe -- in fact, on the Earth (this is clearly assumed in the sentence) in search of an object x which is a person and meets all other requirements, then you will sooner or later find it (and stop). The prediction is that this search is finite.

Sentences of natural languages will never allow to define their meaning in a completely formal way; not until we decompose human thought and soul into billions of billions of elementary units, which may or may not be possible, we do not know yet. But we can move (almost infinitely) in the direction of greater precision and formality. We can write a program which will distinguish between an image of a lamb and that of a wolf. To checkthat x is called Mary, we can refer to her birth certificate, or observe that x answers when addressed as Mary, etc. As in the case of distance measurement, the full definition of a concept should include all relevant tests, and a mechanism to decide on the answer when there are disagreements between...I see that you look wistfully through the window.

SYes, it may be a good idea to have a swim.

T Very well. I only want to make a few remarks to finish with epistemology.

First, my theory of meaning leads to a theory of the value, or usefulness, of information. Shannon's measure of information does not include this aspect. Obviously, one can receive huge amounts of information measured in bits and make no use of it at all. We often hear the question: how to measure useful information? My answer is: in the last analysis, information in any message is meaningful, or useful to the extent it is used for making predictions. Basically, this is the same concept of knowledge and meaning that we have been discussing today. Information is useful to a cybernetic system if it enhances its knowledge, otherwise it can be thrown out as trash. 

SYou reduce meaning to knowledge only, which in your theory is generation of predictions. But what about passing useful instructions? What about skills, the know how? You cannot deny that such instructions have meaning. But I cannot see generation of predictions there.

TNote that you used the words know how, thus treating skills as knowledge, which is quite correct. In my definition of a successful, finite process, you can distinguish two parts: the process proper -- let us denote it as P, and the test T which determines if the stage reached is final, i.e. satisfying the preset requirement. When we want to find a set of predictions, one of the following two cases usually holds. First, we can specify P and then ask what will happen, i.e. which kind of tests Twill be finally successful when following P. This is the most direct meaning of the word ãpredictionä. But equally important is the second case when we specify T and ask what kind of processP will leadto the desirable result. This is your case of useful instructions. The essential content in both cases is the same: that the process PT is finite.

My second remark is that I have tested elsewhere the validity of my approach to knowledge, meaning and truth by applying it in the field which does not allow imprecision and vagueness but requires a complete formalization and unambiguity, ? in mathematics. I have done this in [14], where a ãcyberneticä foundation of mathematics is developed, based exactly on the principle that the meaning of mathematical statements is only in recursive generation of predictions expressed in a formal language. This approach gives answers to the classical questions about mathematics; in particular, it gives a new and constructive interpretation of set theory.

Finally, I have given you no more that a very brief introduction to the way I propose to treat the problems of epistemology. Many aspects of these problems I have left out, for example, the treatment of possibility, as in ãit may be that ·ä. Many other aspects are not yet elaborated at all, and I hope to have a chance to work at those in the frame of the Principia Cybernetica Project.

2.Metasystem Transition

SIt is time to start discussing the concept of metasystem transition,which is, after all, the goal of our meeting.

T Yes, but in a moment I will have to make one more journey into philosophy.

In The Phenomenon of Science [12] I define metasystem transition as follows (see Fig.2). Imagine a system S of some kind. Suppose there is a way to makea number of copies from it, possibly with variations.Suppose that these systems are united into a new system Sâ whichhas the systems of the S type as its subsystems, and includes alsoan additional mechanism which controls the behavior and productionof the S-subsystems. Then we callSâ a metasystem with respect to S,and the creation ofSâ from S a metasystem transition (MST for short).

As a result of consecutive metasystem transitions a multilevel structure of control arises, which allows complicated forms of behavior. I show, further, that the major steps in evolution, both biological, and cultural, are nothing else but metasystem transitions of a large scope. The concept of metasystem transition allows us to introduce a kind of objective quantitative measure of organization and distinguish between evolution in the positive direction, progress, and what we consider an evolutionin in the negative direction, regress. In particular, I offer an interpretation of one of the most important aspect of the biological evolution: the appearance of human thinking and human society. 

SI am distrustful about the notion of progress because it isvalue laden -- and in a very skewed manner at that -- in our Western culture. I merely observe a progression toward complexity.

TThis is your right, of course. But in my value system this progression and the emergence of man, in particular, come with the sign plus. So I call it progress.

