Socion Archive

Arguments for the Polemic on the Two Groups of Bipolar

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Arguments for the Polemic on the Two Groups of Bipolar Traits

Yu. P. Minaev Socionics, Mentology and Personality Psychology, No. 5, 2014, pp. 21–36 UDC 159.9.075+159.923.2 (Section: Discussions)

Abstract

The comparative analysis of two groups of bipolar traits for the set of types of information metabolism is continued. A series of diagrams and tables vividly demonstrates the formal parity (symmetry) of the views, from the standpoints of these groups, of the “ring” structure of the socion. At the same time the “one-sidedness” of these views is shown, which makes it impossible to construct a full-fledged theory of intertype relations while remaining on the standpoint of only one of the two alternative groups.

Keywords: socionics, Jung–Augustinavichiute–Reinin basis, Augustinavichiute–Reinin traits (ARTs), Jung–Minaev traits (JMTs), quadras and squares, Jung’s typology.

Translator’s note: IR and spectrum abbreviations as in the earlier papers (ТО identity, ДУ duality, ЗЕ mirror, АК activation, СЭ super-ego, ПО extinguishment, КФ conflict, КВ quasi-identity, РО kindred, ПД semi-duality, ДЕ business, МИ mirage, Р±/З± supervision/benefit). Reinin’s split-spectrum symbols Iз, Iк, Rз, Rк, μ, ξ, τ, ω and Minaev’s counterparts Dз, Dк, Aз, Aк, ν, λ, ρ, η are kept as in the original.

An extended introduction with acknowledgments and quotations

Thanks to Anna Leonidovna Mitrokhina for her study manual for the basic course “Foundations of Socionics” [12], and to everyone who helped bring this book into the world. In the review by the heads of the International Institute of Socionics, A. V. Bukalov and O. B. Karpenko, printed on the cover, there are these words: “The correct references and quotations create the impression not of the scattered opinions of individual socionists, but reflect the diversity of views of a complex and multidimensional structure. What one hears in this is not discord but a well-coordinated chorus.”

I am not sure that all readers form precisely that impression, but I am ready to join in the words, printed in the same place, of the manual’s scientific editor V. D. Ermak: “One may disagree with this or that consideration and conclusion of the author, but one cannot fail to appreciate his heroic attempt, under present conditions, to provide generalized instructional and methodological material.” True, I do not know whether every beginner in socionics will like the abundance of opinions of individual socionists presented in the book, behind which I, for one, could not always discern the author’s own assessment of the various positions. Perhaps, of course, the time has simply not yet come, and for now it is unrealistic to lay out the foundations of socionics as a logically coherent instructional text.

For my words of thanks in this article there was also a very concrete occasion. Leafing once again through A. L. Mitrokhina’s book, I saw a familiar figure, next to which was written: “The Jung–Augustinavichiute basis after G. A. Shulman” [12, p. 240]. How had I missed such a double name for the basis of bipolar traits for TIMs? For that is exactly how I had wanted, for my own reasons, to propose renaming the “Jung basis”! Perhaps adding also the surname of G. R. Reinin. I open Grigory Alexandrovich’s “Portrait of the Socion” at the corresponding page, and there indeed is a memorable figure titled “The Jung–Augustinavichiute basis” [16, p. 71].

Truth be told, the figure features the symbols not of TIMs but of macro-aspects, for whose set just the two dichotomies indicated there (rational/irrational and extraverted/introverted) suffice. And these are indeed Jungian dichotomies. But the figure contains four numerals, two of which hint at the existence of two more dichotomies, concerning only the set of TIMs: intuition/sensorics and logic/ethics. In C. G. Jung, the analogues of these words were used to designate psychological functions, while in socionics they came to name bipolar traits of TIMs. In socionics the system of four dichotomies (two Jungian and two others) was in fact introduced by Aushra Augustinavichiute (the same ones are used in the Myers–Briggs typology). G. R. Reinin took these very dichotomies as the system of generators for constructing the group of bipolar traits, whose set consists of 16 elements (including the neutral Karpenko–Churyumov element). On this set he defined a binary operation allowing a third trait of the same set to be obtained from two traits. Therefore in the name of the basis (the system of generating elements) for the resulting group it would make sense to indicate not Jung alone. Otherwise C. Jung, with his 8-element typology, appears before readers of the socionics literature as a man who, having at his disposal a basis of four dichotomies, could not correctly raise two to the fourth power (2⁴ = 16, not 8).

