This is chapter 7 of the "The
Phenomenon of Science" by Valentin F.
THE FIRST THING we must do to approach the problem of language and thinking correctly is to clearly separate what we know about thinking from what we do not know. We know that thinking is a process that takes place in the nerve nets of the brain. Because the tern ''representation" to us means a state of some subsystem of the brain it may be said that thinking is the process of change in the aggregate of self-representations. But at any given moment in time only a certain (obviously small) part of these representations is accessible to, as we say, our consciousness. These representations can be consolidated into one (for several subsystems taken together constitute a new subsystem), which is the state of consciousness at the given moment. We do not know what consciousness is from a cybernetic point of view: we have only fragmentary information (specifically, that consciousness is closely related to the activity of what is called the reticular formation of the brain).
Thus, thinking has an external, manifest aspect: a stream of conscious representations. This stream can be fixed and studied, and from it we try to draw conclusions indirectly about those processes in the brain which are illuminated by consciousness. We are fairly sure about some things regarding the stream of consciousness. We know that it is regulated to a significant degree by associations of representations which form under the influence of experience and reflect the characteristics of our environment. Specifically, we receive our ability to foresee future situations to one degree or another thanks to the association of representations. We also know that humans, unlike animals, have the ability to control the process of association; this is manifested as imagination, encoding, and conscious memorization. But we do not know the concrete cybernetic mechanism of this ability or, as a matter of fact, the mechanism of the association of representations. These mechanisms are not given to us subjectively either: in the stream of consciousness we merely observe their appearance, the result of their action. Finally, we are subjectively given a sensation of freedom of choice in our actions: free will. Free will also manifests itself in thinking. We are able to turn our thoughts to any subject we wish. We do not know the cybernetic interpretation of free will either, and this situation is perhaps worst of all.
REPRESENTATIONS of linguistic objects, words and sentences, occupy a distinct place among all representations in the process of thinking. These representations are (with the exception of deaf mutes, of course) a combination of aural and motor representations and (for people who have dealt with written language from childhood) the visual component may also be joined to them. When we picture a certain word in our mind we mentally pronounce it, listen, and possibly see it written. For brevity we will call these linguistic representations. The stream of linguistic representations is precisely what is ordinarily called thinking. The presence of this stream is a specifically human characteristic; it is not found in animals. So-called ''abstract'' thinking is actually thinking in words, the stream of linguistic representations. Without such thinking, the achievements of thought in which the human race takes such pride would have been impossible.
The significance of linguistic representations is that they are uniquely related to words and sentences as the material elements of the material system ''language.'' This system is the aggregate of all words and sentences pronounced orally, transmitted by telephone and radio, written on paper, encoded on punched cards for computers, and so on--in short, the aggregate of what we have called the higher nervous system of the material body of culture. Functionally, a stream of linguistic representations in no way differs from a sequence of their material correlatives: words. The external, observed aspect of thinking may be described as activity consisting of the creation of certain material linguistic objects, for example pronouncing sentences out loud (unfortunately these objects are very short-lived) or writing them on paper. We shall call this activity linguistic.
There are compelling reasons to consider linguistic activity the basic, primary aspect of thinking and the stream of linguistic representations merely a transitional element--a form of connection between the material linguistic objects and the aggregate of all (not just linguistic) representations. In fact, it is precisely the linguistic objects which store and transmit information and operate as the elements of linguistic models of reality. The child is taught linguistic activity in the same way as it is taught to walk, shoot a bow, or hammer nails. As a result the child becomes, so to speak, plugged into the language: he uses the models already available and enriches it with new ones. Furthermore, he may also use language in a noncommunicative manner (for his own purposes) as did the young man Uu of the Nyam nyam tribe when he counted the enemy with his fingers. During noncommunicative use of language there may be a stream of linguistic representations without apparent linguistic activity (''I think!''); but after all, these representations emerged and acquired their meanings as a result of activity involving substantial, material linguistic objects! And often during the process of reflection we whisper certain words and whole phrases, returning them to their material form. The primacy of substantive linguistic activity is especially clear when we are dealing with scientific models of reality. After long, hard study with real, written symbols a person may be able to multiply a few small numbers or reduce similar elements of an algebraic expression in his head. But give him a problem that is a little harder and he will demand a pencil and paper!
Linguistics and logic investigate linguistic activity. Linguistics is interested primarily in the syntax of language (in the broad, semiotic sense) while logic is chiefly interested in semantics. When syntax and semantics are interwoven it is not possible to separate linguistics from logic. It is true that traditional logic declares itself to be the science of the laws of thinking, not the science of language, but this pretentious statement should not be taken too seriously. Of all the fields of knowledge which study thinking, logic has the most external, superficial approach. It does not investigate the real mechanisms of the work of the brain, as neurophysiology does; it does not construct models of mental activity, as cybernetics does; and it does not attempt to record and classify subjectively perceived emotional states, as psychology does. It recognizes only precise, socially significant thoughts (not the ravings of a madman!) as its object of study. But such thoughts are in fact nothing else but linguistic representations with socially significant semantics. Logical (semantic) analysis of language leads to primary, undefinable concepts and stops there; it does not take us beyond language. Logic also contains its theory of proof. If language is used in a form of notation which keeps within the rules of predicate calculus, not in the form of natural language, it is possible to establish the formal characteristics of the correctness of deductions and formal rules which, if used, will always yield correct conclusions from correct premises. These rules (the laws of logic), which are also expressed in the form of a linguistic object, form a metasystem in relation to the statements obtained as a result of application of the rules.
Figure 7.1. Logic as a metasystem.
Sentences are the object and result of work for the theory of proof. Thus, all of logic lies wholly in the sphere of linguistic activity. Its lower stage is semantic analysis and its higher stage is the theory of proof. We will talk about proof theory later; for now we are interested in the lower stage (it may even be called the foundation): the relationship between language and the working of the brain.
We shall consider that by logical analysis we can translate any sentence in natural language into the language of logic. Of course, this somewhat exaggerates the advances made to date, but it is fairly clear that in principle there is nothing impossible about it. Logical analysis reveals the internal structure of language, the fundamental nodes of which it consists. Therefore we shall review the basic concepts of the language of logic, clarify exactly why they are as they are, and discover how they are related to brain activity. Whereas in the last chapter we were primarily concerned with the syntax of language, here we shall pose the question of the semantics of language.