The Phenomenon of Science was written some twenty years ago. Since then I had a chance to read more literature on cybernetics and evolution, and I discussed the concept of metasystem transition with various people in various contexts. I am convinced more than ever that mine is a valid way of seeing the evolution of the world and predicting its future. But I feel a kind of necessity to make the concept of control more definite and precise. In cybernetic literature this concept is often identified with a very specific scheme, which I prefer to call a regulation scheme, where the metasystem's purpose is to keep a certain variable constant; see, e.g. [10]. When I speak of a hierarchy of control, I understand control in a very general sense, which includes the classical regulation scheme and any ways of duplication, variation, integration, manipulation, exploration etc. For example, the creation of the language of formal logic to make mathematical proof into a mathematical object is a typical MST, although it cannot be reduced to a regulation scheme.

So it seems to me that there must be a way of defining and using the MST concept with a concept of control which is very general and fundamental, one of the main features of being; then evolution by metasystem transitions will also become an inalienable feature of the world.But to define such a concept we need the context ofontology, the part of philosophy which is called to tell us what does it mean to be, and what, in the last analysis is the world. To define control, I want first to define being.

SIs it really necessary?

TWe could discuss the world's future without it. But the work I am doing is part of the Principia Cybernetica Project, and its purpose is to create an all-embracing, complete philosophical system on the basis of cybernetic ideas. We want to make this basis into a system of conceptual nodes which could be then used both for construction of intelligent machines, and, possibly, creation of new scientific theories.Also, if we demonstrate that our concepts form a consistent and complete picture of all that is, will make our conclusions about future more convincing. As you remember, I insisted that we start with epistemology and the principle of progressive formalization. We discussed why we needed progressive formalization. Now we shall discuss how to start it.

SWait a minute. You jumped from ontology, which is to me more or less the same as metaphysics, to formalization and intelligent computers. I still do not see the need for you to drown in the bog of metaphysics.

TI said: to start progressive formalization. Metaphysics is often viewed as something opposite to physics and utterly useless for any reasonable purpose. This attitude is a hangover from outdated forms of empiricism and positivism, namely the naive reflection-correspondence theory of language and truth, which sees language as an image, a replica of the world. It is easy to conclude from this theory that any expression of our language which cannot be immediately interpreted in terms of observable facts, is meaningless and misleading. This viewpoint in its extreme form, according to which all un observables must be banned from science, was developed by the early nineteenth-century positivism (August Comte). From this perspective, metaphysics is definitely meaningless.

But our view of language and truth is different. We understand language as a hierarchical model of reality, i.e. a device which produces predictions, and not as an image of the world. This device, especially in its higher levels of structure, need not `look like' the things it is about; it only should produce correct predictions. Therefore, the claim made by metaphysics is now read differently. To say that the real nature of the world is such and such means to propose the construction of a model of the world along such and such lines. Metaphysics creates a mental structure to serve as a basis for further refinements. Metaphysics is the beginning of physics; it provides fetuses for future theories. It may take quite a time to translate metaphysics into an exact theory with verifiable predictions. Before this is done, metaphysics is, like any fetus, highly vulnerable. But we need some metaphysics. On our agenda is the creation of universal models of the world, which would allow us, in particular, to interpret human thought expressed in natural language. How should we start this enterprise? What concepts must be taken as the basis? This is the same as to ask: what is the world? What is its ultimate essence? It is the business of metaphysics to give answers to these questions.

SSo, what is the ultimate essence of the world?

TMy answer is: action [17]. Which means that it is action that must be taken as the ultimate building element in the construction of world models. This is a truly cybernetic approach. Physics is concerned with the material of the world, the matter-energy aspect of it. Cybernetics abstracts from the material and concentrates on control, communication, information. All of these are actions.

Intuitively, we see the world as a collection of objects occupying some space and changing in time. Objects are seen as primary, change as some thing secondary, which could or could not take place. I reverse this relationship. I modify the famous Schopenhauer's formula as 

The world is action plus representation

with action taking ontological precedence over representation.

SFor Schopenhauer it was will, not action.

TYes. But the two concepts are rather close. If I understand Schopenhauer correctly, will is a universal factor that makes action possible. Will manifests itself as action. Taking action as the basis, I get closer to our usual perception of the world, yet far enough not to treat physical objects as the `true' elements of reality. Objects are representations of the world in our mind. They come into being through sensations. But sensations do not exist as objects; they are actions, a form of interaction between the subject of knowledge and the rest of the world. 

SI do not understand your ontological precedence of action over anything else. I would rather understand Schopenhauer's will as existent. At least, will is something definite, permanent. The quality of permanence is necessary for being in existence. That action can exist seems to mea contradiction, a logical absurdity.