And to Grigory Alexandrovich Shulman a separate thank-you, not only for the basis name with two surnames, but also for the extensive quotations from C. Jung and A. Augustinavichiute — in particular in section “3.2. The Genius’s Error. The Typology of C. G. Jung” [16, p. 75]. Rereading the familiar texts, I satisfied myself that G. A. Shulman draws his conclusions from the same material of the classical works as I do. And the fact that the conclusions do not coincide gives occasion to adduce new arguments in defense of my own understanding of the classics.

Consider a quite different situation. You take G. R. Reinin’s book [14] and on p. 146, at the very beginning of the sixth lecture “Traits of the dichotomy of the socion,” you read: “C. G. Jung in his work [19] proposes a description of the space of personality by means of four independent (orthogonal) traits: extraversion–introversion, intuition–sensorics, thinking–emotions, and rationality–irrationality. These traits divide the space of personality into 16 sectors, which correspond precisely to the 16 different types [1, 21].” You follow the indicated reference numbers. Under the first number is A. Augustinavichiute’s work “The Theory of Intertype Relations,” printed in several issues of the leading socionics journal. There is no source No. 21 in the list at all (there are only 19). And under No. 19, instead of the expected Jung, we find Myers–Briggs (in English).

What to do? No need to despair! Let us take Grigory Romanovich’s earlier book [13]. On p. 114 the very same text with the same reference numbers awaits us. But the bibliography (on p. 234) is different! In it, Myers–Briggs is in 21st place, and in 19th — “Jung C. Psychological Types. — Moscow, 1924.” Judging by the “Introduction” to G. R. Reinin’s book [13, p. 6], this is “an abridged translation into Russian with a preface by Professor Ivan Ermakov.” But even after such an investigation it remains unclear which precise place in C. Jung’s voluminous work prompted Grigory Romanovich to the above assertion about what the classic did in his fundamental work.

One more example of a situation in which it is difficult to conduct a constructive discussion. Let us take the 2nd edition of S. I. Churyumov’s “Smile…” [15] and open it at p. 386. Quotation: “C. G. Jung in his typology spoke of eight types. As we understand now, knowing socionics, he did not distinguish kindred types. By the logic of the dichotomies he introduced there should have been sixteen types, and in the Myers–Briggs typology developed on that basis there were already sixteen. However, in all their real fullness they were genuinely presented only by Aushra Augustinavichiute in socionics.”

What was this logic that Jung used, yet could not correctly count how many types should have resulted in his typology in accordance with it? Or perhaps Jung is not the issue?

In G. A. Shulman’s book there is a section “3.3. Why 16 and not 24?” [16, p. 80]. There he says that beginners becoming acquainted with socionics not infrequently pose the question carried into the section’s title. After all, the number of permutations of four (of Jung’s psychic functions) taken four at a time is 4!, i.e. 4 × 3 × 2 × 1 = 24. To answer this question Grigory Alexandrovich proposes returning to the thesis of the prohibition of intuitive-sensoric, sensoric-intuitive, logical-ethical and ethical-logical types.

One wants to ask: did Jung not also have a prohibition on irrational logicians, irrational ethicists, rational intuitives and rational sensorics? Where did this prohibition disappear to in the works of A. Augustinavichiute? After its lifting, behind a Jungian phrase such as “the extraverted intuitive type” an unsophisticated reader may see four socionic types. Moreover, the same reader may develop questions of this sort: if ILE is an extraverted intuitive, is LIE an extraverted logician? Some Jung! Not only did he fail to distinguish kindred types, but with him one and the same type could be called by different names.

Could Jung himself really not see this strangeness of his basis of bipolar traits? Of course he did not see it. For he had no basis at all. He introduced four functions straight away. Their division into rational and irrational was used to explain the opposition of the two functions within each of the indicated classes. And he did not separate kindred types because he attached no particular importance to this — though he pointed out the possibility of doing so should the need arise. I have already written about this in some detail, as it seemed to me, in article [7], and even proposed a basis of bipolar traits that would yield all 16 TIMs of the socion and, upon discarding one bipolar trait, would become a basis for Jung’s typology in which kindred types are indistinguishable.