FIRST LET US try to find direct correlatives of language elements in brain activity. The first concept we introduced in our description of the language of logic was the statement. With what can it be correlated? The answer suggests itself: the association of representations. Indeed, like the brain, language is a system used to create models of reality. In the case of the brain the basic independent unit that can operate as a model is the association of representations, while in the case of language it is the statement.
Now there is a temptation to correlate the representation to the object. At first glance this creates a complete and harmonious interpretation: the object corresponds to the representation; the relation among objects, which is the statement, corresponds to the relation among representations, which is the association. We may take the example of the association ''In the forest there are wolves,'' which we gave in chapter 4, and interpret it as follows: "forest'' and "wolves" are objects and, at the same time, representations, while "In the forest there are wolves'' is a statement and, at the same time, an association.
But a careful analysis shows that this interpretation involves a serious mistaken assumption; we have artificially transferred linguistic structure to the sphere of representations. In reality this sphere has no such structure. Begin from the fact that an association of representations is also a representation. A representation may be correlated with the sentence ''In the forest there are wolves'' just as it may be correlated with the nouns ''forest'' and ''wolves.'' We should recall that an association between representations S1 and S2 is a new synthetic representation U (see figure 3.8). It is true that the association of representations is a model of reality, but if we understand the term ''model'' in the broad sense as a certain correlative of reality, any representation is a model. If, however, we understand model in the narrow sense as a correlative of reality which permits us to predict future states, then not any association can be a model, but only one that reflects the temporal aspect of reality. The process of associating is important, because it leads to the creation of a new model where none existed before. This process permits completely strict logical definition and can be revealed by experiment, similar to the way we easily define and uncover the process of the formation of a system from subsystems. But it is impossible to define the difference between an association of representations and a representation just as it is impossible to establish criteria that would distinguish a system from subsystems.
So the statement elicits a representation and the object elicits a representation and our harmonious system crumbles. The representation proves too broad and too indefinite a concept to be made the basis of a study of the semantics of language. All we know about the representation is that it is a generalized state of the brain, but we know virtually nothing about the structure of the brain.
In chapter 4 we defined language as the aggregate of objects Li each of which is the name of a certain object Ri, which is called its meaning. Concerning objects R we said only that they are some kind of real phenomena. The time has now come to work toward a more precise answer as to what kind of phenomena these are: in other words, the question is ''what are the semantics of natural language?''
In the simplest examples usually given to illustrate the relationship Li-Ri and which we cited above (the word lion--the animal lion, and so on), the object Ri is a representation of a definite object. In general, language emerges as the result of an association between linguistic and other representations, and therefore it is natural to attempt to define the semantics of language by means of those representations which emerge in the process of linguistic activity. It can be said that the meaning of a linguistic object is that representation which it evokes--the change in the state of the brain which occurs when a representation about a linguistic object appears in the consciousness. This definition is entirely correct, but unfortunately it is unproductive because the states of the brain as objective reality are not directly accessible to us, and we make our judgments about them on the basis of their manifestation in human actions only.
Therefore let us take another route. We shall view the brain as a black box; we shall investigate the observed manifestations of its activity without any attempt to understand its internal organization. We are interested in the semantics of language, the connection (associations) between linguistic representations and all others.
Figure 7.2. The brain as a black box.
Because the representations are inside the "black box," however, we shall rely only on the input data corresponding to them-- which is to say the linguistic objects and all the other activity that, for the sake of brevity, we shall call nonlinguistic. This is the input of the black box. Its output is obviously the person's observed actions
Because the system of actions is very complex, we shall not make progress in our attempts to study semantics if we do not choose some simple type of action as a standard. Of course there must be at least two variants of the action so that it will carry some information. Suppose there are exactly two. We shall call them the first and second standard actions. We shall formulate the elementary act in studying semantics as follows. Linguistic objects will be presented to a person who is perceiving a definite nonlinguistic reality and we shall assume that he responds to them by performing one of the two standard actions.
WE CONCEIVED this scheme in a purely theoretical manner as the simplest method of defining the semantics of language under conditions where the brain is pictured as a black box. It turns out that this scheme actually exists in linguistic activity, emerging spontaneously in the early stages of the development of language! In all known languages we find expressions for two standard actions--affirmation and negation. These actions are of great antiquity, as evidenced by the fact that among a large majority of peoples (possibly all) they are expressed in gestures as well as words. If we open the top of the black box just a crack, to the degree shown in figure 7.2, we can define the affirmation as an action performed when the linguistic object and reality are in the relation name-meaning (that is, the necessary association exists between the linguistic and nonlinguistic representations), and we can define negation as the action performed when there is no such relation. But a person learning to use affirmative and negative words and gestures correctly knows nothing, of course, about representations, associations, and the like. At first he is simply taught to say "cat,'' "dog," and so forth while pointing at the corresponding objects, and then he is taught to perform the affirmative action when someone says ''this is a cat'' while pointing at one and to perform the negative action when someone makes the same statement while pointing at a dog. In both instances we learn correct linguistic activity while relying on the brain's ability to recognize and associate; but we have no knowledge of the brain s mechanisms; to us it is a black box.
The last remark explains why it is hardly surprising that the scheme of standard actions has become an established part of linguistic practice. A person's brain is a black box both for himself and for other members of society. This is the origin of the need for a socially meaningful way of determining more precise semantics; this need appears as soon as language reaches a minimum level of complexity.
The standard actions of affirmation and negation are not related to reality itself, as primary linguistic objects are; rather they refer to the relationship between primary linguistic objects and reality. They are elements of a metasystem in relation to the system of primary linguistic objects. The introduction of the actions of affirmation and negation into the practice of society was the beginning of that metasystem transition within linguistic activity whose subsequent stages are the appearance of the language of logic and the theory of deduction. Although affirmation and negation appeared very early in the development of human culture, they did not appear sufficiently early for a prototype of them to be found in animal actions. We know that such prototypes exist for primary linguistic objects in the form of animal signals. Among these signals there are ones which could be described as affirmative and negative, but they have nothing in common with the semantic actions of affirmation and negation which are oriented to the signals themselves and lay the foundations of the metasystem. In this we see one more manifestation of the law of branching (expansion) of the penultimate level. The enormous growth in the number of primary linguistic objects (signals) which is found in human society began simultaneously with the beginning of the metalevel.
