An Axiomatic System Describing Human Behavior






1. A Logical Calculus of Behavior




This analysis had its origin in two papers (Hilgartner, 1968,1965), which, taken together, constitute a theory of the structure of human psycho-dynamics, based on korzybskian premises (Korzybski, 1933). The claim was made that the doctrine which was presented stemmed from assumptions which were more parsimonious than those in general use by students of behavior, and further, that the doctrine was free of self-contradiction. However, this doctrine was stated in a discursive language (English), and hence its logical structure is in principle concealed, at least in part. Claims about the logical structure of a doctrine are greatly strengthened if the doctrine can be stated as an axiomatic system, proceeding from known assumptions, in a mathematical language of known structure; then the logical structure of the doctrine is immediately apparent, and claims about that logical structure can be readily tested.


But if the doctrine under discussion is more than a purely verbal structure, that is to say, if it purports to describe some non-verbal phenomena, like the structure of human psycho-dynamics, then the feat of stating the doctrine in the form of an axiomatic system should confer another, more important advantage, beyond that of facilitating discussion of its logical structure: It should greatly facilitate the process of establishing whether or not the doctrine correctly and adequately depicts the phenomena it is said to refer to.


We have succeeded in generalizing this doctrine and stating it in a set theory notation; and here we present it as a general theory of the interacting (organismXenvironment) field, able to account for both sub-human and human behavior. Such a theory should prove of considerable interest to workers in the diverse fields which make up neurobiology.


In our presentation, we intend to do everything within our power to make this theory accessible to anyone who may be interested in the topic. However, there is a fundamental difficulty which will plague anyone who tries to comprehend this theory solely from a written text, which cannot be helped but can be clearly stated and squarely faced. According to the korzybskian postulates, we are required to distinguish between "the territory" and "our maps of the territory", such as our raw 'perceptions' or the symbol-systems we use to describe "the territory". When this theory is presented in the form of a series of lecture-demonstrations, the fundamental non-verbal events and phenomena which it describes can be directly elicited in or produced before the members of the audience, and then the theoretical formulations can be presented and compared with the actual phenomena they purport to describe. But in a written text, there can be no actual non-verbal happenings, only symbols: words, equations, descriptions of the events in question, etc. If it should happen that the symbols used in the text refer to phenomena which are not within the 'conscious' experience of a specific reader, then he is as if lost at sea: until he has some kind of 'conscious' dealings with the phenomena in question, he is unable to determine whether or not the theory correctly describes some set of non-verbal phenomena.


The magnitude of this difficulty is better understood when it is realized that the scope of this theory is such that virtually everyone will find something unfamiliar in it. Indeed, this includes the authors of the theory themselves, neither one of whom could have produced it single-handed.


Since the presentation is lengthy and the theory synthesizes diverse points of view, the following brief "road map" may prove helpful.




The mathematics used in this theory is very simple and elementary; nothing as complex as calculus is required here.


The Appendix contains ...




I. Premises


The undefined terms of a korzybskian system are structure, order and relations. These are rendered in our analysis as follows: The existence of relations is indicated by the choice of the Bourbaki algebraic set-theory notation of a Cartesian product space (Ashby, 1962) in which to represent the interactions at the boundary in the (organism X environment) field (Perls, Hefferline & Goodman, 1951). Order indicated by the use of time-indices on the terms which represent these interactions. The resulting array of ordered relations, then, gives the structure of the interacting (organism X environment) field. (The symbol A1 is to be read as "The set A at time t1".)


In this notation, the fundamental postulates of a korzybskian system, which are designated as non-identity, non-allness, and self-reflexiveness, are stated:*


*To make explicit the constrast between the korzybskian postulates and the traditional Aristotelian assumptions, the latter are stated, first in ordinary set theory notation, and then in the notation of the interacting (organism X environment) field, in the next paper of this series, The Structure of 'Unimpaired' Behavior.





No "thing" is identical with any other "thing"; a map is not the territory which it represents. (Identical is used in the sense of "the same in all respects".)


(Premise 1)




No map can show all the characteristics of the territory which it represents.


Let A stand for the set of characteristics of x E (the territory); and let B stand for the set of characteristics of an organism's picture of x ; and let D stand for "the detectable". Then


(Premise 2)


(Premise 3)


(Premise 4)




No action or utterance of any organism is free of self-reference.


Any term, proposition, propositional function, doctrine, or doctrinal function implies and assumes at least one entire metaphysics. As an example, any map of an urban neighborhood (on which the present position of a possible user of the map can be represented) implies a map of the city of which it is a part; the latter implies in turn maps of the state, the country, the continent, the planet, the solar system, the galaxy and the universe of which they are part. (As Dettering (1958) points out, for psycho-logics, "It will be essential at the outset to ignore the conventional distinction between words and deeds. No one need be foolish enough to deny that there is a recognizable difference between what we call 'talking' and 'acting', but we must stress that, for the purposes of this new psychology, attention to this difference will be dangerously misleading. We must try instead to join verbal and non-verbal behavior into one total, logically unified symbol-system....")


In the (organism X environment) field, an organism O which comes into contact with an environmental object or situation x E necessarily organizes the elements of his interactions with this object or situation into a Gestalt, that is to say, a structure comprising a figure of focal interest to the organism, bounded by a ground or context more or less empty of interest. But the organism becomes focally 'aware' of x E only by means of a set of active processes, which we refer to as "the Self"; focal 'awareness' of x E can occur if and only if there is subsidiary 'awareness' of those processes by means of which the Gestalt is organized (Polanyi, 1958, pp. 55-65). This polarity of focal and subsidiary 'awareness' implies the existence of an intra-personal Cartesian product space, which we designate as the (self X other) space (not captialized, and abbreviated Sf X Ot ). We use the symbolism "x/(E-x)i", including the quotation marks, to mean a Gestalt, the focal 'awareness' of x E via sensory modality i ; and we use Sfi , including the reversed quotation marks, to ;mean the subsidiary 'awareness' of the processes of the Self, by which the focal 'awareness' is organized. Then the postulate of self-reflexiveness is stated in this notation as


(Premise 5)


To paraphrase Polanyi's arguments, the distinction between focal and subsidiary 'awareness' is of the same form as the distinction between external objects and the parts of one's body; and we shall show how, in principle, the distinction between external objects and parts of one's body is learned, that is to say, is assimilated as a part of the Self, by means of the interplay between focal and subsidiary 'awareness'. In human organisms, this process of assimilation is extended to include learning how to use tools, physical and also social-symbolic, which we then handle as parts of our Selves in our et the existence of social-symbolic components in human behavior produces a fundamental, unavoidable circularity or self-reflexiveness: We must be able to account for the account we are giving [Hilgartner, 1965; cf. also Oliver & Landfield (1963)]. Thus the notational statement of this postulate is in fact equivalent to the statement in terms of interdependent maps.


It will be noticed that the postulate of Non-identity refers to the structure of environmental objects; the postulate of Non-allness refers to the structure of relationships between organism and environment, i.e.d., the interacting of the boundary; and the postulate of Self-reflexiveness refers to the structure of intra-organismic relations.