Thanks to Alexander Valentinovich Bukalov, who referred me to the “Tavistock Lectures” [18] after my talk at the 2013 Conference, where I confessed that I had not found in Jung’s “Psychological Types” the dichotomies intuition/sensorics and logic/ethics ascribed to him. Now I can boldly assert that they are not there [18] either. The “cross” that Jung used to create in his lecture audience a visual image of the idea of the opposition of the two rational functions to each other, and likewise of the two irrational ones, is of course very similar to the “cross” one can see in G. R. Reinin when he explains how, from two sections of the socion by bipolar traits, a third section with its corresponding bipolar trait is obtained [14, p. 147]. But these are fundamentally different “crosses,” though both are formed by two perpendicular segments! Jung spoke of his “image-cross,” without providing an illustrating figure, in one of the appendices to “Psychological Types” as well: “These four functions, arranged geometrically, form a cross with the axis of rationality running at right angles to the axis of irrationality” [17, p. 658]. As we see, in Jung rationality and irrationality are represented by two axes, not by the two ends of one axis or by two half-planes obtained by cutting the plane with one axis (as in G. R. Reinin). Note that, unlike the “Tavistock Lectures,” “Psychological Types” contains no figures at all, which of course makes the text harder to take in.

In Jung, the segments forming the “cross” join into pairs the opposite functions, which cannot “work” effectively at the same time since they hinder each other. Jung has four functions in all, but by their nature they split into two pairs, and each function “wars” only with its partner in the pair. Intuition, thinking, sensation and feeling are terms used by Jung not to name the poles of dichotomies but to designate the functions themselves. The words “rational” and “irrational,” on the other hand, are used to designate the poles of a dichotomy of the set consisting of the four named functions. Under such a cutting of this four-element set, thinking and feeling fall to the rational pole, and sensation and intuition to the irrational. And Jung explains the point of introducing such a dichotomy. For him, establishing the existence of the four functions is the recording of an experimentally observed fact, while the division of this set by the bipolar trait rational/irrational is the result of analyzing an empirically obtained set of objects of study.

Does it make sense to divide this same set into such pairs: intuition+feeling and sensation+thinking, or intuition+thinking and feeling+sensation? An unambiguous answer to such a question was hard to give without a preliminary investigation. It was clear in advance — and evidently not to everyone at that — only that the benefit of introducing the corresponding bipolar traits might turn out far from equal. Moreover, there could be no a priori certainty that the four-element set should be divided into two pairs rather than into a triple and a single separate element. With empirically obtained sets anything can happen. And Jung specially emphasized that what was at issue was work with empirical material, and that the deductive exposition of results should not throw readers off.

Of course, one can deductively construct sets that are in some sense interesting and study them, and then, turning to real life, look for sets of objects for which the artificially constructed sets could serve as more or less adequate models. That too happens in science.

And if there exists a developed apparatus for deriving logical consequences from postulates given on such artificially constructed sets, one can fairly quickly “generate” a large number of facts concerning these sets. By the coincidence or non-coincidence of such theoretical facts with the corresponding experimental results one can judge the limits of applicability of the model in the given concrete situation.

It must be noted that G. R. Reinin classifies C. G. Jung’s typology as theoretical [14, p. 208], despite the fact that Jung himself, already in the “Introduction” to “Psychological Types,” writes of his typology as a generalization of his own practical medical experience. Let us give a rather long quotation:

“Experience has convinced me that, in general, individuals can be distributed not only by their universal trait of extraversion and introversion, but also by their individual basic psychological functions. External circumstances and inner disposition bring about the predominance of extraversion or introversion, but promote, in addition, the predominance in the individual of one of the basic functions over the others. Relying on experience, I have called the basic psychological functions — namely those which differ essentially from all others — thinking, feeling, sensation and intuition. If one of these functions habitually dominates over the others, the corresponding type is formed. Therefore I distinguish the thinking, feeling, sensation and intuitive types. Each of these types, moreover, can be introverted or extraverted…” [17, p. 33].

And there are all 8 Jungian types (4 × 2 = 8). Where here are the “four independent (orthogonal) traits” (G. R. Reinin)? And by what “logic of the introduced dichotomies” (S. I. Churyumov) should the types have numbered not 8 but 16?

What development of C. Jung’s 8-element typology would not contradict its internal logic, as I understand that logic? One could proceed thus. One should ask oneself: how many functions can lay claim to the role of the “second” (or “auxiliary”) if the place of the “first” is already taken? Of the three remaining functions, only the two that differ from the first in rationality can be candidates. It is here that one would need the realization that of the four psychological functions two are rational (judging) and the other two irrational (perceiving).

For two types in which the pole of the dichotomy extraversion/introversion coincides and the first function is the same, differentiation can be made on the ground that their second function does not coincide — and this is precisely the distinguishing of socionic kindred types. And C. Jung was aware of the fundamental possibility of such a distinction, but attached no particular importance to it [17, p. 494]. If one does attach importance to it, the number of types doubles and becomes 16. And there are no problems at all with the names. For example, in place of the Jungian thinking extraverted type two kindred types would form: the thinking-intuitive extravert and the thinking-sensation extravert. Using the terminology and symbolic designations introduced by A. Augustinavichiute, this would come out as: the logical-intuitive extravert (ЛИЭ, LIE) and the logical-sensoric extravert (ЛСЭ, LSE). Note that C. Jung, on the page just cited, has “speculative intellect” and “practical intellect” (without indication of version).

