The Impossibility of Non-identity Languages

by Ralph E. Kenyon, Jr.

OCT 17, 1988

Published in

General Semantics Bulletin 55, 1990

We often hear the cry, from us general semanticists, that the structure of our language is not similar to the structure of events. We use the extensional devices to remind us of this fact and bemoan the lack of a language with a structure similar to the nonverbal "reality". (1) Let us examine what would happen if we try to devise a language with a structure which does mirror the structure, as we understand it, of nonverbal "reality", the event level. I shall show that such a language is impossible. Claims of impossibility don't seem to be well received -- to quote someone who said it well:

Historically speaking nobody "likes" a "negative" demonstration of this type. Everyone who finds his current endeavors proved in principle impossible to complete hates to have his personal judgment of what problems in his field of interest merit labor and study, and his self-esteem concerning what challenges he can hope to meet and surmount, so conclusively disconfirmed; and almost everybody else finds such demonstrations "hard to understand".

Yet in every instance I know of, the "negative" demonstration has had highly "positive" consequences. (2)

To strive for precision about what 'impossible' means in this context, we need to consider what we normally mean by 'language'. If by 'language' we mean a symbol system used for communicating, then a non-identity "language" is truly impossible. If, on the other hand, by 'language' we mean a token system satisfying certain structural rules, but having nothing to do with communication, then this kind of (uninteresting and useless) "language" may be possible to construct, but cannot be used for communication.

How do we describe the structure, as we understand it, of nonverbal "reality", the event level? We often cite Heraclitus as the father of the general-semantic view that the world is a continually changing process, that never are two things the same, and that, at the macroscopic level, nothing remains the same for even the shortest period of time. We use the extensional device called 'dating' to indicate that the things referred to are constantly changing (Process nature of reality.) Heraclitus of Ephesus (about 500 to 460 B.C.) said: "You cannot step twice into the same river, for other waters are continually flowing on." (3) Riverstep 1 ceases to be and riverstep 2 comes to be. (This sure sounds like dating to me!) We also use the extensional device called 'indexing' to indicate that the things referred to by the same word are different (no two things are the same). (Dog1 is not Dog2, etc.) To use the extensional device called the 'hyphen', and speak in terms consistent with our view of modern physics, we would say "No distinct space-time events are identical1".

As a matter of fact, our usual notion of event is unclear in terms of space-time coordinates. We usually treat events as having the character of "atoms" -- indivisible -- but anything we normally call an event can usually be described as composed of smaller events. Between any two distinct such events, we can find others. So, what we mean by the term 'event' bears a closer examination. A single "event" in space-time, "identified" by its space-time coordinates, has no duration and no extension; this kind of "event" is not very interesting as the topic of a discussion (except, perhaps, among particle physicists). I won't go further into the examination of the difficulties with the notion of "event" here, as it is less significant to the main thrust of this paper, but we do need to be aware of the problematic nature of "events".

Dating distinguishes different temporal coordinates among events and indexing distinguishes different spatial coordinates among events. We can argue that 'indexing' is a more general term and that dating is a special case of indexing, one limited to differences in time. In any case, we distinguish among space-time events referred to with the same word by adding an indexing scheme.

I indexed 'identical' above because I will be distinguishing among different uses of the term. 'Identical1' is the kind of "sameness" that "things were said to be" back in the time of the ancient Greek philosophers. The philosophers' way of showing the nature of the concept of the identity1 of a thing is to argue that if two things are the same, then there weren't two things after all; there was only one thing called by different names. Identity1 has sometimes been called 'self-identity'.