II. Biologically 'Purposive' Activities


In neurobiology, we face a double problem: We try to deal with the most complex phenomena known, i.e.d. the dual question of what 'brains' do, and how they do these things; and yet the theoretical frameworks generally available for the purpose of accounting for these phenomena are utterly inadequate. Indeed, the formulations ordinarily used to account for the phenomena of biologically 'purposive' activities, and the general nature of 'life', are structurally equivalent to the notion of 'the rational soul' proposed by Aristotle some 2300 years ago. This point was convincingly demonstrated by Sommerhoff:


Consider a concrete example. If we say that we 'try' to catch a fly, we regard this as a perfectly legitimate use of the verb 'to try'. But if we next say that the fly in the hollow of our hand will 'try' to escape, our modern scientific training intervenes and warns us that in the second case we are committing an illicit anthropomorphism. The fly, we are warned, is not a conscious rational agent, and therefore does not in any literal sense 'try' anything. This rigor of thought is very laudable. Yet in spite of these wise injunctions the incontrovertible fact surely remains that there is a unique something about the observed behavior of the fly which quite emphatically invites this anthropomorphism and which renders this behavior far better suited to such an analogy and teleological conception than, say, the behavior of a falling stone.


It is not difficult to see why exact science has been unable to cope with the purposive or goal-directed aspect of organic nature: science still lacks really exact concepts in terms of which it can even as much as describe it, let alone interpret it. Biologists have been too keen to explain things before they were able to state in exact terms what they wanted to explain and what objective system-properties they were studying. Instead of scientific theories about the exact spatio-temporal relations and types of order involved in the organization of living systems, we find but hazy descriptions of the various purposive aspects of life in terms of such vague and often anthropocentric concepts as 'adaptation', 'subservience', 'co-ordination', 'regulation', 'integration', 'organization', 'final causation', etc., none of which, as they stand, attain to that standard of exactness which modern mathematical theory has shown to be indispensible to a strict and deductive scientific system. The result is a welter of discordant opinions about the general nature of life, and that typical inability to reach agreement, which so often accompanies the use of philosophical concepts whose inherent vagueness allows of almost as many readings as there may chance to be readers. None of these traditional biological concepts tell us much more than that there is in nature something analogous to the purposive behavior of Man; but what this biologists have so far been unable to say with precision. It is the main task of our analytical biology to remedy this failure. (Sommerhoff, 1950, p. 11)


In korzybskian terms, since, in the usual biological terminology, the ordered relations which comprise the structure of biologically 'purposive' activities cannot be specified, these traditional terms imply animistic constructs, that is to say, they tacitly assume and imply the existence of a little "inner man" which directs the organism. But this is the precise equivalent of Aristotle's notion of 'the rational soul'.*


*One manifestation of this inadequacy of traditional biological theory is pointed out on p. [321]: "The notion of 'organism' isolated from 'environment', although historically important in Western society, enters into this system only when we consider constructs arrived at under conditions of repression." See also the citation from Perls et al. (1951).


Since a map is not the territory for which it stands, the only possible relationship between map and territory must be some kind of similarity of structure. As Korzybski puts it,


...The only link between the objective and the verbal world is exclusively structural, necessitating the conclusion that the only content of all 'knowledge' is structural. (Korzybski, 1933, p. 20)


And, since animistic constructs preclude adequate specification of the structure of the phenomena to which they refer, the "failure" of 'theoretical biology' to which Sommerhoff refers is profound indeed. But Sommerhoff's criticism was not solely destructive; he has provided a rigorously defined mathematical relationship which is similar in structure to the apparently 'purposive' behavior of living organisms. Since this notion is crucial to our analysis, let us here present it in some detail. (See also the discussion of directive correlation in Appendix I.)


Unnumbered figure 1 -- p. 299


Here, arrows are used to indicate the existence of causal (physical) relationships; and the assertion of the diagram is that if the rifleman (gun-aiming device) has 'adapted' the aim of the gun to the actual trajectory of the target, then the further development of the system involves a higher-than-chance probability of achieving the 'goal' of a direct hit. But the existence of such a moment of 'adaptation' implies the existence of a prior moment t0 , at which were active one or more variables which bear a causal relationship to the environmental situation at Et1 (the position-and-velocity of the target) and also to the response of the regulator (rifleman) at Rt1 . So a more complete representation of the system would be as follows:


Unnumbered figure 2 -- p. 229


The assertion of this diagram is that Rt1 and Et1 , which from our point-of-view exist at one given instant and therefore are incapable of being causally related to one another, are related through joint causation: that is to say, there is some prior environmental state of affairs which enters into the causal determination of both Et1 and Rt1 . Sommerhoff calls this necessary common causal determinant of both Et1 the coenetic variable of the adaption, and he replaces the term goal by the term focal condition.


On the strength of these considerations we shall now formulate the following provisional definition to introduce a new concept which will play a leading part in the remainder of the book, viz. the concept of directive correlation. It will become our main instrument for expressing in precise terms the various forms of purposiveness found in nature.


Definition. Any event or state of affairs Rt1 occurring at time t1 is directively correlated to a given simultaneous event or state of affairs Et1 in respect of the subsequent occurrence of an event or state of affairs Gt2 (or FCt2 ) if the physical system of which these are part is objectively so conditioned that there exists an event or state of affairs CVt0 prior to T1, and a set of possible alternative values of CVt0, such that


(a) under the given circumstances any variation of Cvt0 within this set implies variations of both Rt1 and Et1;


(b) any such pair of varied values of Rt1,Et1 (as well as the pair of their actual values) is a pair of corresponding members of two correlated sets of possible values R't1, R''t1, R'''t1,... and E't1, E''t1, E'''t1,..., which are such that under the circumstances all pairs of corresponding values, but no other pairs, cause the subsequent occurrence of Gt2 (Sommerhoff, 1950, pp.5455)


He then presents an array of differential equations which express the formal characteristics of directive correlation, assuming the functions are all continuous, and then a different array, utilizing set theory, assuming that the functions are discontinuous. Thus, he presents a mathematical expression, of known structure, which is similar in structure to the apparently 'purposive' behavior of living organisms. He then proceeds to use this formulation to analyze the content of key biological terms and phenomena. His summary follows:


The main instrument we have developed for analyzing the purposiveness of vital activities and the abstract organizational relationships which distinguish living systems from inorganic objects, is the concept of directive correlation. In Chapter III it was demonstrated that, in principle, this concept can be formulated in terms of mathematical relations between physical variables. It was shown that this could be done, for instance, in a restricted sense in which certain functions were assumed to be differentiable, but, if required, also in a general sense in which no such restrictions were imposed. In either case we had to distinguish between 'directively correlated' variables, 'coenetic' variables, and 'focal' variables.


In the subsequent chapters it was shown how this concept of directive correlation could be used to analyze, and to express without loss of meaning, all the most essential aspects of vital organization, purposiveness, or goal-directed activities in nature. The most important explications arrived at in this manner were the following:


Degree and range of directive correlation. By these we have come to understand the scope of a given directive correlation as indicated by the maximum permissible range of coenetic variation and by the number of correlated variables respectively.


Adaptation. The value of a biological variable is 'adapted' to the value of another variable if both variables are directively correlated and an antecedent value of the latter variable figures as a coenetic variable in this correlation.


Co-ordination. A set of biological activities is 'co-ordinated' if they are directively correlated and if each activity also plays the part of a coenetic variable in at least one of the directive correlations concerned.


Regulation. The most characteristic case of a biological 'regulation" is the case of a directive correlation in which the focal condition consists of the maintenance of one or more physiological variables at a constant value.


Organic integration. A set of organic activities is 'integrated' in the biological sense if the activities are directively correlated and if these correlations themselves are again directively correlated inter se (e.g. if their respective focal conditions may in turn be regarded as a set of directively correlated variables).


Self-preservation. The activities of a living organism have a 'self-preserving' character in that they are connected by a set of directive correlations which has as an ultimate focal condition the continued existence of the organism throughout a finite span of time.