NOW IT WILL not be difficult for us to interpret the basic concepts of logic from the point of view of the phenomenological (''black box'') approach. The statement is obviously the linguistic object to which the actions of affirmation and negation refer. The semantics of a language appear to an external observer as the function of two free variables (the statement and the true state of affairs); the function assumes one of two truth values: ''true'' (''yes,'' ''truth'') and ''untrue' (''no,", ''falsehood"). The value of this function is worked out by the black box, the human brain, which knows the given language. How this happens the external observer does not know.
The statement is the basic unit of language. In considering language as a system we must discover how the statement, a system of statements of subsystems, can be constructed. Thus we come to the introduction of logical connectives, which were discussed in the preceding chapter.
Reality is perceived by the human being through the medium of the sense organs; it appears to the human being as an aggregate of receptor states, a situation If a person were unable to control his sense organs and concentrate his attention on certain parts of the situation, that is, if the situation always appeared to a person as something whole and completely given from outside, then all logic would probably be limited to propositional (statement) calculus. But a person can control his sense organs and can, for example, fix his vision on a particular object. Therefore the situation is not simply reality, it is reality with an attention characteristic--that is, with an isolated area (approximately defined) which we are speaking about and on which we concentrate our attention. The concept of attention also has a psychological aspect, but we shall try to bypass it. We can determine from observing a person what he is looking at (or feeling, smelling, and so on), because the attention characteristic can be determined objectively. Reality with the attention characteristic can therefore be viewed as a free variable of the function in the ''black box" approach. People resort to gestures or verbal clarifications to define the position of the area of attention more precisely. In either case the result will be the same. If you say, ''I am looking at the thick book the girl in the pink dress is holding in her hands,'' the person you are talking to will look around until he locates the girl and the book.
The temporal aspect of the input data of semantics must also be taken into account. If the reaction of the brain were determined only by the situation at one specific moment, unrelated to situations close in time, once again logic would probably be limited to propositional calculus. In fact, however, the brain stores its memory of many past situations; the brain's reaction (and specifically, the standard action) is therefore always a function of the moving picture of situations. We often fail to recognize this because there are in the environment around us objects which show a relative invariability, and when we concentrate our attention on the invariant object it seems to us that we are not dealing with a moving picture but rather with a single frame. In actuality, the analysis of the concept of object which was given above shows that the time aspect plays the decisive part in it. Now, when we have introduced the concept of the attention characteristic we can define the object as a moving picture of situations with the attention characteristic represented by one continuous line.
The extent to which we are inclined to ignore the dynamic aspect of perception can be seen from the situation we ordinarily describe as the existence of at least two distinct objects. It seems to us that we are perceiving each object separately and still we distinguish among all the objects and concentrate our attention on them simultaneously. But the simplest psychological self-analysis will persuade us that in fact in such a case our attention darts rapidly from one object to another. In the moving picture of situations, the line of the attention characteristic will be broken; it will, indeed, easily become possible to make several (according to the number of objects) continuous lines .
Figure 7.3. Broken line of attention out of which two continuous lines can be formed
We have now come to defining the concept of the object in logic. We have established that the "nonlinguistic activity," shown in 7.2, which is fed to the input of the black box is often broken, divided up in space and time. It can be imagined as a moving picture on which the line of movement of the attention characteristic is drawn in. Moreover, it turns out that this line can be broken to become several continuous lines. These continuous lines are the objects.
Thus the object of logic is wholly liberated from its material meaning; this is transferred to statements about the given object. The object is an identifier. Its only attribute is to be identical to itself and it signifies a continuous line of attention. This proposition has already been explained in sufficient detail in the preceding chapter.
When in place of undivided reality we feed to the input of the black box a reality divided into objects, the statement becomes dependent on the method of division--that is, on the objects we are singling out; the statement is converted into the predicate.
WE HAVE ALMOST completed our analysis of the fundamentals of logic from the black-box point of view. We have still to define the general concept of ''logical concept,'' but that is simple: the concept is the predicate or logical connective. The grounds for this are that predicates and connectives are those basic functional nodes we discover in linguistic activity. The concept of function in the sense that we have defined it above may not be elevated to the rank of the basic logical concept because, as we have seen, it can be expressed through predicates and connectives. But in the broader sense both logical connectives and predicates are functions--that is, correlations by a certain method of values (truth values in the given case) to free variables. Thus it can be said that the logical concept is a function whose free variables are linguistic objects and situations and whose values are linguistic objects. The result of a logical analysis of language is a breakdown of linguistic activity into homotypic functional elements: connectives and predicates.
Every logical concept is defined in the first place by its material carrier, the linguistic object (in most cases a word or phrase), and in the second place by the method of using this object in linguistic activity in society. The second point offers an opportunity to refine the first. The words ''koshka,'' ''koshka,'' ''KOSHKA,'' and koshka [Russian for ''cat''] are different linguistic objects (the first two differ by their placement while the third and fourth also differ by their type face) but we consider them to be carriers of a single concept because they appear indistinguishable in linguistic activity. The same thing can be said--with certain restrictions--about the German die Katze, for it is used analogously (but only analogously!) to the Russian koshka.
The concepts of a language form a hierarchical system. In certain specialized languages (sublanguages) used by the exact sciences this hierarchy is determined in a completely clear and strict manner. The concepts located higher in the hierarchy acquire their meaning by logical definitions through concepts of a lower order--that is, it is pointed out how, being able to determine the truth values of the predicates at a lower level, one can determine the value of the predicate of a higher level. In natural languages there is no strict hierarchy, but there is an approximate one. We can therefore assess the ''degree of remoteness'' of a concept from the direct data of experience by logical analysis and breaking complex concepts down into simpler components; the degree of remoteness of a concept from direct experience can be equated with its elevation in the hierarchy. This estimate of position in the hierarchy is approximate, because the breakdown in the components is not unambiguous, the actual method of subdividing has not been fully formalized, and no one has yet done such work for all language. Perhaps the most firmly established fact is that the predicates which cannot be subdivided at all are primary (belonging to the lowest level of the hierarchy).