THere we face the most intriguing part of metaphysics: the concept of ãreal existenceä. Our cybernetic epistemology, according to which all meaningful statements are hierarchical models of reality, has a double effect on the concept of existence. On the one hand, theoretical concepts, such as mechanical forces, electromagnetic and other fields and wave functions, acquire the same existential status as the material things we see around us. On the other hand, quite simple and trustworthy concepts like a heavy mass moving along a trajectory, and even the material things themselves, the egg we eat at breakfast, become as uncertain and open to discussion as theoretical concepts. 

One could argue that there is simply no need in the concept of real, or ultimate, existence, because all theories, in the last analysis, explain and organizes observable facts, which all are, and will always be, facts of our perception. This is formally true. But we still do feel a need for our theory to start with such basic entities that their existence is impossible to deny. Somehow it seems that such a theory has better chances for success.

You require permanence for things that exist. But you know that there is nothing really permanent in this world. It seems to you that there is a logical contradiction between action and existence because from the beginning, subconsciously, you identify existence with being an object. When I define existence as a feature of a theory of the world, this contradiction disappears. Thus I take the concept of action in abstracto, and on this basis try to interpret the fundamental concepts of our knowledge: what are objects, what is objective description of the world, what is space and time, etc.

SYou did not yet define what is representation.

TSure. You remember that according to our epistemology every meaningful statement is a model of reality, a dynamic entity. There are certain correspondences between the actions of the model and the actions in the real world: the former mimic the latter. All the rest in the statement, is representation. A statement is made significant by the actions involved in it; the representations used are secondary. Two models may be similar but based on completely different representations, as when we compare analogue and digital computation. While actions in our models reflect actions elsewhere in the world, our representations reflect nothing; they have no meaning of their own.

SSo, representations are objects? Passive?

TUsually we see them as objects. But the concept of an object itself isnot independent of actions; it is only an expression of a certain stability in relations between actions.

SMmm...

TI see that I must explain what in my metaphysics is an object. Suppose I am aware of a tea-pot on the table in front of me. I recognize the image on my retina as belonging to a certain set of images, the abstraction ãtea-potä. But there is more to it. I perceive the tea-pot as an object. The object ãtea-potä is certainly not a definite image on the retina of my eyes; not even a definite part of it. For when I turn my head, or walk around the table, this image changes all the time, but I still perceive the tea-pot as the same object. The tea-pot as an object must, rather, be associated with the transformation of the image on my retina which results from the changing position of my eyes. This is, of course, a purely visual concept. We can add to it a transformation which produces my tactile sensations given the position and movements of my fingers.

The general definition of an object suggested by this example consists of three parts. 

1.First we define a set R_ob of representations which are said to represent the same object; in our example this set consists of all images of the tea-pot when I look at it from different view-points, and possibly, my sensations of touching and holding it.

2.Then from the set of all possible actions we separate a subset A_cogn of actions which will be referred to as cognitive; in our case A_cogn includes such actions as looking at the tea-pot, turning my head, going around the table, touching the tea-pot etc. ? all those actions which are associated with the registration of the fact that a tea-pot is there.

3.Finally, we define a family of functions f_a(r), where for every cognitive action a ë A_congthe function 

f_a :R_ob? R_ob

transforms a representationr ? R_ob into f_a(r) = r'which is expected as a result of action a.

The most important part here is the third; the first two can be subsumedby it. We define an object b as a family of functions f_a: :

b = { f_a: a ë A_cogn}

The setA_cognis the domain of the indexa; the set R_obis the domain and co-domain of the functions of the family.

When I perceive an object b, I have a representationr which belongs to the set R_ob ;I then execute some cognitive actions, and for each such actiona I run my mental model, i.e. perform the transformationf_aonr.If this anticipated representation f_a(r) matches the actual representationrâ after the actiona:

f_a(r)=râ

then my perception of the objectb is confirmed; otherwise I may not be sure about what is going on. Observing a tea-pot I check my actual experience against what I anticipate as the result of the movements of my head and eye balls. If the two match, I perceive the tea-pot as an object. If I travel in a desert and see on the horizon castles and minarets which disappear or turn topsy-turvy as I get closer, I say that this is a mirage, an illusion, and not a real object.