Living organism. A living organism may be described as a compact physical system of mechanically connected parts whose states and activities are related by an integrated set of directive correlations which, over and above any proximate focal condition, have the continued existence of the system as an ultimate focal condition. Death may be described as the breakdown of these directive correlations.


Instinctive and learnt behavior. Animal behavior is 'instinctive' if it is primarily an instance of short-term and long-term directive correlations. 'Learnt' behavior, on the other hand, is behavior that is primarily an instance of short-term and medium-term directive correlations.


Integrated social units. An association of living organisms is an 'integrated social unit' or 'society' if there exists a system of integrated directive correlations between the states or activities of the members which has the continued existence of the association as an ultimate focal condition.


Biological progress. We identify 'biological progress' with the observed tendency in nature gradually to evolve biological forms whose self-preservation is based on ever larger degrees and ranges of directive correlations (especially short-term correlations). We regard the development of esthetic, moral and religious faculties in Man as intimately connected with this process. (Sommerhoff, 1950, pp. 194-196)


Ashby (1962) gave a summary of the algebraic set theory notation of Bourbaki; and as his first worked example, he translated Sommerhoff's notion of directive correlation into that set-theory notation. He derived the element-free expression for directive correlation, quoted in our Appendix.


As our first application of the notion of directive correlation, we shall use it to define the notion of 'similarity of structure'. This notion implies that an organism is somehow comparing the structure of two 'things'; and as we shall show in greater detail later, this 'comparing' implies that we are dealing with a 'purposive' term ('comparing' for what 'purpose'?).


In order to state this relation explicitly in the terminology of directive correlation, let us set up a specific example: Let us say that you are to have dinner at my home with me tonight at 8:00 p.m., and that you have come to Rochester, NY and, at my suggestion, have checked in at Y Motel, which, allegedly, is not far from my home. Furthermore, my letter included a sheet of paper on which were scrawled several intersecting lines, a couple of words which you guess comprise street-names, and two crosses, one labeled "Y Motel", and the other labeled with my home address. The question can be phrased as "Is this map 'similar in structure' to the streets in that district of Rochester?" We would answer "Yes" to this question iff by "following" the map you find my home. In this situation, the pertinent coenetic variables include whatever business you have with me which would require that you come to Rochester, the social customs you follow concerning the inter-personal transactions involved in filling the role of 'dinner-guest', and your own 'need' for food. Arrival at my home constitutes the focal condition. The directively correlated transactions between you and your 'environment' include your locomotion, guided by the process of (a) looking at the map, (b) looking at the streets, and (c) performing a comparison, for the 'purpose' of orienting yourself as to which direction to go. If it turns out that you do in fact "follow"g the map and arrive at my home, then we can say that the "outcome" is such that the focal condition is fulfilled, and therefore for this 'purpose' the map was similar in structure to the territory. If you "follow" the map and do not arrive at my home, then the 'outcome" is such that the focal condition is not fulfilled, and therefore for this 'purpose' the map was not similar in structure to the territory. If you get mixed up and fail to "follow" the map, then the "outcome" is inconclusive and therefore the question of 'similarity of structure' has received no test.


But, of course, a rough map of that sort would not suffice for the 'purpose' of settling a legal dispute over urban property-lines.


In science, the structure of the 'territory' is regarded in principle as unknown, i.e.d. 'known' only inferentially (and therefore to some degree inaccurately and incompletely). If a theory has undergone extensive testing without disconfirmation, then we may tentatively guide our activities as if the theory is in fact 'similar in structure' to the 'territory'; but the question of 'similarity of sltructur[' is answered mainly by experimental test. Here, the focal condition comprises the constructing of a 'map' of the 'territory' which, after extensive testing, is not disconfirmed by these tests.


Meanwhile, innocent of these developments in biological theory, Perls, et al. (1951), presented a fairly coherent theory of an interacting organism/environment field, which included a series of experiments which could be done by interested readers, with no other guidance than their book, and which allow one to test the viewpoints they presented. They relied on the usual fuzzy terminology of 'adaptation', 'co-ordination', 'organismic self-regulation', etc. (Their awareness of this limitation was clearly indicated (ibid., p. 268): "The man with Gestalt pachydermatitis founders in a morass of sludgy terminology.") Even so, their effort has been a valuable guide to our own inquiry.


III. 'Perception' as Transaction


As the next step in our analysis, let us now quote a brief passage concerning the transactional nature of 'perception' (Cantril & Livingston, 1963):


The basic problem of 'how' an individual perceives the external world around him has preoccupied many psychologists for many years since even the simplest perception is an enormously complex activity involving a wide variety of factors. Among the factors except for which perception would not serve as the meaningful signal it is, we would list the following:


(1) Some sort of 'externality' -- some object, person, symbol, etc., in the world outside the individual.


(2) Some physical energy related to this 'externality', which has the capacity to initiate a physiological process in the sense organs, as, for example, the light rays reflected from an automobile we see coming down the street.


(3) Some physiological excitation, including the stimulation of peripheral nerve endings and the entire path of neural transmission both leading to and coming from the higher neural centers.


(4) Some assumptions, or weighted averages derived from past experience, that have been somehow registered in the nervous system and are activated by the particular situation we are confronting, and that indicate the probability that what is 'out there' is what we assume is 'out there'.


(5) Some purpose or some intention that catalyzes the individual to pay attention in order to experience or to avoid a particular consequence....

IV. Set-theory analysis


These conditions will now be stated in set-theory notation, as interactions occurring at the boundary in an (organism & environment) field (F) occupying an O & E space. (See p. xxx for a translation of the first 10 set-sentences into words.)


(1) "Some sort of 'externality', etc."


In order to specify some sort of 'externality', it is sufficient to specify the existence of an organism (O), and of an environment (E), and the relations between them. As a beginning, this can be accomplished by specifying our set-space, and three mappings on this space, i.e.d. section (W), and projection with respect to the first and second variables (Pj1 and Pj2).










In this notation, O will be used to refer to an organism, with o Î O . The use of time-indices implies that the relations between O and E are dynamic: any interaction progresses to an outcome (Oc).




(2) "Some 'physical energy', etc."


To satisfy this condition, it is sufficient to specify sense organs, physiological processes in them, and physical energies capable of initiating these physiological processes. For this purpose, we shall define the boundary (B) as a subset of O & E ; we shall specify physical functions which map elements or sets of E into the set of stimuli (St); we shall define two subsets of stimuli, and their complements; and we shall specify the process of integration from elements of (o,e) interactions to sets of (o,e) interactions.


(a) "Experience occurs at the boundary between the organism and its environment, primarily the skin surface and the other organs of sensory and motor response" (Perls, et al., (1951), p. 227; italics ours). Sensory receptors (S), proprioceptors (P), motor apparatus (M) and integument (Ig).


(b) The receptors have characteristic thresholds (LM) related to the absolute-magnitude-and-duration of the stimulus. Supraliminal stimuli shall be designated LM; subliminal stimuli L_M_.


(c) The sensory receptors also have thresholds related to the rate of change of the stimulus relative to the boundary-surface, such that if the stimulus is a member of LM, but this rate of change is less than a certain range of values, the receptor becomes habituated. Supraliminal-for-habituation is designated LH ; subliminal L_H_ .


(d) There is a subset of the environment, termed the novel or novelties, (N), which is composed of those elements of the environment which, when mapped into the set of stimuli, gives that subset of stimuli which is supraliminal for both magnitude and habituation.