Between the concepts of a language there are numerous interconnections given by the set of all true statements in which the concepts under consideration are included. Language is a system and its concepts have meaning only as elements of the system. The meaning of a word is determined by the way this word is used in linguistic activity. Each word, so to speak, bears the imprint of all the sentences in which it has ever been included; it is an element of the system. When traditional logic speaks of concepts, the two functions of the concept are pointed out: to serve as an element of reasoning--that is, a method of shaping thought--and at the same time to concentrate already existing thoughts and knowledge of an object in oneself. This duality is a result of the system nature of the concept. The linguistic object (word) which expresses a concept is used as an element for constructing a model of reality and is associated functionally--that is, in linguistic activity (and therefore also in our imagination)--with all models in which it participates. Therefore, although a trained dog does distinguish between a square and a circle, it cannot be said that it has mastered the concept of ''square''; this word includes many things about which the dog does not have the slightest idea. Therefore also the most exact translation from one language to another is by no means always a literal translation; the difference between the systems must be taken into account. Strictly speaking, an absolutely exact translation is generally impossible (with the possible exception of statements which contain only primary concepts accessible to a dog).
WE HAVE DEFINED the logical concept as an element of the functioning of the linguistic system. We shall now attempt to give a more general definition of the cybernetic concept of ''concept,'' relying on the structural rather than the functional approach.
Let us again consider the concept ''inside'' in application to the picture discriminator. How would we begin to build a system that contains the concept inside''? It is apparent that at first we would have to construct classifiers for the concepts of ''spot'' and ''contour." Let us recall that the classifier is a cybernetic system that recognizes the affiliation of an input state (''situation'') with a definite set (Aristotelian concept), and converts it to an output state that reflects the most important characteristics of the situation. The spot classifier, for example, recognizes the existence of a spot and fixes the coordinates of the points which bound it.
In figure 7.4 we have designated the classifiers of spots and contours by the letters [pi]1, [pi]2,. . .. and K1, K2, . . . These classifiers form the first level of a hierarchy, for their input is the states of the receptors. They translate the situation from the language of illuminated points to the language of spots and contours.
Having constructed the first level, we begin work on the second. We construct classifier B (as in figure 7.4) to whose input is fed the output of one spot classifier, [pi]i, we shall assume, and one contour classifier, Kj. Classifier B must have just two output states: one (''yes ') occurs when the spot fixed by classifier [pi]i lies inside the contour fixed by classifier Kj, while the second (''no'') occurs in the opposite case. We would like classifier B to be applicable to any pair ([pi]i, Kj). But it would be insanity to make as many copies of B as there are pairs ([pi]i, Kj)! therefore we need some kind of switching device by means of which information from different points of the system could be fed to the one and only device B. Because it is meaningless to feed information directly from the receptors or from any other inappropriate points to a classifier, the switch should be designed so that it is able to feed information from any of the pairs ([pi]i, Kj) and nothing else.
Classifier B is located on the second level of the overall system. It may possibly be used as an input for the third level. For example, let us suppose that the system is required to recognize the concept "enter into . . ." This is a dynamic concept related to time. As the input here we must consider not one situation but rather a series--that which above was called a moving picture of situations. With such a moving picture we say that the spot has ''entered into'' a contour if at first it was outside the contour and then assumed a position inside it. It is apparent that the discriminator of the concept ''enter into'' (in figure 7.4 it is designated BB) will require at its input the output from discriminator B or from several discriminators B' related to different frames of the moving picture (in the first case it should have a device for storing the sequence of ''yes'' or ''no'' answers).
A hierarchy of classifiers has been obtained. For us this is not new; in chapter 2 we considered hierarchies of classifiers. But in that chapter we limited ourselves to Aristotelian concepts, and the hierarchy of classifiers acted solely as a means of recognizing concepts and was not included in the definition of the concept of the ''concept.'' We defined the concept of the ''concept'' (Aristotelian) independently of the organization of the hierarchy of classifiers as a certain set of situations--in other words a function that assumes a truth value of ''true'' in the given set of situations.
But now, searching for a cybernetic interpretation of such concepts as ''inside,'' we see that we cannot define the more general concept of ''concept'' by relying on the level of receptors alone; instead it can only be defined as an element of a system of concepts. Corresponding to the concept of ''inside'' in figure 7.4 is the classifier B, not only as a device which converts the given input into the given output but also as a subsystem of the total recognition system-- that is, as an element connected in a certain way with other elements of the system (in the particular case, receiving input information from one type [pi] classifier and one type K classifier).
We have constructed a cybernetic model of the concept ''inside'' But how is this model related to reality? What relationship does it have to the true concept of "inside,'' which manifests itself in language and appears to us as one of the elements of our thinking? Can it be asserted that the brain has a classifier that corresponds exactly to the concept of ''inside''?
Although the general appearance of the diagram in figure 7.4 with its receptors and classifiers reflects neurophysiological findings, the concrete functions of the classifiers and their interrelationships reflect logical data. Therefore our diagram is not a model of the organization of the brain, but rather a model of the functioning of the linguistic system--or more precisely a structural diagram of a device that could perform the functions discovered in linguistic activity. In this device the classifiers perform the functions described by logical concepts and the switching devices (which are not shown in the diagram but mentioned in the text) fix the domain of definition of the concepts .
The diagram shown in figure 7.4 may be embodied in a real cybernetic device whose sources of information will be the illuminated points of a screen. But even if such a device works very well it will not, strictly speaking, yet give us the right to consider it a model of the organization of the brain. Possibly the division of the nerve nets into classifiers as suggested by figure 7.4 or analogous diagrams taken from the functioning of language does not reflect the true organization of the brain at all!
WE HAVE BEFORE US two cybernetic systems. The first system is the human brain. Its functioning is individual human thinking. Its task is to coordinate the actions of separate parts of the organism in order to preserve its existence. This task is accomplished, specifically, by creating models of reality whose material body is the nerve nets and which we therefore call neuronal models. We know that the brain is organized on the hierarchical principle. We call the structural elements of this hierarchy classifiers. The functions of the classifiers. considering their systems aspect--which is to say their interrelationships--are the individual concepts (in the cybernetic sense of the word, which simply means according to the cybernetic definition of the concept of ''concept''), which may be identified in the functioning of the brain as a whole. We will call them neuronal concepts. The second system is language. Its functioning is linguistic activity in society. Its task is to coordinate the actions of individual members of society in order to preserve its existence. This task is accomplished, specifically, by creating models of reality whose material body is linguistic objects and which we therefore call linguistic models. Like the brain, language is organized hierarchically. The functional elements of this hierarchical system are the logical (linguistic) concepts.