So what is the argument about? For that is exactly how it all began (see, e.g., [1, p. 15]). Indeed, in Table 2 of A. Augustinavichiute’s work “On the Dual Nature of Man” the TIMs bear names of this sort, and the kindred types occupy neighboring rows. Problems arose in the further development of socionics. And they are closely connected with the supposition of the uniqueness of the group of bipolar traits whose system of generators became the Jung–Augustinavichiute–Reinin basis — a basis in a certain sense out of keeping with the spirit of Jung’s typology.

Consider an example of how a seemingly insignificant difference in designations can lead to essentially different theoretical conclusions. At issue are the three-letter and four-letter codes of TIMs. The three-letter code is an abbreviation of the type names, which can be viewed as refined Jungian ones in which the kindred types are separated. For example, ИЛЭ (ILE) is the intuitive-logical extravert (i.e. the logical subtype of the Jungian intuitive extraverted type), and ИЭЭ (IEE) is the intuitive-ethical extravert (i.e. the ethical subtype of the same Jungian intuitive extraverted type). The four-letter code is a string of designations of the poles of the following bipolar traits: extraversion/introversion (E/I), intuition/sensorics (N/S), logic/ethics (T/F), irrationality/rationality (P/J). Thus ИЛЭ ≡ ENTP and ИЭЭ ≡ ENFP.

How does one determine from the codes which Jungian function (in socionic terminology — intuition, sensorics, ethics, logic) is the first and which the second (auxiliary)? In the case of the three-letter code everything is obvious: in both cases considered, the first function is intuition (as witnessed by the first letter of the code — И), while the second function in the case of ИЛЭ is logic (Л), and in the case of ИЭЭ — ethics (Э). In the four-letter code it is likewise immediately seen which Jungian functions fall into the first+second pair, but to determine which is after all the first and which the second, one must turn to the last letter of the code. If the letter there is P, the first will be the function that is irrational; if J, then only a rational function can claim first place. In our examples intuition (N) is an irrational function, while logic (T) and ethics (F) are rational (J). And since in both cases the four-letter code shows P, in both types the first function is intuition.

It would seem there is no fundamental difference! For now this difference does not catch the eye. But the situation changes cardinally if one tries to use these two varieties of codes in constructing a matrix formalism of intertype relations (IRs).

The point is this. One can speak of an operator that transforms the letter code of one TIM into the code of another TIM. Can such an operator be called an IR operator? That will depend on what we understand by intertype relations. But for now let us sort out the operators which, acting on the code of one TIM, give the code of another. In what form should these operators be represented? What are the rules of their action on the TIM codes? I have already answered these questions in my articles [4; 5]. Here I shall only recall the result.

It proved convenient to represent the IR operators as matrices which, multiplied by the column vectors of the letter codes of TIMs, yielded as a result the column vectors of the codes of other TIMs. Thus, to each ordered pair of TIMs it proved possible to assign an operator (in matrix form) which allows the code of the first TIM in that pair to be mapped to the code of the second.

Given that an ordered pair may contain two identical TIMs, the ordered pairs number 256 = 16 × 16 in all. But the distinct matrices (for a fixed choice of the kind of letter code for the TIMs) turn out to number only 16. One could then look at which TIMs are joined into ordered pairs by one and the same operator (represented by a matrix). And here is what emerged. Those matrices which joined the three-letter codes of TIMs did so in the manner of the IR operators per Augustinavichiute [1, p. 131]. And those matrices which joined the four-letter codes of TIMs did so in the manner of the IR operators per Reinin [14, p. 168]. This result is due to the fact that the three-letter code, as it turned out, reflects the structure of the model of the TIM, which is fully determined by the IAs processed by the EGO block, while the four-letter code is rigidly tied to the trait-based approach.

As is known, the 16-element sets of IRs per Augustinavichiute and IRs per Reinin have only 8 common elements. Recall that G. R. Reinin built his theory of IRs “from the standpoint of the group of bipolar traits,” recording the sets of coinciding poles of the bipolar traits in the pair of TIMs whose relations were the subject of study. One could of course see at once that in this way the four IRs called asymmetric in A. Augustinavichiute’s theory cannot be obtained; but the “splitting” (G. R. Reinin’s term) of the mirage, business, kindred and semi-dual relations was not easy to foresee.