(e) If there is the couple of a sensory element with a supraliminal stimulus, at time t0 , then at time t1 the sensory element is in an activated state, which is designated by an asterisk. The exact structure of activated states is not specified in this theory, and may well be as yet unknown. We assume that an activated state is not equivalent to a single propagated discharge of the sensory element, but would more likely constitute a structured train of discharges.
















These set-sentence would be read in words as


(1) The field and the O & E Cartesian produce space are composed of the same elements.


(2) The section over little o (at time ti) is a set composed of all those little e's (at time ti) for which the couple of o with each of these e's (at time ti) is an element of the field.


(3) The first projection [i.e.d. projection with respect to the first variable of the couple (o,e)] (at time ti) is a little o (at time ti) which is an element of the set the organism.


(4) The second projection of the couple (o,e) (at time ti) is a little e (at time ti) which is an element of the set of the environment.


(5) If there is the couple (o,e) (at time ti), then there is an outcome (at time ti) which is an element of the set of Outcomes.


(6) Every element of the boundary is an element of the O & E Cartesian product space, such that every element of the set composed of the union of sensory receptors, proprioceptors, motor apparatus, or integument is an element of the boundary.


(7) There is a set of physical functions, f , such that the set of the environment is mapped into the set of stimuli.


(a) If x (at time ti) is an element of the environment, then physical functions of x (at time ti) are elements of the set of stimuli.*



(b) Every element of the set of novelties is an element of the environment, such that the physical functions of these novelties (at time ti) and the subset of stimuli made up of stimuli supraliminal for magnitude and supraliminal for habituation (at time ti) are composed of the same elements.*


*Note concerning (7a) and (7b): If taken literally, the fact that we did not advance the time-indices for the physical functions which map environment into stimuli implies the absurdity that these mappings occur in 'no time'. The intent was instead to assert that (i) the velocities of light, of sound, etc., are an order of magnitude greater than the velocities with which stimuli are mapped into [the central nervous system] C , and (ii) we are more interested in characterizing the neurobiological events than the exact details of the physical events which elicit them.



(8) If there is the coup\le (s,e) (at time ti), with little s an element of the set of sensory receptors and little e an element of the set of stimuli which are supraliminal for magnitude, then there is an activated sensory element (at time ti), which is an element of the boundary (and every element of the boundary is an element of the O & E Cartesian product ;space .


(9) If there is an activated sensory element with respect to e (at time t1), and e is an element of the set of stimuli which are supraliminal for magnitude, then (at time t2) the not-activated sensory element is an element of the boundary.


(10) An activated sensory element (at time ti) is an element of the set of activated sensory receptors (at time ti); every element of the set of activated sensory receptors (at time ti) is an element of the set of sensory receptors, which itself is a subset of the boundary.


This verbalization of the set-theory sentences vividly displays how economical the mathematical notation is in conveying the relationships involved. By analogy, a mathematician sees at a glance the meanings of


[an integral equation]


and his progress would be hopelessly delayed if he had to stop and express in words the notions conveyed by the symbolism.


(3) "Some 'physiological excitation', etc."


To satisfy this condition, it is sufficient to specify a central nervous system (C), and to imply a peripheral nervous system, and to specify physiological excitations in these which are relative to those in the sensory receptors. For this purpose, we shall specify three operators, nine mappings, and two subsets of the organism which themselves are organized as Cartesian product spaces.


(a) There exists a state-activity of the organism (an operator), which we shall call attending (At) (or 'paying attention'), in which the organism uses its motor apparatus in such a way as to prevent habituation. For example, visual scanning, tactile exploring (caressing), "cocking an ear," sniffing, etc. (i.e.d. At = M(S)). Its complement (A_t_) would involve using the motor apparatus in such a way as to enhance habituation (e.g. staring, averting the gaze, suppressing the caress, shrinking from touch, etc.).


(b) There is another operator, termed 'interest' (In), which makes use of a mapping (which we shall not specify explicitly) from the central nervous system C onto the sensory receptors Si, the effect of which is to decrease the magnitude-threshold and the habituation-threshold, i.e.d. to act so as to increase the organism's sensitivity to stimuli. ('Interest' and attending, then, would be synergistic, though they can operate independently.) The complement of 'interest' (I_n_) serves to desensitize the sensory receptors.


(c) In general, in any situation, an organism must make a fundamental and unavoidable choice: It must either approach (Ap) or avoid (Av) the further development of this situation (Ap+Av). (This expressions refers to the symmetric difference -- see Appendix.)


(d) There is a mapping, (rho), which maps activated boundary states (e.g. S*, P*, etc.) into the set of central representations of activated boundary states (e.g. "S*", "P*",). This set shall be termed 'present experience' (Ep).


(e) There is a mapping, (alpha), which, by means of intersecting two or more values (subsets) of Ep, produces a set called 'awareness' (Aw).


(f) 'Awareness', a subset of the organism, in human organisms is itself organized as a Cartesian product space, (self & other) (Sf & Ot). As with the O & E space, three mappings on this space adequately specify its relations. Cp1, Cp2, Correspondences; V, section.


(g) There is a mapping, (beta), which, by means of intersecting all the different stages of boundary interactions, including operators, produces a set called 'consciousness' (Cs). As with Aw , this subset of the organism is itself organized as a Cartesian product space (Se & Oe). The subtle differences between Cs and Aw will not be discussed until later (pp. 319 ff). Again, three mappings on this space adequately specify its relations: Cq1 and Cq2, correspondences; U, section.






















(4) "Some 'assumptions', etc."


To specify this condition, it is sufficient to specify the registration of Cs into the central nervous system, the organization of Cs into Gestalten or 'generalizations' or 'meanings' (G), and the activation of G in a new 'present situation', as 'expectations' (Ex). For this purpose, we shall specify three mappings.


(a) There is a mapping, (mu), which maps Cs into the set of 'records" (R).


(b) There is a mapping, (gamma), which, by means of intersecting a series of Cs's , maps into the set of Gestalten (G). An alternative operation which maps into G consists of the composition of the inverse of (mu) with (gamma).


(c) There is a mapping, (omega), which maps G into the set of 'expectations' (Ex).


(d) In sentence (24), p stands for probability.











(5) "Some 'purpose' or 'intention', etc."


In order to specify some kind of 'purpose', it is sufficient to specify the characteristics of the (organism&environment) field. In particular, since 'purpose' is to be expressed in terms of directive correlations, we shall specify the types of coenetic variable (CV) which can operate, and the hierarchy of focal conditions (FC) which are involved, and then, by means of examples (e.g. Myth1 and the Trapezoidal Window) we shall illustrate the types of interactions (transactions) which occur at the boundary in an (organism&environment) field occupying an O&E space, starting with the simplest situations and progressing to the more complex.



The notion of the (organism&environment) field implies an origin of 'life', biological evolution, ecological relationships between organisms, and biological death of organisms.


(a) The origin of 'life' (cf. Oparin, 1924)


'Life' evidently arose in the sea; but since the dissolved contents of the sea arose from the weathering of the land masses, and from the primordial atmosphere, it is in a sense truer to say that 'life' arose on (and from) the planet.* Since all living things on this planet are made up mainly of one set of optical isomers (e.g. L-amino acids, D-sugars, etc.), we may assume that there was only one origin of 'life' (or that there were multiple equivalent origins, which is essentially equivalent)(Cf. Eyring's 1965 AAAS address).