These systems are by no means independent. The linguistic system is set in motion by the human brain. Without the brain, language is dead. On the other hand, the brain is strongly influenced by language.
Now the problem may be formulated as follows: what is the relationship between neuronal and logical concepts? Let us survey the sources of information about these systems of concepts. Logical concepts are on full display before us: phenomenologically speaking, we know virtually everything that can be known about them. We know very little about neuronal concepts. Neurophysiological research offers some information about the lowest levels of the hierarchy only; about the higher levels we have absolutely no information which is independent of language. But we do know that language is an offspring and, in a certain sense, a continuation of the brain. Therefore a close relationship must exist between the highest stages of neuronal concepts and the lowest stages of logical concepts. After all, logical concepts came from somewhere! The logical concept of an object unquestionably has a very definite neuronal correlative; that is, long before the appearance of language and independent of it the world presented itself to people (and animals) as an aggregate of objects. From the ease with which people and animals recognize some relations among objects (in particular transformations in time) we may conclude that there is also a special neuron apparatus for relations among a small number of objects. It can scarcely be accidental that the languages of all people have words that signify the objects surrounding human beings and words for the simplest relations among them--such as the relation of ''inside,'' which we used as an example above. Thus figure 7.4 can be considered a model of brain organization with a certain probability after all!
When speaking of neuronal models and concepts we have in mind not only the inborn foundation of these concepts but also those concrete concepts which form on this foundation through the action of the stream of sensations. In higher animals and human beings the formation of new concepts as a result of association of representations plays an enormous part, as we know. It begins from the moment the individual appears on earth and develops especially intensively at a young age, when the conceptual ''flesh'' fills out the congenital conceptual ''skeleton.'' This introduces a new element into the problem of the mutual relations of neuronal and logical concepts. Those initial neuronal concepts which form in a baby before it begins to understand speech and talk can be considered independent of language, and then logical concepts can be considered reflections of them. But the more complex concepts form in a baby under the direct and very powerful influence of language. The associations of representations which make up the basis of these concepts are dictated by society's linguistic activity; to a significant degree they are thrust upon the child by adults during the process of teaching the language. Therefore, when we analyze the interrelations of linguistic activity and thinking and attempt to evaluate the degree to which the language is a continuation of the brain we cannot view neuronal nets as a given against which the logical concepts of the particular language should be compared. Considering the inverse influence of linguistic activity on thinking, the question can only be put as follows: what would the neuronal and logical concepts be like if the development of language were to follow this or that particular path?
THE INFORMATION capacity of the brain is incomparably greater than that of language (in the process of speech). Language does not reflect the full wealth of sensations and cognitive representations. We know, for example, that the ancient Greek language had just one word for both dark blue and green; as a result they had just one concept in place of our two. Does this mean that they perceived color differently? Of course not. The human eye distinguishes hundreds of nuances of color but only a few words exist to denote them.
The primary logical concepts may be compared with buttresses or, better, with pilings driven into the ground of the neuronal concepts. They penetrate to a certain depth and occupy just a small part of the area. Floor by floor the entire building, the hierarchy of concepts of the language, is erected on these piles. We take pride in the building because it contains concepts which were not even conceived of at ground level, among the neuronal concepts. But have the pilings been driven well? Could they have been driven at other points and is it too late now to drive additional ones? How does this affect the building? In other words, is the selection of primary predicates fundamental for the development of language, culture, and thinking? We rarely ask ourselves this question because we do not see the ground itself; it is covered by the edifice of language. But if we go down under the floor we can touch the original soil and feel around in the darkness with our hands. By doing this we may learn once again how much of the ground is not touched by the pilings (especially in the sphere of spiritual experience) and we shall recall the words of the poet Tyutchev: ''The thought expressed is a lie.''
From this metaphor one more question arises: how good is the architecture of the building? Is it the only possible architecture, and if not, how much does its selection influence the functioning of the edifice, the possibility of expansion, remodeling, and so on? In other words, is the grammar of language (at least in its most important, fundamental features) something external and unimportant for thinking, or does it fundamentally affect thinking and direct its development?
We have formulated both of these questions, concerning the effect of selection of primary predicates and of grammar, in a form requiring a yes or no answer only for purposes of clear presentation. The point is not, of course, to answer them simply by yes or no. The answer will always, in the last analysis, contain a conditional element, and the fact that there is some influence is undoubted. Our job is to investigate real findings regarding language's influence on thinking.
THE WORK of two American linguists, E. Sapir and B. Whorf, is very interesting from this point of view. The following quote, which Whorf used as the epigraph to his article ''The Relation of Habitual Thought and Behavior to Language,'' gives an idea of Sapir's views:
Human beings do not live in the objective world alone, nor alone in the world of social activity as ordinarily understood, but are very much at the mercy of the particular language which has become the medium of expression for their society. It is quite an illusion to imagine that one adjusts to reality essentially without the use of language and that language is merely an incidental means of solving specific problems of communication or reflection. The fact of the matter is that the ''real world'' is to a large extent unconsciously built up on the language habits of the group.... We see and hear and otherwise experience very largely as we do because the language habits of our community predispose certain choices of interpretation.
B. Whorf takes this conception as his basis and gives it concrete form in his studies of certain Indian languages and cultures and his comparisons of them with European languages and culture. We will present some of Whorf's observations and thoughts on such logical categories as space and time, form and content.
Whorf notes that to correctly evaluate such categories one must first reject those views regarding the interaction of language and thought which are ordinarily considered an integral part of ''common sense'' and are called, by Whorf, ''natural logic.'' He writes:
Natural logic says that talking is merely an incidental process concerned strictly with communication, not with formulation of ideas. Talking, or the use of language, is supposed only to express what is essentially already formulated non-linguistically. Formulation is an independent process, called thought or thinking, and is supposed to be largely indifferent to the nature of particular languages. Languages have grammars, which are assumed to be merely norms of conventional and social correctness, but the use of languages is supposed to be guided not so much by them as by correct, rational, or intelligent thinking.
Thought, in this view, does not depend on grammar but on laws of logic or reason which are supposed to be the same for all observers of the universe--to represent a rationale in the universe that can be ''found" independently by all intelligent observers, whether they speak Chinese or Choctaw. In our own culture, the formulations of mathematics and of formal logic have acquired the reputation of dealing with this order of things, i.e., with the realm and laws of pure thought. Natural logic holds that different languages are essentially parallel methods for expressing this one-and-the-same rationale of thought and, hence, differ really in but minor ways which may seem important only because they are seen at close range. It holds that mathematics, symbolic logic, philosophy, and so on, are systems contrasted with language which deal directly with this realm of thought, not that they are themselves specialized extensions of language.