Identity1 was just what concerned Aristotle in his famous work De Generatione et Coruptione. (4) In his efforts to disambiguate the "many ways in which things are said to be" he required the indication of two distinct levels (of abstraction) to distinguish between two usages. In the implied use where it is said "a thing changes" both levels are conflated. How can a thing change? Then there would be two things, not the same, yet we do say (Bob Pula's "change thinging" notwithstanding) "It is the same thing that changed". In order to resolve this difficulty, Aristotle differentiated between the substratum, which did not change, and the (unnamed) level at which change did occur. Aristotle explained (within the limits of his language) that what we say is the "same thing", but changed, requires that that which remains the same be the substratum. While he was ostensibly reporting on the differences in opinion of earlier philosophers, he clarified and explained the different ways "things were said to be" in a way very consistent with our modern general-semantic view. (From today's paradigm, we would say that he disambiguated the uses of the verb 'to be'.) He pointed out that at the level at which change occurs, the process of change entails that one thing "ceases to be" as the other "comes to be". In modern general semantics terms, we would say that the level at which change occurs (something ceases to be while being replaced by another that comes to be) corresponds to lower levels of abstraction, while Aristotle's substratum corresponds to our higher levels of abstraction. The "river" (the substratum which is the abstract general-semantic "relative invariant") remains the same, while "riverstep 1" ceases to be and "riverstep 2" comes to be.

Now, from a general-semantics perspective, we deny that there "is" a "river", since that very ascription is a projection onto the event level by the static shape of our words. Our words embody identity1. If we were to point out some event/thing (even though that may be problematic itself), the language we use to point to such an "event" would have to be highly indexed. As general semanticists, we do not deny that there may be some structure at the event level, but we do deny that we can know that structure other than by maps which are necessarily different from "it". But we do assume that we can talk about it, although in an indirect way. We do talk about "rivers", and in communicating with others, these more abstract levels of "organizing" our experiences are just what we do want to talk about. But I'm getting ahead of myself. We know today that the observer sees and reacts to "things", and in the process, evaluates two "things" as being "identical2".

This new use of the term 'identical', which we shall call a new term 'identical2', is different from self-identity. In identity2 someone is evaluating different things, making an implied classification scheme, and evaluating things as to which category in that (implied) classification scheme the things fit, namely, the same class. The mathematical identity relation is this kind of identity2 and could be called 'class-identity'. Self-identity and class-identity differ in level of abstraction. Aristotle's substratum corresponds to a reification of our level of abstraction focusing on those properties of an object that remain the same during a change of some other properties; it reifies the category into which the prior and subsequent things are evaluated as "being".

The problem of conflating or confusing these two levels of abstraction gives rise to a third form: identity3 -- confusing two levels of abstraction. This technical use of the term 'identity3' in general semantics describes our evaluation process in which we react to one level of abstracting as if it were another level of abstracting. For example, we can identify3 a description with an evaluation. We can forget that our own mental map (of "reality") is only a map and react as if it were "reality". When we do this we are identifying3.

Let us examine the structure, order, and relations among these three forms of identity and put them into perspective. Identity1 applied to "physical reality" focuses on metaphysical issues; it speaks to the nature of an event without regard for questions about how we might know about the nature of the event. Since general semanticists focus on epistemological issues, such a metaphysical question is deemed moot. However, identity1, applied to higher levels of abstracting, focuses on whatever categories and classification schemes we use to organize our experiences and perceptions. Each category we form is relatively "self-identical" for the duration of its use. Identity1 may be said to apply to each category (itself) during the period of its relative invariance. identity2 however, applies at a level of abstraction below a particular category scheme. Individual items at a lower level of abstraction may be viewed by us "in terms of characteristics" abstracted to one of the higher level abstraction categories. By virtue of being assigned to, or abstracted into the "same" category, two distinct items get related as identical2. Identifying3 is treating or responding to an item in a category as if it were the category itself. Gilbert Ryle called it "a category mistake" (5) and we general semanticists call it confusing orders of abstraction. It seems to me that identifying3 equates across orders or levels of abstracting. To sum up, identity1 applies to one thing (at a time), identity2 applies to two things at the same level of abstraction, and identity3 applies to two things at different levels of abstracting. Each requires more "structure" than its predecessor.