*Since this passage was written, I have become aware of the studies of Sille'n (1967) on The Ocean as a System. From his studies of the physical chemistry of three-phase systems, Sille'n concludes that the ionic composition of the ocean, its pH, etc., are dynamically stabilized: "To a mixture of these phases one could add large amounts of KOH or HCl; at equilibrium the system would return to the same pH and [K+] as long as no phase disappeared completely and [Cl-] was kept constant. Hence we have a pH-stat rather than a buffer."


An examination of these physical chemical relations discloses that they meet the criteria for classification as a directive correlation, in which the coenetic variables include the proportions of the chemical elements which make up the planet Earth, their distribution at the point when the surface temperature dropped below 100oC (e.g. the proportions of basaltic and granitic rock forming the bed of the ocean), the composition of the atmosphere, and the supply of non-volatile solutes provided by the weathering of rocks. The directively correlated variables include the possible chemical reactions among the dissolved contents of the ocean, and the solubility constants of the different reaction products. The focal conditions include relative constancy of pH, ionic strength, chemical composition, etc., of the sea water.


The discovery of at least one directive correlation which would be operative even on an abiotic planet drastically alters our perspective on the problem of the origin of 'life': instead of the puzzle of how 'organisms' which are characterized by sets of integrated directive correlations could arise from a planet devoid of directive correlations, ('inanimate nature'), we find instead that the 'inorganic chemistry' of a three-phase system analogous to the ocean of an abiotic planet is characterized by at least one directive correlation. This finding gives immediate empirical support to some of the speculations of Whyte (1948), Teilhard de Chardin (1959), and Korzybski (1921).


Against this altered background, the famous experiment of Miller (1953) takes on new significance. He set up a sealed refluxing condenser containing boiling distilled water under an atmosphere of methane and ammonia, through which a high-voltage electric discharge was passed. After being subjected to these conditions for a period of a week, the reaction mixture was found to contain many organic chemicals, including amino acids. Perhaps further examination of conditions which include Sille'n's three-phase systems in conjunction with Miller's abiotic genesis of organic chemicals will disclose still further directive correlations, which might turn out to be integrated (directively correlated inter se). In that case, an abiotic planet would meet the criteria for classification as a 'living system', and the problem usually referred to as 'the origin of life' would turn out to be isomorphic with the problem of biological evolution, the development of more numerous, complex, and highly integrated directive correlations.


(b) Primordial organisms


Sommerhoff defines a living organism as "...a compact physical system of mechanically connected parts whose states and activities are related by an integrated set of directive correlations which, over and above any proximate focal condition, have the continued existence of the system as an ultimate focal condition. Death may be described as the breakdown of these directive correlations." (Sommerhoff, 1950)


The sea today makes a fairly good constant-condition bath, in which temperature, pH, ionic strength, oxygen concentration, chemical composition, etc., vary rather little with time in a given small region. We shall assume this was true in the primordial sea also. Given relatively constant conditions, the first living organisms would have comprised structures which showed simple directive correlations making use of the free energy of chemical reactions, with the focal condition being the preservation-and-growth of the structure (organism). [Dounce (personal communication) has suggested that the simplest organisms might have consisted only of a boundary and a simple information system, containing information about how to make a boundary and an information-storage system from substances available in the sea.] Survival, however, was contingent on the fortuitous maintenance of these crucial sea-variables within the viability-limits of the organisms, and on the continual flux of the relevant chemicals through the organism's processing-structures (metabolism).


(c) Biological evolution (cf. Sommerhoff (1950) and Teilhard de Chardin (1959))


With the passage of time, organisms developed more and more numerous, complex and highly integrated directive correlations, giving them ever increasing numbers of degrees of freedom from environmental contingencies [e.g. multicellular, central nervous system, amphibian, land-dwelling, euthermic, parental fostering, placental embryogenesis, social organization, and finally, time-binding (Korzybski, 1921)]> Al;l of these developments made it possible for the evolving organisms to regulate their survival-variables, to maintain these within viable limits, under conditions which would have destroyed less highly-correlated organisms.


Multicellular organisms carry around their own "private" seas -- and survive only as long as they maintain the survival-variables in their own seas within definite limits (which are phylogenetically determined). This "private" sea is termed the internal environment -- and is capable of becoming a novelty (cf. discussion of coenetic variable).


(d) Ecological relations


Fairly early in the history of 'life', virtually all the chemical substances capable of nourishing heterotrophic organisms were taken up and organized into living organisms; so that ever since, one organism can be nourished only at the expense of another. The food-getting relations between organisms range from obligatory symbiosis, through predation and parasitism, to domestication.


(e) Death and degeneration


An organism preserves itself only by growing. Self-preserving and growing are polar, for it is only what preserves itself that can grow by assimilation, and it is only what continually assimilates novelty that can preserve itself and not degenerate. (Perls., et al., 1951, p. 373)


When an organism finally fails to preserve itself, and its integrated set of directive correlations breaks down, then: (i) its part-processes, no longer integrated together for the preservation of the organism, lead to the degeneration of the fine-structure of the form; (ii) its composition is such that it represents a rich local concentration of the raw materials from which living things can be constructed; and so its form is also destroyed by other living creatures, and its raw materials are utilized for the growth of these other creatures (Laborit, 1963).


To summarize these arguments, the notion of a directively correlated (organism&environment) field allows us to account for the origin and evolution of living organisms, and the present observable inter-relatedness of the biosphere. Let us now attend to the detailed structure of the apparently-'purposive' behavior of living organisms.




A detailed discussion of the mathematical structure of directive correlations has already been given. Here we shall present a brief discussion of the types of coenetic variables which can operate in an (organism&environment) field, and of the hierarchy of focal conditions which is involved.


(a) Coenetic variables


In general, the coenetic variables which initiate the interactions (transactions) at the boundary might comprise exigencies arising in the organism (e.g. 'needs'), or exigencies of the environment which impinge on the organism.


(i) Deficit. Any deficit can, by rearrangement of the dimensions, be represented as a surfeit, and vice versa: e.g. too low a concentration of glucose per unit blood can be expressed as too high a concentration of blood per unit glucose, etc. Deficit (Df).


(ii) Interoceptors. In order for a physiological deficit to become a novelty and mobilize behavior, there must exist a class of interoceptors (Ic), a subset of proprioceptors, which are sensitive to the parameters of interest.


(iii) The hierarchical nature of 'needs'. Each most pressing unfinished situation assumes dominance and mobilizes all the available effort until the task is completed; then it becomes indifferent and loses consciousness, and the next pressing need claims attention. The need becomes pressing not deliberately but spontaneously. Deliberateness, selection, planning are involved in completing the unfinished situation, but consciousness does not have to find the problem, rather it is 'identical' with the problem. The spontaneous consciousness of the dominant need and its organization of the functions of contact is the psychological form of organismic-self-regulation. (Perls, et al., 1951, p. 274)


(b) Focal conditions


The ultimate focal condition of all organisms is the preservation-and-growth of the organism (Pr) throughout some finite time-interval. Every activity which can in any sense be called 'purposive' will have at least one proximate focal condition (and even 'non-purposive' play is 'purposive', i.e.d. directively correlated); but these proximate focal conditions, if correctly understood, can be shown to subserve the ultimate focal condition of preservation-and-growth.


To summarize the consideration up to this point, we have defined 'the organism' as including six mappings which, in ordered sequence, map into a series of six subsets. Figure 1 shows these relationships (but does not show the various operators and other relations defined). (Rho), (mu) and (omega) are shown as requiring finite intervals to perform the operation of mapping; (alpha), (beta) and (gamma) are shown as requiring the process of intersecting successive values of their domains in order to perform the mappings, and therefore also require finite intervals.