This conception has taken such deep root that we are not even aware that it can be subjected to critical analysis. Similarly, we are only aware that we breathe air when we begin to experience a scarcity of it. Whorf gives one more illustration. Suppose that owing to a certain defect in vision a certain people can perceive only the color blue. For them the very term ''blue'' will be deprived of the meaning which we give it by contrasting it with red, yellow, and the other colors. In the same way, a large majority of people who talk, or at least think, in only one language are simply unaware of the limitations it imposes and the arbitrary element it contains. With nothing with which they can compare their language, its limitations and arbitrary character naturally seem to them universal and unconditional. When linguists conducted critical investigations of large numbers of languages, the structures of which differed greatly, they encountered violations of rules they formerly had considered as universal. It turned out that grammar is not simply an instrument for reproducing thought, but a program and guide for the thinking activity of the individual. Whorf writes:
'We dissect nature along lines laid down by our native languages. The categories and types that we isolate from the world of phenomena we do not find there because they stare every observer in the face; on the contrary, the world is presented in a kaleidoscopic flux of impressions which has to be organized by our minds--and this means largely by the linguistic systems in our minds.'' 
It should be noted here that Whorf is plainly carried away when he speaks of organizing the stream of impressions, and he incorrectly describes the division of labor between the neuron system and the linguistic system, ascribing the organization of impressions ''largely'' to the linguistic system. In reality, of course, a very large part of the work of initial organization of impressions is done at the neuron level and what language receives is no longer the raw material, but rather a semifinished product processed in a completely definite manner. Here Whorf makes the same mistake in relation to the neuron system as ''natural logic'' makes (and Whorf correctly points out!) in relation to the linguistic system. He underestimates the neuron system because it is the same in all people.
It is difficult to conclude that the linguistic system is important for the organization of impressions if we restrict ourselves to a comparison of modern European languages, and possibly also Latin and Ancient Greek. In their fundamental features the systems of these languages coincide, which was an argument in favor of the conception of natural logic. But this coincidence is entirely explained by the fact that the European languages (with minor exceptions) belong to the single family of Indo-European languages, are constructed generally according to the same plan, and have common historical roots, moreover, for a long period of time they participated in creation of a common culture and in large part this culture, especially in the intellectual area, developed under the determining influence of two Indo-European languages: Greek and Latin. To estimate the breadth of the range of possible grammars one must refer to more linguistic material. The languages of the American Indians, the Hopi, Shawnee. Nutka, and others, serve as such material for Whorf. In comparison with them the European languages are so similar to one another that, for convenience in making comparisons, Whorf consolidates them into one "Standard Average European'' language.
STANDARD AVERAGE EUROPEAN has two types of nouns which denote material parts of the world around us. Nouns in the first group--such as ''a tree,'' ''a stick,'' ''a man,'' and the like--refer to definite objects which have a definite form. Nouns of the second group--such as ''water,'' ''milk,'' and "meat''--denote homogeneous masses that do not have definite boundaries. There is a very clear grammatical distinction between these groups: the nouns which denote substances do not have a plural case. In English the article before them is dropped, while in French the partitive article is placed in front of them. If we think deeply about the meaning of the difference between these two types of objects, however, it becomes clear that they do not differ from one another so clearly in reality as in language, and possibly there is no actual difference whatsoever. Water, milk, and meat are found in nature only in the form of large or small bodies of definite shape. The difference between the two groups of nouns is thrust upon us by language and often proves so inconvenient that we must use constructions such as ''piece of meat'' or ''glass of water,'' although the word ''piece'' does not indicate any definite shape and the word ''glass,'' although it assumes a certain shape, introduces nothing but confusion because when we say ''glass of water'' we have in mind only a quantity of water, not its shape in the container. Our language would not lose any expressive force if the word "meat" meant a piece of meat and the word ''water'' meant a certain amount of water.
This is exactly the case in the Hopi language. In their language all nouns denote objects and have singular and plural forms. The nouns we translate as nouns of the second group (substances) do not refer to bodies which have no shape and size, but rather to one where these characteristics are not indicated, where they are ignored in the process of abstraction just as the concept of ''stone'' does not indicate shape and the concept of ''sphere'' does not indicate size.
Therefore the concept of substance as something which has material existence and at the same time cannot in principle have any shape could obviously not occur among the Hopi or be understood by a person speaking only the Hopi language. In European culture the concept of substance emerges as a generalization of the concepts which express nouns of the second group while the generalization of concepts which express nouns of the first group leads to the concept of the object. For the Hopi, in whose language there is no division of nouns into two groups, only one generalization is possible and it leads, of course, to the concept of object (or body), for it is possible to abstract from the shape of an observed material object but it cannot be said that it does not exist. The intellectual division of everything existing into a certain nonmaterial form (shape) and a material, but non-form content (substance), which is so typical of traditional European philosophy, will probably seem to the Hopi to be an unnecessary invention. And he will be right! (This is not Whorf's remark, but mine.) The concept of substance, which played such an important part in the arguments among the Medieval Scholastics, has completely disappeared in modern science.
WE WILL NOW take up one more interesting difference between the Hopi language and the Average European Standard. In the European languages the plural forms and cardinal numbers are used in two cases: (1) when they signify an aggregate of objects which form a real group in space and (2) to classify events in time, when the cardinal number does not correspond to any real aggregate. We say ten men" and ''ten days.'' We can picture ten men as a real group, for example ten men on a street corner. But we cannot picture ten days as the aggregate of a group. If it is a group, then it is imagined and consists not of ''days,'' for a day is not an object, but of some objects which are arbitrarily linked to days, for example pages of a calendar or segments in a drawing. In this way we convey a time sequence and a spatial aggregate with the same linguistic apparatus, and it seems to us that this similarity is in the nature of things. In reality this is not true at all. The relations to be "later'' and ''to be located near" do not have anything in common subjectively. The resemblance between a time sequence and a spatial aggregate is not given to us in perception, but rather in language. This is confirmed by the existence of languages in which there is no such resemblance.