Most general semanticists generally eschew identifying3; however, it seems to me that this need not "always" be the case. Sometimes identifying3 is undesirable, such as when we are self-blocking by confusing "I don't know how to do it" with "It cannot be done". Sometimes identifying3 is desirable, such as when we read words and respond in terms of their meanings rather than their shapes. The undesirable kind is emphasized by general semanticists and the desirable kind is all but ignored. Imagine reading as a process wherein we were most aware of the shapes of the words and had to consciously stop and dredge up the associated meaning for every word read. It would be a slow and tedious process not unlike the beginning student of a foreign language who has to stop and translate every word with conscious effort. The sooner the person internalizes responding to the shape of the words (low level abstraction) in terms of their "meanings" (high level of abstraction), the faster that person becomes facile with the language. But, responding to the low level of abstraction in terms of the high level of abstraction is just what we mean by "identifying across levels of abstraction"; and that is just what we mean by identity3. Let me not skip over a very important qualifier; the response must be immediate to be properly called identifying3. It must also be done "unconsciously". If we are not conscious that we are abstracting from the lower level shape to the higher level associated meanings, and we are responding immediately, then we are identifying3 the (lower level) shape with the (higher level) meaning.

In terms of human processing, we respond to our inputs by finding an "appropriate" level of abstraction. If we do not abstract enough and respond in terms of an organization scheme which is too detailed (getting bogged down in details, or missing the forest for the trees), or if we abstract too far and respond in terms of an organization scheme which is not detailed enough (fails to make significant differentiations, or can't get down to cases), then our response would not be "appropriate". Responding to our inputs with either too detailed a level of organization or too little organization usually reduces our "success" in dealing with our environment.

Our perceptual categorization scheme, when projected onto our environment, embodies identity1. Taken to the extreme in the focus on the "physical world", we would say that a single "event" (labeled with some space-time coordinates) has the character of being self-identical; it is identical1 with itself and nothing else. Of course, we admit that we can never "get ahold of it"; we can only have our map of "it". Nevertheless, it is only at this "bottom level" in the "mad dance of electrons" that a single point-event has the self-identical property. We are not even sure how that could be pointed to, what with quantum mechanics and Heisenberg uncertainty issues affecting our means of knowing about "it". It's believed that even this lowest level "is" only the projection of our category onto "what is going on". As such, it does has the property of being "self-identical".

Organizing our experience into categories which are self-identical often takes place at nonverbal levels of abstracting. We experience the trapezoidal window as a "square" oriented at a particular angle (which is changing) (6); this experience, which we label with the term 'square', is one of the (many) nonverbal categories that we organize our experiences into. In the process, many varied and different lower level experiences get abstracted into one relatively invariant category. These many varied and different experiences are "identical2" to each other and are "identified3" into the "identical1" experience category which we subsequently label with the term 'square'.

Two levels of abstraction are involved; items which at their particular level of abstraction are each self-identical, but distinct from each other, are also identical2 by virtue of their being related to the identical1 item at a higher level of abstraction in an inter-level order relation called 'identity3'.

In our perceptual and conceptual organizing structure, we tacitly "decide" at what level of abstraction to organize our individual experiences. The undesirable use of identifying3 applies in the case in which someone responds to their experience in terms of an organization scheme which is too abstract. Confusing the map with the territory is often cited as an example. (Strictly speaking, the response must also be "tacit" or unconscious in order to qualify as identifying3 and is usually also an "immediate" response. More on this is the topic of another paper.)

Often people verbalize the "first evaluation that comes into their mind", and such verbalizations may express nonverbal evaluations which are at too high a level of abstraction to be appropriate. For example, it is a common response for people to evaluate something as being "impossible, it can't be done", as their first verbal response to some putative task; their experience is that they have never heard of it being done and haven't the foggiest notion of how it might be done. A verbal rendition of the argument might go: "It hasn't been done because it can't be done; if it could have been done, it would have already been done, and I'd have heard about it." This is particularly true of so-called "experts" (and they often turn out to be right), but the argument is flawed.

The philosophers know that this is a fallacy confusing the epistemological and the metaphysical issues by not distinguishing between the possibility of something and the knowledge of it. The evaluation process in which one unconsciously or "tacitly" abstracts from "we do not know how [creativity] could be taught" to the more abstract evaluation "[creativity] cannot be taught" is a specific example of identifying3 in this pejorative sense. The abstraction process takes place at nonverbal levels until the final stage when one assigns words to describe one's experiences. Higher level verbal abstraction can continue -- such as when we react to our own formulations and produce more formulations.