One more very important point connected with the trait-based approach in socionics. For a fixed 16-element set of TIMs, the group of bipolar traits (a 16-element commutative group with 4 generators) is not determined uniquely! For me this assertion was so obvious that at the end of the article “A comparative analysis of the Augustinavichiute–Liashkiavichius and Reinin intertype relations tables on the basis of the matrix formalism” I confined myself to this remark: “Note that one can develop a theory of bipolar traits containing no traits sensorics/intuition and logic/ethics — which, incidentally, Jung did not have either. That is precisely why we put in quotation marks certain words connected with his surname. And this theory would in no way affect Model A or the three-letter codes of TIMs (which reflect the informational aspects processed by the EGO block), but some of the Reinin traits would have to be replaced by others, though their total number would not change. True, it would not be suitable for explaining intertype relations either, but perhaps in it bipolar traits would be obtained that lend themselves to diagnosis more easily than the already known ones. But that is a matter for future investigations, and not only theoretical ones” [5].

To be honest, I did not intend to engage in these “future investigations” myself — at any rate, not in the near future. Semyon Ivanovich Churyumov pushed me toward them. He declared that no group of bipolar traits other than the ARTs (Augustinavichiute–Reinin traits) can exist. And then it dawned on me that if the justice of my remark about the non-uniqueness of the choice of the group of bipolar traits was not obvious even to Semyon Ivanovich himself, more detailed explanations had to be given, up to and including the presentation of an alternative group. But even the presentation of an alternative group did not help. Semyon Ivanovich was sure that the new bipolar traits proposed by me were simply unrecognized Reininian ones.

Initially I built a group of bipolar traits that would be an alternative to the ARTs in order to show that this is possible in principle. What I disliked was that with the bipolar traits from the ART group, which is generated by the “Jung basis,” one cannot reach Jung’s typology. In other words, one cannot organize a successive division of the socion by four traits from the ART group in such a way that after three steps of division one obtains diads which are pairs of kindred types, whose separation would be effected by the fourth trait. That is why I spoke of constructing a group of bipolar traits that would correspond to the spirit of Jung’s typology in the sense that one could indicate in this group three traits by means of which the successive division of the socion would lead to diads consisting of kindred types, and there would also be the possibility of naming one more trait allowing them to be distinguished.

Since C. G. Jung in his 8-element typology tied himself unambiguously to the first (principal) function, and regarded the second (auxiliary) merely as a way of singling out subtypes [17, p. 494], it was clear that the basis of the sought group of bipolar traits could be constructed as follows. One must take three independent bipolar traits of the informational aspects, stipulating that these traits will refer to the 1st function, and then add one more trait that would distinguish the two possible variants for the 2nd function once the first is given (i.e. would separate the kindred types). Precisely this way of constructing the group of bipolar traits alternative to the ARTs is described by me in some detail in [7].

A more detailed study of the resulting group made it possible to give the traits absent from the ART group names transparent in their formal meaning, connected with the IAs and the numbers of the EGO-block FIMs that process them (internal/external-1; internal/external-2; detached/involved-1; detached/involved-2; α/γ-1; α/γ-2; β/δ-1; β/δ-2). Eight other traits (including the neutral element of the group — the Karpenko–Churyumov trait) were the same as in the ART group. The intermediate results of the comparative analysis of the ART group and mine — which, as it seems to me, corresponds better to the spirit of Jung’s typology — were reflected in a series of articles.

Comparing the group of bipolar traits I obtained with the ART group, I discovered a certain symmetry between these two groups. G. R. Reinin’s approach to IRs “from the standpoint of the group of bipolar traits,” applied using my group, likewise yielded a “splitting” of four symmetric relations — but different ones (mirror, activation, conflict and quasi-identity) — while the asymmetric ones “split” not along the line irrationality/rationality but along the line democratism/aristocratism [9]. Of the 15 possible partitions of the socion into four fours, inside each of which the sets of three IRs per Augustinavichiute would be identical, only 11 can be obtained by means of pairs of bipolar traits from a fixed group. Moreover, which sets of the 4 (15 – 11 = 4) partitions with the indicated property cannot be obtained by dividing the socion with two bipolar traits depends on which of the two compared groups of bipolar traits is used [8].