In the Hopi language the plural forms and cardinal numbers are used only to designate objects which may form real groups. The expression ''ten days'' is not used. Instead of saying '"They stayed ten days," the Hopi will say ''They left after the tenth day." One cannot say ''Ten days is more than nine days,'' one must say "The tenth day is after the ninth.''
Whorf calls the European representation of time objectiviced because it mentally converts the subjective perception of time as something ''which becomes later and later'' into some kind of objectively (or, it would be better to say, objectively) given objects located in external space. This representation is dictated by our linguistic system, which uses the same numbers both to express temporal relations and to measure spatial quantities and designate spatial relations. This is objectivization. Such terms as ''summer.'' "September,'' morning," and "sunset'' are nouns in our languages just as the words which designate real objects are. We say "at sunset'' just as we say "at a corner,'' "in September", just as we say ''in London.''
In the Hopi language all time terms such as summer, morning, and the like are not nouns, they are special adverbial forms (to us, the terminology of the Average European Standard). They are a special part of speech which is distinguished from nouns, verbs, an even from other adverbs. They are not used as subjects, objects, for any other noun function. Of course they have to be translated ''in the summer,'' ''in the morning,'' and so on, but they are not derivatives of any nouns. There is no objectivization of time whatsoever.
In European culture the very concept of ''time'' is a result of the objectivization of the relation of ''earlier-later'' combined with our notion of substance. In our imagination we create nonexistent objects such as year,'' ''day,'' and ''second,'' and we call the substance of which they consist "time.'' We say ''a little time'' and ''a lot of time" and we ask someone to give us an hour of time as if we were asking for a quart of milk. The Hopi have no basis for a term with this meaning.
The tripartite (past, present, future) verbal system of the Average European Standard directly reflects the objectivization of time. Time is represented as an infinite straight line along which a point is moving (usually from left to right). This point is the present, while to its left is the past and to the right is the future. In the Hopi language, as one might assume, things are different. Their verbs do not have tenses as the European verbs do. Verb forms reflect the source of information and its nature. And this corresponds more closely to reality than the three-tense system. After all, when we say "we shall go to the movies tomorrow,'' this does not reflect what will actually occur but only our intention to go to the movies, an intention that exists now and may change at any minute. The same thing applies to past time.
ALL THAT HAS BEEN said in no way leads to the conclusion that the objectivization of time is a bad thing, that we ought to renounce it and change to a Hopi-type language. On the contrary, the most important traits of European culture which have secured such an outstanding place for it--its historical sense (interest in the past, dating, chronicles) and the development of the exact sciences--are linked to the objectivization of time. Science in the only form we yet know it could not have existed without the objectivization of time. The correlation of temporal to spatial relations and the following step, the measurement of time, amounted to the construction of a definite model of sensory experience. It may be that this was the first model created at the level of language. Like any model, it contains an element of arbitrary and willful treatment of reality, but this does not mean that it must be discarded. It must, however, be improved. To improve it, we must conceive of it as a model, not as the primary given. In this respect linguistic analysis is extremely useful because it teaches us to distinguish the relative from the absolute; it teaches us to see the relative and conditional in what at first glance seems absolute and unconditional. Thus, Whorf calls his conception the conception of linguistic relativity.
There is a curious similarity here with the physical theory of relativity. Objectivized time is the foundation of classical Newtonian mechanics. Because the imagined space into which we project time is in no way linked to real space, we picture time as something that "flows'' evenly at all points in real space. Einstein dared to reconsider this notion and showed that it is not upheld in experimental data and that it should be rejected. But as we know very well, this rejection does not come without difficulty, because, as Whorf writes: "The offhand answer, laying the blame upon intuition for our slowness in discovering mysteries of the cosmos, such as relativity, is the wrong one. The right answer is: Newtonian space, time, and matter are no intuitions. They are recepts from culture and language. That is where Newton got them.'' Once again here we should temper the statements of the enthusiastic linguist. Newtonian concepts, of course, rely directly on our intuition. But this intuition itself is not a pure reflection of primary sensory experience, of the ''kaleidoscopic flux of impressions''; rather it is a product of the organization of this experience, and language and culture really do play a considerable part in this organization.
LANGUAGE EMERGES when the phenomena of reality are encoded in linguistic objects. But after its origin language itself becomes a phenomenon of reality. Linguistic objects become very important elements of social activity and are included in human life like tools and household accessories. And just as the human being creates new tools for the manufacture and refinement of other tools so he creates new linguistic objects to describe the reality which already contains linguistic objects. A metasystem transition within the system of language occurs. Because the new linguistic objects are in their turn elements of reality and may become objects of encoding, the metasytem transition may be repeated an unlimited number of times. Like other cybernetic systems we have considered in this book, language, is a part of the developing universe and is developing itself. And like other systems, language--and together with it thinking--is undergoing qualitative changes through metasystem transitions of varying scale, that is to say, transitions which encompass more or less important subsystems of the language system.
With all the physical-chemical differences that exist between the linguistic system and the neuronal system it is easy to see that, functionally, metasystem transitions in language are a natural continuation of the metasystem transitions in the neuronal structures, serving to create more highly refined models of reality. To clarify this thought let us look again at the diagram in figure 7.4, this time viewing it as a diagram of a device for processing information coming from an illuminated screen and, consequently, as a partial (and crude) model of the organization of the brain. In the diagram we see classifiers which correspond to the concepts of ''spot,'' ''contour,'' "inside,'' and "enter into.'' These concepts stand at different levels of the hierarchy and the number of levels is in principle unlimited. But let us ask: how is it possible that there could be a metasystem transition of such large scale that it would be represented not by adding a new level to figure 7.4 but as a departure from the plane of the drawing in general, as the creation of a new plane'?
If we compare our artificial system to real biological systems it corresponds to a nerve net with a rigidly fixed hierarchy of concepts This is the stage of the complex reflex. To reach a new plane would signify the transition to the stage of associating, when the system of connections among classifiers becomes controlled.