Later, for the sake of proofs, we shall require several composition relations involving these mappings, for example a relation which maps from E into the Ot component of Aw , or for E into the Oe component of Cs, via the sensory modality j . These relations are given respectively by the following expressions:






In setting up our logical calculus, we have shown meticulous care to indicate the temporal order of the processes involved; now, in writing these composition relations, we have not advanced the time-indices. Our intent is not to eliminate order, but rather to indicate that, in the boundary interactions represented by the composition relations, the durations of the interactions are an order of magnitude greater than the durations of the interactions indicated in the first 44 sentences.


V. The Form of Any Encounter


Examples: Myth1 and the Windows


We now have a visitor in our presence, Myth1, the man from Mars, has just arrived here on Earth (never mind how), and thus represents an adult time-binding organism with no experience. We shall consider several of his encounters with terrestrial objects: a series of 'experiments in 'perception' and its consequences':




(1) Coenetic variable . Deficit of orientation (Df(Or))


Myth1 needs to orient himself well enough to navigate safely on Earth. Specifically, he must learn ("find-and-make") a set of RULES (possibly non-verbal) FOR RELATING PATTERNS OF RETINAL STIMULATION TO ENVIRONMENTAL CONDITIONS.


(2) Restrictions (cf. preceding sections on 'perception' as transaction)


(i) There must exist a physical-biological-social field, of which Myth1 is one term.


(ii) Myth1 must have a light-sensitive retina, with afferrent-efferrent connections with a complex central nervous system.


(iii) Myth1 must have motoric "feelers," analogous to our arms and legs, with touch-receptors and with proprioceptors, both of which have afferrent-efferrent connections with his central nervous system.


(iv) Myth1 must be capable of forming generalizations (verbal and/or non-verbal), which implies the capacity to "remember".


(v) Myth1 must be capable of forming discriminations (closer approximations), which implies the existence of 'needs', 'expectations', 'attitudinal sets', etc.; and implies also the ability to compare the actual outcomes of his encounters with the 'needs', 'expectations', etc.



(Thus Myth1 must show directive correlation, contact, growth and self-correction.)


(3) Strategy


When he detects a pattern of retinal stimulation at a given moment, Myth1 must reach out with his "feelers", approach, and locate the object (if any) corresponding th these patterns. (This can be shown as a temporal deployment of his activities.)


(4) Possible outcomes, and focal conditions


If x E comprises a flight of stairs going down, or the edge of the Grand Canyon, and if Myth1 is unwary in approaching x , in his efforts to touch it, then he may precipitously end up at the bottom. If x represents a fire, Myth1 may end up with singed "feelers. By such reasoning, the need for orientation is seen to comprise one aspect of self-preservation (Pr); and the experience of contacting x will necessarily include an intrinsic feeling-tone of pain-or-pleasure, states of 'tension' or 'release' of the boundary, which give primary evidence of his progress toward achieving his focal condition. Excitement (Ec), affect (Af).


Thus, the focal conditions in Myth1's starting situation, in increasingly proximate series, are:


(i) The organism's preservation-and-growth;


(ii) Achieving orientation, getting his bearings in the initial situation, i.e.d. finding out how to behave in these circumstances in order to get what he needs and not get disrupted;


(iii) Achieving some basis for predictions concerning subsequent situations, i.e.d. finding, and testing, the relation(s) between the central nervous system representation of the pattern of stimulation on his retina produced by f(x) and that pattern of stimulation of his touch-receptors produced by his tactile exploration of x . In general, a contact situation usually involves a sequence which shifts from interactions via the disthant-senses to interaction via the close-senses (cf. Houssay et al., 1955, pp. 866 ff).


Let us now show these relations in the notation we have developed. There are five notational conventions which will be required, which have not yet been defined. ML designates the operator locomotion. The subscript v refers to visual processes; the subscript t refers to tactile processes. The element xd designates a skin deformation produced by touching x E . The element xeh(nu) designates light reflected off x E .
















By time t8, Myth1 has detected a pattern of retinal stimulation, and thus has achieved his initial focal condition. The feeling-response of excitement (or better, delight) gives a primary and indispensible indication of the progress of this boundary interaction, as is made clear in the passage which follows:



















The focal condition of time t9 having been achieved, this now 'feels' like a finished rather than an unfinished situation; Myth1's interest wanes and he ceases attending to it, as he turns it over to the 'unaware' processes of assimilation.












(1) Any encounter as being directively correlated


The process described in set-sentences (25) through (42) unmistakably meets the criteria for a directive correlation, in which the coenetic variables are (a) deficit of orientation, and (b) an encounter (or contact) with the object x E; the focal condition is the formation of a 'generalization' or Gestalt, Gi , which can then be translated into an 'expectation' concerning the next similar encounter:




and the interactions represented by the expression (psi)(f(d),(g(d)) or its element-free equivalent UNNUMBERED EXPRESSION IN TEXT (P. 316) are given in detail in set-theory sentences (25) through (42). These considerations establish that the mathematically-defined model behaves as we said it must, i.e.d. up to this point it is self-consistent.


(2) Encounter as contact


This process comprises an example of contact, an organism contacting a novelty, in a mainly perceptual situation.


We speak of the organism contacting the environment, but it is the contacting that is the simplest and first reality. (Perls, et al., 1951, p. 227


In the O & E field, every point (element) is an (o,e) interaction.


There is no function of any animal that is definable except as a function of such a field.|- Organic physiology, thoughts and emotions, objects and persons are abstractions that are meaningful only when referred back to interactions of the field.


|- This should be obvious, but the abstractions have become so ingrained that it is useful to insist on the obvious and point out the common classes of error.


(a) Standing, walking, lying down are interactions with gravity and supports. Breathing is of air. Having an external or internal skin or envelope is an interaction with temperature, weather, fluid, gaseous and solid pressures and osmotic densities. Nutrition and growth are assimilations of selected novel materials that are bitten, chewed, sucked, digested. In such cases, however, there is a common tendency to abstract the 'organism,' as a man 'eats for his health,' without addressing himself to the food; or he tries to 'relax,' without resting on the earth; or he tries to 'breathe', without exhaling as well as inhaling.


(b) Communication, imitation, caring-for, dependency, etc., are the organic social nature of certain animals. Personality is formed of interpersonal relations, rhetorical attitudes; and society, contrariwise, is bound together by intrapersonal needs. The symbiosis of organisms and inanimate forces is an interaction of the field. Emotions, concern, and so forth are contact-functions, definable only as relations of needs and objects. Both identification and alienation are ways of functioning in a field. In these cases, however, the common tendency is to abstract both 'organism' and 'environment' in isolation, and recombine them secondarily. (ibid., p. 372)


By contacting we mean food-getting and eating, loving and making love, aggressing, conflicting, perceiving, learning, locomotion, technique, and in general every function that must be primarily considered as occurring at the boundary in an organism/environment field. (Ibid., p. 373)


(a) 'Present experience' and 'awareness'. In our model, the first consequence of visual contact between Myth1 and x E is that the pattern of retinal stimulation S*v(xeh(nu))3 is mapped into C as "S*v(xeh(nu))"4 , a subset of Ep , 'present experience'; and successive values of Ep are mapped into the set Aw , 'awareness' [sentences (25) to (27)]. Thus, 'awareness' is shown as an activity, an active process, which is required by the 'difficulties' represented as coenetic variables, those operators which require behavior. If Myth1's situation posed no 'difficulties', then no 'awareness' would be required, and there is no reason why his deficit should not be satisfied while he sleeps on; but encounters with novelties are full of dangers and difficulties, and therefore Myth1 must work for his own preservation-and-growth.