The impression formed that the view of IRs from the standpoint of one group of bipolar traits is just as “one-sided” as from the standpoint of the other. But the fact that the trait-based approaches to IRs founded on the alternative groups of bipolar traits proved inadequate on non-coinciding sets of IRs gave hope that these two views from different standpoints might complement each other. And indeed, it proved possible to construct a simple algorithm that can replace, for beginners in socionics, the memorization of the Augustinavichiute–Liashkiavichius IR table. This algorithm is based on checking for coincidences of poles of just a few bipolar traits in the two TIMs of the pair whose IR one wants to ascertain. But this short list of traits contains representatives of both groups [11].

The present article will present the next results of the comparative analysis of the two groups of bipolar traits. Once again I wish to note that my investigations in this direction were initiated by Semyon Ivanovich Churyumov, who refused to agree that a group of bipolar traits other than the ARTs, applicable to the TIMs forming the socion, is possible. For this he has my great thanks. The investigation carried out proved interesting and instructive for me. Will its results be interesting to other socionists? Time will tell. For now I shall present additional arguments for our polemic with Semyon Ivanovich on the possibility of the existence of two not fully coinciding groups of bipolar traits of TIMs.

Explanatory text for the diagrams and tables demonstrating the symmetry and complementarity of the views of the ring structure of the socion from the standpoints of the two groups of bipolar traits

In my article [10], in considering the question of the “strict ordering of the set of types in the socion” posed by S. I. Churyumov, a figure was given in which, for various ordering variants, the IRs between neighboring TIMs were reflected in a ring arrangement of their symbolic designations. I essentially made use of Semyon Ivanovich’s idea of reflecting IRs (in a ring structure of the “Churyumov Square” type) by segments joining the signs of the corresponding TIMs, but advanced an additional requirement: the picture of links between TIMs corresponding to a given IR must coincide with itself when rotated about the center by an angle that is a multiple of 90°. This requirement corresponds to the quadral periodicity of the IRs. But even this additional requirement did not yield a uniquely possible variant of ordering the TIMs in the socion, though some variants were discarded — among them S. I. Churyumov’s.

I proposed a “new variant” of ordering the socion, which has a certain, at least didactic, advantage over the other variants that successfully passed all the tests considered in that article. Therefore in the present article I shall use precisely this “new variant” whenever the socion is cut by bipolar traits from the ART group. When the socion is cut by traits from the alternative group I proposed, which corresponds to a greater degree to Jung’s typology, the sequence of TIMs in the socion will be closely connected with the “new variant.” The connection consists in the fact that both sequences can be obtained from one and the same “ring arrangement” of the symbolic designations of TIMs, simply by “breaking” the ring in different places.

How the “new variant” of ordering the socion is obtained by successive division with four bipolar traits from the ART group is shown in Fig. 1. The analogous diagram for the four basis bipolar traits from the group alternative to the ARTs is given in Fig. 2. Of course, the basis four in the second case is specially coordinated with the basis four of ARTs used in the first case. It is easy to notice that, by closing the row of linearly arranged TIM symbols into a ring, we obtain in both cases absolutely identical rings.

With the linear arrangement of the TIM symbols in the first case (use of ARTs) the quadras are clearly visible, each of which, in turn, consists of the successively placed right and left diads. In the second case, the socion appears as consisting of four squares, each of which consists of two dual pairs (and at the same time of two kindred pairs and two semi-dual ones).

For the squares I introduced the designations δ-α, α-β, β-γ and γ-δ. A square consists of the left diad of the quadra that comes first in the square’s designation, and the right diad of the quadra that comes second in the square’s designation.

If a quadra is a four of TIMs within which the intertype relations ДУ, ЗЕ, АК hold, then a square is a four of TIMs with the IRs ДУ, ПД, РО. With the ring arrangement of the TIM symbols — if the ring is obtained by closing the linear sequences presented in Figs. 1 and 2 — the division of the socion into quadras and squares is clearly discernible. But the paradox is that by a successive two-step cutting of the socion into fours by means of two ARTs it is impossible to reach the “square-wise” division. I have already written in some detail about this and other similar situations in [6].

On the other hand, no two bipolar traits from the group I proposed will make it possible, by successive cutting of the socion, to obtain the customary “quadra-wise” division. In this sense both compared groups of bipolar traits give “one-sided” views of the ring structure of the socion.

Note that in both cases, among the 4 basis bipolar traits we used to reach a definite sequence of TIMs, there was necessarily a trait belonging exclusively to one of the groups. In the first case it was the trait merry/serious, and in the second — α/γ-1. To the pole α-1 of this latter unfamiliar trait belong all TIMs whose 1st function processes IAs belonging to the values of the α quadra, and to the pole γ-1 — the TIMs whose 1st function deals with the γ-values.