The concept of an object naturally (one is tempted to say, inevitably)arises in the process of evolution. It is simply the first stage in the construction ofthe world's models. Indeed, since the sense organs of cybernetic animals are constantly moving in the environment, these actions are the first to be modeled. In the huge flow of sensations a line must be drawn between what is the result of the animal's own movements, and the other changes which do not depend on the movements, are objective. Looking for objectivity is nothing else butfactoring out certain cognitive action. Function f_a factors out the actiona by predicting what should be observed when the only change in the world is the subject's taking actiona.If the prediction comes true, we interpret this as the same kind of stability as when nothing changes at all. The concept of object fixates a certain invariance, or stability, in the perception of a cybernetic system that actively explores its environment.

SStill I find it difficult to accept your view. It goes against the whole of modern science, according to which the world exists as a collection of objects, while actions are transitions between states of the world.

TBut I do not reject this approach, I am perfectly ready to go along. The question is: what are those states? You consider them as something primary. I go further and define a state of the world as the set of all actions that can take place in this state. If these sets are identical then the states are identical. Note that in this way I reduce two basic concepts, action and state, to one: action. You cannot do the same taking leaving only state. Action as a change of state is a new concept; change cannot be expressed in static terms, as we have known starting with Zeno's paradoxes. So, on the purely logical reasons we are tempted to accept action as the only foundation of the world.

Now, consider this in the context of physics. According to our present understanding of the world, all the variety of events we observe result from elementary acts interactions between elementary particles. These acts constitute unquestionable reality, while both our theory, and our intuitive picture of the world, are only representations of reality. Furthermore, it is the physical quantity ofactionthat is quantizedby Plank's constant h. This can be seen as an indication that action should have a higher existential status than space, time, or matter. 

SWell, it is not immediately clear whether the concept of action as we understand it intuitively and the physical quantity that has the dimension of energy by time and is called ãactionä are one and the same, or related at all. 

TThis is true. That the physicists use the word ãactionä to denote this quantity could be a misleading coincidence. Yet the intuitive notion of an action as proportional to intensity (intuitive understanding of energy) and time does not seem unreasonable. Furthermore, it is operators, i.e., actions in the space of states, that represent observable (real!) physical quantities in quantum mechanics, and not the space-time states themselves!

Even if we reject these parallels and intuition as unsafe, it still remains true that neither space, time, nor matter are characterized by a single constant omnipresent quantum, but a combination of these. Is it not natural to take this combination as a basis for the picture of the world ? if not for a unifying physical theory?

SIt may be.

TWhat concepts have we already defined in our metaphysics of action?

SRepresentation, object, and state.

TGood. Now I want to define agent, freedom, and related concepts.

When we speak of an action, we speak also of an agent that performs the action. Formally, we can define an agent as a set of actions which is organized both sequentially and in parallel. We say then that every action from this set is performed by the sameagent. In a given state of the world there may be many possible actions for a given agent. We say that this agent has the freedom to choose between them. When one agent's action restricts the freedom of another agent, we speak of causation. In the extreme case no freedom may be left to the agent; such an agent is referred to as a (deterministic) machine.

SWhy do agents only restrict other agents? Why you exclude the cases where an action increases the freedom? For example, you can let somebody out of jail, thus increasing his freedom.

TNote, however, that I let the guy out by restricting the freedom of locks and jailers to keep him inside. I think this is a general rule. Whenever an action increases freedom, it does so by restricting restrictions. 

Agents are, of course, representations, not actions. But we distinguish them from passive objects.We break down all representations into agents and objects. Both agents and objects are defined, in the last analysis, by actions; agents - by those actions they perform, objects by the actions through which they are perceived, as those I denoted f_a(r) above.

SYou defined agents as sets of actions. Now you say that agents are representation, not actions. Is this not a contradiction?

TNo. From a purely formal set-theoretical point of view, a set of actions is not an action itself. I used the set-theoretical language in order to give a concise definition, as they do in mathematics. You remember that one of the definitions of a real number in calculus is that it is a set of rational numbers. Here is does not mean is the same as you may see the same girl on two different pictures. A real number is a concept on its own, an element of our prediction machines. A set of rational numbers defines one real number as different from others.

Now I introduce an important relation between agents andobjects, which I will call, following[8] and [6], the semantic relation. The action which an agent A is about to perform very often depends on a certain object b. We shall call b acode, agent A its interpreter, the action ofAinterpretation, and the relation betweenAandba semantic relation; we say thatbinformsA. Often we want to distinguish between the objectband the information it carries. Information is an abstraction from the object in a semantic relationship, where only those features are left which have bearing on the actions ofA. Thus two texts carry the same information for the reader if they different only in the font they are set in.

I believe that the existence of semantic relations is such a fundamental feature of the world that it cannot be reduced to, or defined through, anything more primitive. If there were no semantic relations, there cou