Identifying3 (and the associated identifying2) take place largely at nonverbal levels of abstracting. A maze-wise flatworm presented with a new maze will treat the new maze as if its map of the old maze were correct. (7) The flatworm has no consciousness of abstracting, so cannot discover its error. It must learn the new maze by trial and error until it replaces its old map with a new one. A person looking at the trapezoidal window and "seeing" a square has identified3 before any verbal levels of abstracting have been achieved.

According to our best neurological and anatomical "knowledge", we are very much aware that our experience of "seeing" is abstracted from the event level and happens in our brain after the events which gave rise to the sensations of seeing things. We project our brain experience on "reality" and identify3 our brain experiences with "reality" so well that it has taken centuries of science to make ourselves aware of the process, and even then we constantly forget that "We ain't seein' IT." Socrates (469-399 B.C.) described the process using the parable of the cave, recorded in Plato's Republic. (8) The dialogue tells of mankind seeing only the shadows on the wall of the cave. This so-called "metaphor of the cave" is an early recognition of our modern general-semantics principle that we cannot directly know what is going on (the event level); we can only construct maps of "it".

A main difference between Plato and us is that Plato took what we call the higher level of abstraction, toward the "intellect", as being the greater "reality", while we now ascribe a greater ("physical") reality to the lower levels of abstraction, toward the event level. There is still the contrast between major schools of philosophy, namely Idealism and Realism, which differ in the direction each claims is toward the greater reality. Of course, Realism with its many subtle variants is more in vogue today than Idealism, and the views of the more subtle forms seem to be approaching closer and closer to the general-semantics view. (But that is a topic for another paper.)

"Plato's heaven", as the ideal plane is sometimes called, forms a significant part of our environment, while the "What Is Going On" (WIGO) comprises another significant part. Our semantic environment seems as "real" to us as does our "physical" environment. We take numbers, for example, for granted. Of course the general-semantics orientation which "prefers" an extensional orientation would claim that this kind of "real" exists only in our semantic reactions, and is somehow, therefore, "less real". A semantic quibble. Our semantic environments are just as important, and affect us just as much as our physical environment. Our usage of the term 'real', which stems from the Latin 'res' (a thing) and used to mean only that which "physically exists" is evolving and we now apply it to that which is not a "thing".

I argue that since we react to and are affected strongly by both directions, it is moot to argue which has "more reality". (It's essentially a "political" argument about how we should use the term 'real'.) By taking this pragmatic point of view, I claim we can get on with more important tasks.

As part of the belief that lower levels of abstraction are "closer" to "reality", some general semanticists seek to devise languages with structures more similar to the structure of nonverbal "reality" (as we believe it to be) than is the structure of the language we currently use. When Korzybski (9) indicated the extensional devices for use in pointing toward the region where nonverbal "reality" differs from our language structure, he started the trend among general semanticists. It would seem only natural that one of his followers continue the "implied" direction and attempt to design or engineer a language with a structure similar to nonverbal "reality" with the purpose of achieving the "ideal" Korzybski seemed to be pointing toward. Dr. C. A. Hilgartner (Andy) has spent 25 years of his life working toward exactly that goal. According to Andy, he has "built up [his] language theory three times and shot it down twice". (10) Unfortunately, it's time for a third shooting.

I regret to report that a careful analysis of the problem shows that the difficulty with creating such a language is more than just a technical matter. It is, in principle, flawed by a misconception regarding what language does for us; in short, the task is not possible. Andy keyed on certain of Korzybski's insights and attempted to design a language which satisfies several general-semantics notions and principles. To take the observer into consideration was a goal that seems to be achieved. Moreover, to embody the notion of abstracting so that that which is selected is indicated (easy) and that which is not selected is also indicated (not so easy) seems to have been incorporated. However, when Andy claimed to have built non-identity into the language he went too far. According to Andy, his new formal language "disallows" identity in all three forms. Even if such a goal were desirable, and there is significant question regarding whether it is, Andy has not achieved it.