It also makes sense to note the ordinal numbers of the basis bipolar traits (1 = 2⁰; 2 = 2¹; 4 = 2²; 8 = 2³). These same numbers are used in Tables 1 and 2. The remaining bipolar traits in these tables are likewise arranged in no random order. In third place comes the trait obtained from the first and the second by the principle indicated in his time by G. R. Reinin [14, p. 147]. Traits 5–7 are obtained from 4 and 1–3, and 9–15 from 8 and 1–7 respectively. In the “zeroth” place, denoted by the letter “E,” stands the neutral element of the group (the existence trait, or Karpenko–Churyumov trait).

Fig. 1. Successive partition of the socion arriving at the quadras and the “new variant” of ordering the TIMs within the quadras.

[Dichotomy tree over the socion with basis ARTs: 1) merry/serious; 2) democrat/aristocrat; 4) right/left; 8) static/dynamic. The leaves give the quadras: α = ILE SEI LII ESE; β = LSI EIE SLE IEI; γ = SEE ILI ESI LIE; δ = EII LSE IEE SLI.]

Table 1. Membership of the TIMs in the poles of the bipolar traits of the ART group.

Columns: E — the K–Ch trait; quadral: 1 merry/serious, 2 democrat/aristocrat, 3 judicious/decisive; dyadic: 4 right/left, 5 carefree/farsighted, 6 irrational/rational, 7 yielding/obstinate; individual: 8 static/dynamic, 9 logician/ethicist, 10 questim/declatim, 11 intuitive/sensoric, 12 positivist/negativist, 13 tactician/strategist, 14 extravert/introvert, 15 constructivist/emotivist. The last column gives the designation of the coincidence spectrum of trait poles in the pair (this TIM with ILE).

TIME123456789101112131415Spectrum
ILE++++++++++++++++ТО
SEI++++++++––––––––ДУ
LII++++––––++++––––ЗЕ
ESE++++––––––––++++АК
LSI++––++––++––++––Iк
EIE++––++––––++––++Iз
SLE++––––++++––––++μ
IEI++––––++––++++––ξ
SEE+–+–+–+–+–+–+–+–СЭ
ILI+–+–+–+––+–+–+–+ПО
ESI+–+––+–++–+––+–+КФ
LIE+–+––+–+–+–++–+–КВ
EII+––++––++––++––+Rк
LSE+––++––+–++––++–Rз
IEE+––+–++–+––+–++–τ
SLI+––+–++––++–+––+ω

Fig. 2. Successive partition of the socion arriving at the squares and the “new variant” of ordering the TIMs within the squares.

[Dichotomy tree with basis traits from the alternative group: 1) α/γ-1; 2) irrational/rational; 4) left/right; 8) static/dynamic. The leaves give the squares: δ–α = IEE SLI ILE SEI; α–β = LII ESE LSI EIE; β–γ = SLE IEI SEE ILI; γ–δ = ESI LIE EII LSE.]

Table 2. Membership of the TIMs in the poles of the bipolar traits of the group alternative to the ARTs.

Columns: E — the K–Ch trait; square: 1 α/γ-1, 2 irrational/rational, 3 δ/β-1; dyadic: 4 left/right, 5 δ/β-2, 6 aristocrat/democrat, 7 γ/α-2; individual: 8 static/dynamic, 9 detached/involved-1, 10 extravert/introvert, 11 internal/external-1, 12 negativist/positivist, 13 internal/external-2, 14 declatim/questim, 15 involved/detached-2. Spectrum column: coincidence spectrum with IEE.

TIME123456789101112131415Spectrum
IEE++++++++++++++++ТО
SLI++++++++––––––––ДУ
ILE++++––––++++––––РО
SEI++++––––––––++++ПД
LII++––++––++––++––Dк
ESE++––++––––++––++Dз
LSI++––––++++––––++ν
EIE++––––++––++++––λ
SLE+–+–+–+–+–+–+–+–СЭ
IEI+–+–+–+––+–+–+–+ПО
SEE+–+––+–++–+––+–+ДЕ
ILI+–+––+–+–+–++–+–МИ
ESI+––++––++––++––+Ак
LIE+––++––+–++––++–Аз
EII+––+–++–+––+–++–ρ
LSE+––+–++––++–+––+η

With this order of traits, the table of membership of TIMs in the poles of the bipolar traits assumes a highly ordered appearance, which in its degree of orderedness is not inferior to the “Table of Reinin traits” from O. B. Karpenko’s article “The structure of the socion” [2]. Juxtaposing Tables 1 and 2 with the diagrams in Figs. 1 and 2 will help one grasp better the connection between the order of TIMs in the socion and the order of the bipolar traits, if one wants to obtain precisely such an ordered appearance of the table’s “body.” Comparing Tables 1 and 2 with each other, one can notice that under the odd numbers come traits belonging to only one of the compared groups, and under the even numbers — coinciding traits (the difference can only be in the order of the poles).