This logical machinery makes of 'awareness' a shifting phenomenon, changing from moment to moment. This is immediately consonant with personal experience: if, as I sit here at the typewriter, I take note of what I am here-now 'aware' of (as suggested in Perls, et al., 1951, pp. 31ff), I find that I become 'aware' first of the sound of our furnace, then of the TV going upstairs, then tension in my back muscles, then the feel of my feet on the floor, etc. My 'awareness' is constantly shifting back and forth from aspects of myself to aspects of my environment. However, as a relatively skilled observer, I find that, in a moment of 'awareness' of an aspect of my environment, I can feel myself reaching out toward the stimulus; and in a moment of 'awareness' of an aspect of myself, I can feel the environmental contribution. (True, I became 'aware' of the feel of my feet; but the feeling I became 'aware' of was 'sensed' as the feel of mly feet on the floor.) This aspect of 'awareness' is represented in our model by showing Aw , 'awareness', as being organized as a Cartesian product space, Sf & Ot , i.e.d. resolvable into focal 'awareness' of the stimuli related to x E, and subsidiary 'awareness' of the processes of the Self by which the focal 'awareness' is organized.


There are certain logical complexities which arise when we consider a human being examining the conditions of his own experience. In the paragraph above, I said, "I take note of what I am here-now 'aware' of."The expression take note, a stenographic image, implies the muscular act of taking notes. In our notation, the operator At , attending, was defined as a muscular act, in which the organism uses its motor apparatus in such a way as to prevent habituation. Thus, if we translate my "take note" sentence into the terms of our notation, we have the expression






This process illustrates the phenomenon of the multi-ordinality of terms (and of human activities), e.g. 'awareness' of 'awareness', as described by Korzybski (1933). It also serves further to illustrate the proposition (Hilgartner, 1965) that "Even the most complicated and elusive of those phenomena which most people call 'the mind' are demonstrable physical activities, which require nothing beyond the equipment our bodies are already provided with."


(b) 'Consciousness'. The set Cs , 'consciousness', is shown as being formed by the intersecting of all the various stages of the boundary interactions, including operators (e.g. CV , motor operators, etc.) as well as sensory mappings. Thus, in a sense, it differs from Aw mainly in degree: if the organism's focal conditions are achieved easily, with little delay, then there is little to enter into Cs which is not already represented in Aw ; but in difficult encounters, where satisfaction is delayed, then Cs becomes markedly different from Aw ; i.e.d., "... consciousness is the result of a delaying of the interaction at the boundary" (Perls, et al., 1951, p. 259). This logical machinery makes of Cs a mechanism which is, on the basis of incomplete information, capable of keeping track of a changing organism interacting with a changing environment.


Again, this rendition is immediately consonant with personal experience. As I sit here at the typewriter, I am 'conscious' not only of my sensory and proprioceptive intake, but also, for example, of my need to select an example of my own 'consciousness' which correctly illustrates my view of the operations of 'consciousness', and to describe it in words, aptly and succinctly. Thus, in the example of five seconds of my 'awareness' cited above, if we now take into account the fact that, although I do want the house warmed, generally I hate the noise of the furnace; and also, that the TV I heard was the showing of a movie my wife and I had wanted to see but had previously missed; then it becomes apparent that, at the level of awareness, I was reaching out toward an annoyance and a distraction. This suggests that theory-writing was proving onerous to me that evening; and so, the back-muscle tension probably represented my impulse to go away from the typewriter, opposed by my decision to continue working on the theory. Perhaps the feet on the floor represented acceptance of continuing the struggle with the theory. At any rate, I did decide that the four items listed constituted a sufficient example of the "spotty" nature of 'awareness', and did go on to the next topic.


Thus, 'consciousness', in personal experience, includes considerations of one's deficit, needs, or other coenetic variables which require behavior; it includes one's sensory and proprioceptive intake; and it includes the related topics of one's picture of his Self (i.e.d his theory of the structure of human psycho-dynamics), and the asking and answering of the orientation-questions: Who am I?, Where am I?, What am I doing?, and Why am I doing it? (Hilgartner, 1965, p. 6).


Like Aw , Cs is organized as a Cartesian product space: and like Aw , Cs is multi-ordinal, i.e.d we can write an expression for Csj(Csi)) (subset) Cs. As we shall see in detail later, these two considerations make it possible to show the structure of some of the most baffling aspects of human experience; and further, to indicate the existence of, and to explore, essential aspects of human experience which are systematically neglected in Western cultures, and which each of us can ill afford to continue to exclude from our behavioral repertoire (e.g. Hilgartner, 1965). For the moment, for the sake of a superficial translation between the different aspects of Cs and personal experience, it is sufficient to point out that, while Aw is entirely non-verbal, Cs includes both non-verbal and verbal structures; and of the verbal subsets of Cs , these range in level of abstraction from subsets analogous to the pointing-act of a small child, who walks up to a thing he is interested in, touches it with his right index finger, and says, "That!," to subsets as complex as the act of writing or understanding a mathematical theory of the structure of human 'consciousness'.


Finally, as shown in sentences (37) and (38), the formation of a subset of Cs comprises "final contact" with a situation, culminating in the climax of the encounter; and this is followed by loss of interest and cessation of attending, as the experience is turned over to the unaware processes of assimilation. This sequence of events is shown clearly in the example cited above: The interpretation of the recorded five seconds of my 'awareness' seems quite convincing; the whole experience "hangs together", and though readers may regard it as a "good example," by the time we finish interpreting it, it seems thoroughly understood, and no longer compels attention. "Aha, that's it!" we say, and go on to the next topic.


(c) Gestalt formation


Gestalt formation always accompanies awareness. We do not see three isolated points, we make a triangle out of them. The formation of complete and comprehensive Gestalten is the condition of mental health and growth. Any incomplete Gestalt represents an 'unfinished situation' that clamors for attention and interferes with the formation of any novel, vital Gestalt. Instead of growth and development we then find stagnation and regression. (Perls, et al., 1951, p. ix)


In our text so far, it might appear that we use the notion of a Gestalt in two different senses: (a) a "little" Gestalt, Cp2(Awii) = "xi/(E_x)i , a figure of interest in one sensory modality against the detectable background in that modality; and (b) a "big" Gestalt, Gji = (gamma)((intersection) Csi) , where we define Gji as a Gestalt, 'generalization', or 'meaning'. But in the passage quoted above, the relationship between these two senses is displayed, i.e.d. the "little" Gestalten are the partial components of the"big" Gestalt. In terms of personal experience, it is immediately evident that, in each modality, our 'perception' at every instant is given as a figure of interest against a background relatively empty of interest; and it is equally evident that our considered picture of any environmental object x E is formed by putting together the evidence gained by the use of the several different sensory modalities.


A Gestalt, then, comprises a completed interaction of organism and environment in the field; though it may then proceed to serve as the coenetic variable which initiates a further interaction.


(d) Excitement. No organism could survive at all if it did not have the capacity to monitor and keep track of the progress of its own activities toward the achieving of its focal conditions; but since the exact details of this "achieving" are unknown a priori, being worked out as the organism proceeds, and since perhaps the entire nature of the focal condition itself may be unknown to the organism, by what mechanism might the organism monitor its progress? ("The coming but as yet unknown solution" (Perls, et al., 1951, p. 234).) In a situation in which the organism is vitally involved, in which its survival is in some way or other at risk, the organism is to some degree or other excited; and each alternative it faces promises to increase or to decrease the excitement. Furthermore, its own state of excitement is apparent to the organism, by proprioception. And finally, each choice it makes which brings it nearer to the achievement of its focal condition serves to increase the level of excitement, up to the climax of the experience. Excitement, then, comprises a feedback-process without which directively correlated activities in principle could not achieve the focal condition, i.e.d. could not exist.