The insights Andy used to provide direction for his effort seem to be good ones, and may be used in enhancing our consciousness of abstraction; they can even be used to develop a formal language which does allow identity1 and identity2. No language, however, can be engineered in such a way as to completely eliminate identity3 because that form of identity is not always a function of the structure of the language. It takes place in the nervous system at lower levels of abstracting than verbal. Even flat-worms do it. The structure of our language can not change the fact that we see the trapezoidal window as oscillating when it feels to be rotating. My earlier discussion has shown that identity3 is a general activity of nervous systems and not a property of language structure alone. One cannot engineer a language with a structure that always prevents what happens at neurological levels.

It is only through our use of language to build a complex model of the abstraction process that we can point to where in the model of that process identification3 takes place. The language in which we build this structure has terms which are self-identical (identity1), and it includes various verbs which allow identifying2 and identifying3. 'To be' is popular because it does both jobs, verbally representing the processes that we undergo predominately at nonverbal levels. The very model itself is a complex organization of many distinct instances of the process into a relatively invariant structure.

Andy says we should build a language whose structure neither embodies nor allows any of the three forms of identity. Well, any term or symbol must embody identity1 (if it is to be written more than once). Also, the fact that persons engage in identifying2 or identifying3 at nonverbal levels limits any "preventing" effect from the structure of the language. In those cases abstracting further into a language structure would be on the basis of the identifying2 or identifying3 having already been done.

By using our present language (which does embody "identity") to depict the process of abstracting as an organization scheme for our behaving, we can point at the various parts in the process and thereby help to educate one to reduce inappropriate identifying3. However, since these processes take place largely at nonverbal levels, changes in the language structure itself can not automatically correct for "wrong" evaluation.

Andy Hilgartner characterized words as being self-identical, and therefore not having a structure similar to "reality" (which we characterize as continually changing). In devising his language, he required that the correct syntax entail four terms that embody the Korzybskian undefined terms 'structure', 'order', and 'relation'. Each correct statement required, first, one term from the three; second, one of the remaining two terms paired; and third, the remaining term. Each term includes subscripts and superscripts in both prefix and postfix positions. The superscripts and subscripts, among other things, embody the dating and indexing extensional devices. (11) (12) (2)

These details do not matter when it comes to showing the impossibility of designing a language free from identity1. To use one of Andy's insights, we need, for a moment, to flip "figure" and "background" and talk about (some of) the context in which language use takes place.

The business of life consists in organizing our life experiences into a categorization scheme so that that scheme may be used to effectively respond to future life situations. In this scheme, experiences in one category are identified2 as being "the same". While they are not the same, the degree to which they differ does not make a noticeable difference in terms of our responding behavior. Also, our individual responding behaviors will differ from time to time, but often not to the degree that our classification scheme need be changed.

In practice we will periodically revise both the classification scheme for organizing our experiences as well as that which organizes our behavioral options, but for some periods of time the categories will be unchanging. During such periods each category will be self-identical (identical1 to itself).

When we communicate with others, what is of interest as time-binders is sharing with them information about our individual categorization schemes themselves. We will cite examples in the process, but that which constitutes time-binding is the passing on of the information we have learned about organizing our life's experiences. We talk about the self-identical categories themselves.

Now, a language which has self-identical terms is ideally suited for communicating about such a category scheme, in which the categories are self-identical. However, a language in which there are no self-identical structures cannot communicate about anything that is self-identical. Every "correct" expression in the (non-identity) language would have to be unique. (Remember, the language does not embody identity in any of its forms, and its structure mirrors physical "reality".) Since there are no self-identical structures in such a language, there is no way to refer to self-identical categories. Therefore, the language cannot be used to talk about the very things which are of the most interest in time-binding. Since no two expressions are the same, nothing can be expressed twice. And, since we cannot express anything more than once, it can never be talked about again. In a nutshell, a language without "identity" cannot be used for communication. Bob Pula has been expressing a concern over the past several years as to what totally non-identifying persons would be like. Well, totally non-identifying language users cannot be time-binders, because they cannot communicate.

On the other hand, suppose the language was modified so that one expression could be "correctly" written more than once. Since the second writing is the same expression as the first writing, the language is embodying the very identity it is supposed to prevent.