The concepts involved in figure 7.4 are taken from language. In addition, there are in language concepts that ''go outside the plane'' of the diagram. Regarding the concept ''inside'' we can say that it is an example of a spatial relation among objects. Other examples of spatial relations are the concepts ''touches,'' ''intersects,'' and ''between" Classifiers to recognize these concepts could be added to the diagram But how about the very concept ''spatial relation"? It is the sought-for metaconcept in relation to the concepts ''inside,'' ''between, and so on; its relation to them is that of name to meaning. If we were able to think of a way to embody the concept of "spatial relation in the form of some kind of device that supplements the device in figure 7.4, it would plainly have to form a metasystem in relation to such classifiers as "inside,'' ''between,'' and others. The task it would be able to perform would be modifying the structure of work of these classifiers or creating new ones that recognize some new spatial relation. But is not the very purpose of the appearance of the concept of ''spatial relation'' in language itself to achieve a better understanding of how the linguistic system works--to modify it and create new concepts? Most certainly it is. The metasystem transition in the development of language performs the same role as it does in the development of neuronal structures.
CONCEPTS SUCH AS that of "spatial relation'' rely on reality indirectly, through the mediation of intermediate linguistic structures. They become possible as a result of a certain linguistic construction, and therefore we shall call them constructs. Statements containing constructs demand a certain linguistic activity to establish their truth or falsehood. Concept-constructs do not exist outside the linguistic system. For example, the concept of ''spatial relation'' cannot arise where there are no words "inside,'' "between,'' and so on, although the corresponding neuronal concepts may have existed for a long time.
We can now make a survey of the levels of language viewed as a control hierarchy. We shall take the signals of animals for the zero level of language. The appearance of the standard actions of affirmation and negation, logical connectives, and predicates is, as we have already said, a metasystem transition. They create the first level of language. The next metasystem transition forms the second level of language, whose concepts are constructs. Among the concepts are grammar and logic. At the first level, grammar and logic are the highest control systems that create language but are not themselves subject to control; however, at the second level they become objects of study and control (artificial construction). The second level of language may be called the level of constructs, and also the level of selfdescription.
The level of development of language determines the relation between the linguistic and the neuronal systems. At the zero level. Language transmits only elementary control information: at the first level it acquires the ability to fix and transmit certain models of reality, but only those models which already exist at the neuronal level. First-level language may be represented as a copy or photograph of neuronal models (taking into account the inverse of language as corrective). Finally, at the level of constructs language becomes able to fix models of reality which could not (bearing in mind the given biological species of the human being) occur at the neuronal level. Such models are called theories.
We have cited numbers and operations with them as the simplest and most graphic example of models that do not exist at the neuronal level and are created at the language level. Arithmetic was one of the first theories created by the human race. It is easy to see that numbers, or more precisely large numbers, are constructs. Neuronal concepts correspond to the numbers two and three; we distinguish two objects from three and from one at the first glance. But the number 137 is a construct; it has meaning only to the extent that the number 136 has meaning, which in its turn relies on the number 135 and so on. Here there is a metasystem transition, the emergence of the process of counting which generates concrete numbers. Within the framework of the metasystem of counting, a hierarchy by complexity arises: the natural series of numbers. The appearance of the concept of ''number'' marks a new metasystem transition which assumes that counting has become an established part of everyday life. An abstract concept of ''number'' is not required for counting: it only becomes necessary when people begin to think about counting. The concept of the number is a construct of a higher level than concrete numbers. The concepts of arithmetic operations are located at the same level.
On the second level of language we have consolidated all the concepts which do not rely directly on neuronal concepts but rather require auxiliary linguistic constructions. With such a definition the second level is the last one formally, but it contains a control hierarchy that forms through metasystem transitions and may in principle be as high as one likes. We have seen this in the example of concrete numbers and the concept of ''number.'' Metasystem transitions can differ in scale and occur in relation to different subsystems of language. Therefore, second-level language has a complex structure which can be figuratively pictured not in the form of even layers lying one upon the other but in the form of a building or complex of buildings with vertical and horizontal structure. Different control hierarchies and hierarchies of complexity generated by the subsystems become interwoven and form a multifaceted architectural complex. Second-level language is the language of philosophy and science. First-level language is ordinarily called ''everyday'' or "conversational'' language.
IT IS SOMETIMES SAID that the human being can think in abstract concepts, whereas abstract concepts are inaccessible to the animal, who can attain only a few concrete concepts. If the term ''abstract'' is understood (as is the case here) to mean devoid of nonessential characteristics, this assertion will not withstand even the slightest criticism. We have seen that the crucial distinguishing feature in human thinking is the presence of control of associations, which manifests itself above all as a capability for imagination. As for a difference in the concepts, in any case it cannot be reduced to an opposition between abstract and concrete. Every concept is abstract. The concept of cat is abstract for the dog because, for example, it contains an abstraction from the coloring of the cat (a nonessential characteristic). If we measure mental capabilities by the degree of abstraction of concepts the frog will prove to be one of the most intelligent animals, for it thinks with just two concepts, albeit extremely abstract ones: "something small and rapidly moving" and ''something large, dark, and not moving very rapidly.'' As you see, our language does not even have special terms for these concepts.
The truly profound difference between the conceptual apparatus of higher animals and that of human beings is that animals cannot attain concept-constructs; these concepts assume a capability for linguistic activity. It is not abstract concepts which distinguish human thinking; it is concept-constructs. In partial justification of the statement above, we should note that the expression "abstract concept" is commonly used to refer to precisely what we call the concept construct, and people talk about the degree of abstraction where they should actually speak of the ''construct quality" [''konstruktnost''--the degree to which constructs are used--trans.]. It is true that the concept of number is formed by abstraction starting from concrete numbers and that the concept of the spatial relation begins from concrete relations; but the distinctive feature here is not actual process of abstraction (which, as we have seen, appeared in the very early stages of the cybernetic period of life), rather it is the fact that in the process of abstraction linguistic objects play the most essential part. The principal thing here is construction not abstraction. Abstraction without construction simply leads to loss of meaning, to concepts such as ''something'' and "some."
 Quoted from Novoe v lingvistike (New Developments in Linguistics). No 1. Moscow, 1960. [Original Whorf article in Language, Culture, and Personality, Menasha. Wisconsin, 19 41, pp 75-93.
 I have taken the quotes by Whorf from the above-mentioned Soviet publication.
 [Original article, ''Science and Linguistics,'' in The Technology Review 42 no 6 (April 1940), Massachusetts Institute of Technology.]
 "Science and Linguistics."
 [Original article, ''The Relation of Habitual Thought and Behavior to Language," published in Language, Culture and Personality (Menasha, Wisconsin: Sapir Memorial Publication Fund 1941), pp. 75-93.]