(3) Encounter as growth


This process also comprises an example of growth, in the sense that, as is shown in sentence (41), the organism has taken in and assimilated some new material (the Gestalt G19). In detail, the structure of growth is as follows: the organism has a need (for orientation), which it accepts as its own; and it scans the environment, looking for a likely object with which to satisfy its need. Having located and chosen a likely object, it then overcomes the obstacles (e.g. distance between the object and its "feelers"); it makes final contact with the situation, explores x with visual and tactile scanners (equivalent to the climax); and finally it lets go, turning the experience over to the unaware processes of assimilation (formation of the Gestalt). Thus the operations of the Self and the process of growth are synonymous.


(4) Encounter as self-correction


Finally, the process described in set-sentences (25) through (42) defines Myth1 as a self-correcting system, i.e.d. a system for generating and testing hypotheses: One of the fundamental propositions of psycho-logics (cf. Dettering, 1958) holds that any action can be interpreted as the non-verbal equivalent of a verbal statement, and vice versa. Thus, by the action of exploring in this situation, Myth1 has done the equivalent of saying, "In the midst of my confusion, I see something (x); I assume there is an object 'out there' to be seen, and I judge it not to be dangerous; and I expect that if I reach out with my feelers, I'll bump into it and thus be able to feel it too." By then proceeding to reach out, by touching and exploring x , he has put this expectation to test; and the outcome is experienced and recorded by his nervous system, as a Gestalt ('generalization'), which is then available to influence his subsequent behavior. Assuming no fatal mishap occurred, Myth1 has partially relieved his deficit of orientation: he now know one "manipulation" he got away with, and presumes he can get away with subsequent similar "manipulations".


The relevance of the consideration of growth and self-correcting to personal experience will be amply demonstrated in the sections describing Myth1's encounters with rectangular windows and then with the Ames trapezoidal window, and the implications of these encounters.


Although the full importance of this point will not become obvious until (in a later publication) we come to the operational definition of repression, please note that all of the terms defined, i.e.d. directive correlation, contact, 'present experience', 'awareness', 'consciousness', excitement, Gestalt formation, growth, and self-correction, are defined only as binary relations, i.e.d. as (organism&environment) interactions, or "relations with self-and-others" (Hilgartner, 1965). The notion of "organism" isolated from "environment", although historically important in Western society, enters into this system only when we consider constructs arrived at under conditions of repression.




When we consider the confrontation between Myth1 and the windows, we shall need to be able to distinguish between frustration, danger and emergency; and in order so to distinguish, we must first consider an encounter in which an ordinary physiologic deficit or 'need' serves as coenetic variable.


(1) Physiologic need: Thirst


The essential relationships concerning an organism's water balance can be summarized as follows: At a given moment Ti , an organism can continue to life iff its total water concentration, oci , lies within certain limits.




If at any time tf , the water concentration of the organism drops to a value of v , the organism cannot live.




Moreover, for any organism there will be some irreducible rate of water loss, z ml/hr, which the organism cannot further diminish by any homeostatic means available to it. Thus the water concentration of the organism at any instant ti can be represented as




Thus the organism, if it would survive, is required to take in more water before Tf . Intake (It). We shall use the operator seek (Sk), which serves as a convenient abbreviation for the process of examining object x1 E and, if it has nothing to do with the FC , losing interest and moving on to examine x2 E ; and if it has nothing to do with the FC , losing interest and moving on to examine x3 E , etc. Icos designates interoceptors for blood osmolarity.


Let us now consider Myth1 and the Drinking Fountain:








This is an operational definition of the phenomenon of dominance, as described in Perls, et al. (1951, p. 274)






(2) Emergency


Any situation in which there is a likelihood that the sensitive (organism&environment) boundary will be damaged or destroyed constitutes an emergency (Em). The probability that the damage or destruction will occur gives a measure of the severity of the emergency.


Any emergency in which the coenetic variable involves mainly the stimulation of interoceptors (or proprioceptors comprises a situation of frustration (Fr); according to this definition, this would include situations of starvation and illness. An emergency in which the coenetic variable involves mainly the stimulation of exteroceptors comprises danger (D).


In both these cases, of excess of danger and frustration, there are temporary functions that healthily meet the emergency with the function of protecting the sensitive surface. These reactions may be observed throughout the animal kingdom, and are of two kinds, subnormal or supernormal. On the one hand, panic 'mindless' flight, shock, anesthesis, fainting, playing dead, blotting out a part, amnesia: these protect the boundary by temporarily desensitizing it or motorically paralyzing it, waiting for the emergency to pass. On the other hand, there are devices to cushion the tension by exhausting some of the energy of tension in the agitation of the boundary itself, e.g. hallucination and dream, lively imagination, obsessive thought, brooding, and with these motor restlessness. The subactive devices seem to be adapted to protecting the boundary from environmental excess, shutting out the danger; the superactive have to do rather with proprioceptive excess, exhausting the energy -- except that when, in starvation or illness, the danger-point is reached, fainting occurs.


We have thus come to another function of consciousness: to exhaust energy that cannot reach equilibrium. But note that this is again, as in the primary function, a kind of delaying: previously the delay consisted of heightened awareness, experimentation, and deliberateness in order to solve the problem; here it is delay for the sake of rest and withdrawal, when the problem cannot otherwise be solved.... (Perls, et al, 1951, pp. 261-262)


In order to specify these conditions, we shall require three more operators: Urgency (Ur) involves intensified motor activity, with an affect of desperation, i.e.d. solve this problem or die. Hallucination (Ha) comprises the process of interpreting one's sensory intake, in the absence of an object with which to satisfy the focal condition, as if it indicated the presence of such an object; the decreased selectivity of such an operation is indicated by representing it as a series of unions of sets instead of intersections of sets. Fainting (Ft), obviously, involves the cessation of motor activity and other signs of responsiveness. Emf designates a fatal emergency.


Frustration: Myth1 in the Desert


(45), (46), (47), (48), (49), and (50) hold.
















We have listed our undefined terms, stated our premises, given what we claim to be an adequate account of the structure of biological 'purposiveness', and set up an algebraic set-theory notation which describes the transactional nature of 'perception'. We have used this notation to describe the structure of any (mainly 'perceptual') encounter, and have used the resulting model to define our key terms. Finally, in order to test the adequacy of our model, we have deployed this logical calculus in the not-mainly-'perceptual' situations of ordinary physiological 'need' and satisfaction, of frustration, and of danger; and as judged by its handling of these situations, our model appears adequate.


In the next paper of this series, we shall analyze the structure of 'undistorted' or 'unimpaired' human behavior, starting with the intrinsically interesting situation of finding a contradiction between what we expect and what we observe, and the consequent process of changing our premises.


In a later paper, we shall explore the structure of 'unimpaired' human inter-personal transactions, leading up to a detailed analysis of the neuro-biological events which occur when two strangers meet in an otherwise deserted hallway, and exchange a glance and a warm smile, but no words. Subsequently, we shall explore the structure of 'distorted' or 'impaired' human behavior and experience, and the structure of the processes by which "distortions" or "impairments" of behavior and experience can be corrected.