This poses a significant dilemma. If we are successful in designing a language free from identity1, we cannot communicate with it. On the other horn, if we have a language in which we can communicate, then it must embody identity1 and provide for identity2. Moreover, no language can eliminate the possibility of identity3.

This does not mean that we cannot change features of a language to help us remember that identification takes place. The general-semantics principles, consciousness of abstracting, levels and orders of abstracting, and the structural differential, all help us to remember that we can identify3 across levels of abstraction.

There is no substitute for a communications environment in which nigh everyone continually uses the general semantics principles and helps us to remember. Unfortunately, it can be easy to slip into "bad" habits in an environment of colleagues not schooled in general semantics; "when in Rome do as the Romans do...".


This paper has shown several results:

1. A language which is free from identity can not be used for communication and no language that can be used for communication can be free from identity.

2. No language can be designed to "engineer out" identification across orders of abstracting.

3. Time-binding requires languages with identity.


1. As a supplement to the usual conventions, I use the standard philosophical convention in which double quotes are "scare" quotes and single quotes indicate the distinction called the 'use-mention distinction' (Frege's name of a term). In this sentence, the first occurrence of the word 'word' is used, while the second occurrence is mentioned. Single quotes are used to set off a mentioned term; however, there is a convention to eliminate the quotes when it is clear that the term is mentioned. I could leave off the quotes in the above sentence without risking confusion because the presence of 'the word' clearly marks the second occurrence as a mention. "Scare" quotes derive from Frege's "sense" of a term; the quotes explicitly warn the reader that the "sense" of the term in the immediate context may not be the usual one. On Sense and Reference (1892), Readings in Semantics, University of Illinois Press, 1974. [This convention varies from the customary GSB style, in which single quotes are cautionary, and double quotes or underlining would signal the "mention" mode. -- Ed.] [See my paper On The Use of Quotation Marks, Etc.: A Review of General Semantics Vol. 51, No 1, Spring 1994. Back to the document

2. Hilgartner, C. A., "You can't get there from here!", Eco-Logos, Vol XXIV, No. 90, 4th Quarter 1978. Press your browser back button to return to the document

3. Wheelwright, Philip, Heraclitus, Princeton University Press (1959), Atheneum reprint (1971), p. 29. (Fragment 21) Back to the document

4. Aristotle, De Generatione et Coruptione, translated by C.J.F. Williams, Clarendon Press, Oxford, 1982. Back to the document

5. Ryle, Gilbert, The Concept of Mind, Barnes & Noble, Inc., New York, 1949, pp. 16-19. Back to the document

6. At past seminars the device known as the Ames 'trapezoidal window' has been demonstrated. A cardboard cutout of a window which has been distorted to resemble a window angled away from us as it would be seen in perspective has the actual shape of a trapezoid. Shading is painted in place on the figure and it is placed on a slowly rotating motor shaft. When viewed from a moderate distance, the object "appears" to us as a square window which is seen not to be rotating, but oscillating back and forth. Our visual system is "fooled" into thinking it is seeing an actual window waving back and forth. Back to the document

7. A flatworm "maze" is very simple, usually consisting of a 'T' with food placed on one end of the crossbar. A new maze involves putting the food at the other end of the crossbar. The flatworm's "map" is expressed behaviorally as simply a tendency to turn to the right or to the left. A "maze-wise" flatworm is one which has a tendency to turn in one direction or the other. Back to the document

8. Plato, "The Republic", Book VII, Five Great Dialogues, Translated by B. Jowett, Van Nostrand, Princeton, 1942. Back to the document

9. Korzybski, Alfred, Science and Sanity, International Non-Aristotelian Publishing Company, Lakeville, CT, 1933; 4th Ed., 1958. Back to the document

10. Hilgartner, C. A., in an address at the International Conference on General Semantics, July 1988. Back to the document

11. Hilgartner, C. A., "A New Formalized Language Based on Entirely Non-traditional Premises" (unpublished). Back to the document

12. Hilgartner, C. A., "A Complete Severance From Traditions", General Semantics Bulletin, No. 47, 1981, pp. 112-9. Back to the document

Annotated bibliography of general semantics papers
General Semantics and Related Topics

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