Recall also that Table 1 has the “quadra-wise” order of TIMs and Table 2 the “square-wise” one. Therefore in Table 2, alongside the customary adjectives attached to the word “traits” (dyadic, individual), one meets a characteristic unusual for traits — square.

An interesting form of the “body” of the table marking the membership of TIMs in the poles of the bipolar traits was proposed by S. I. Churyumov [15, p. 372]. I even managed to write this 16×16 table, filled with felicitously placed “pluses” and “minuses,” as a single formula [3].

But I pointed out at once that such a table “body,” convenient for reconstruction from a single cell by a simple rule, cannot serve as a proof of the “strict ordering of the TIMs in the socion.”

In article [10] I showed which order of ARTs must be chosen so that the “new variant” of ordering the TIMs in the socion results while the “body” of the table in question remains exactly the same as in Semyon Ivanovich’s table.

Table 3. Membership of the TIMs in the poles of the bipolar traits of the ART group (with the Churyumov sign arrangement).

Columns: E; 1 static/dynamic; 2 right/left; 3 positivist/negativist; 4 democrat/aristocrat; 5 questim/declatim; 6 irrational/rational; 7 extravert/introvert; 8 merry/serious; 9 logician/ethicist; 10 carefree/farsighted; 11 tactician/strategist; 12 judicious/decisive; 13 intuitive/sensoric; 14 yielding/obstinate; 15 constructivist/emotivist.

TIME123456789101112131415
ILE++++++++++++++++
SEI+–+–+–+–+–+–+–+–
LII++––++––++––++––
ESE+––++––++––++––+
LSI++++––––++++––––
EIE+–+––+–++–+––+–+
SLE++––––++++––––++
IEI+––+–++–+––+–++–
SEE++++++++––––––––
ILI+–+–+–+––+–+–+–+
ESI++––++––––++––++
LIE+––++––+–++––++–
EII++++––––––––++++
LSE+–+––+–+–+–++–+–
IEE++––––++––++++––
SLI+––+–++––++–+––+

Let us show that exactly the same table “body” (with the Churyumov placement of the ”+” and ”–” signs in its “body”) can be obtained not only with the “new variant” of ordering the socion — where the TIMs are still grouped “quadra-wise” and ARTs are used — but also when the socion is partitioned into squares by means of the bipolar traits from the group alternative to the ARTs. For comparison, tables for both compared groups of bipolar traits are given (see Tables 3 and 4).

The question may arise: how was the order of the bipolar traits chosen in this case? Exactly as described at the abstract level in [3]! Look at Figs. 1 and 2, where a fixed order of TIMs is obtained by means of the 4 basis traits. Replace the numbering of the basis traits by the reverse: 8 → 1; 4 → 2; 2 → 4; 1 → 8. All the other numbers are assigned to the traits by the old principle, using the new numbers of the basis traits.

Note that in obtaining the tables with the Churyumov sign arrangement, the first seven places came to be occupied by traits common to the two compared groups (the eighth may be taken to be the Karpenko–Churyumov trait standing at the head of the list). And the traits that differ between the ART group and the group proposed by me (more Jungian, as it seems to me) occupy positions 8 through 15.

Let me stress once more that tables with exactly the same “body” can also be obtained for certain other orders of arrangement of the TIMs in the socion — including the canonized one printed in every issue of the journals published by the International Institute of Socionics (the Augustinavichiute–Liashkiavichius order).

Table 4. Membership of the TIMs in the poles of the bipolar traits of the JMT group (with the Churyumov sign arrangement).

Columns: E; 1 static/dynamic; 2 left/right; 3 negativist/positivist; 4 irrational/rational; 5 extravert/introvert; 6 aristocrat/democrat; 7 declatim/questim; 8 α/γ-1; 9 detached/involved-1; 10 δ/β-2; 11 internal/external-2; 12 δ/β-1; 13 internal/external-1; 14 γ/α-2; 15 involved/detached-2.

TIME123456789101112131415
IEE++++++++++++++++
SLI+–+–+–+–+–+–+–+–
ILE++––++––++––++––
SEI+––++––++––++––+
LII++++––––++++––––
ESE+–+––+–++–+––+–+
LSI++––––++++––––++
EIE+––+–++–+––+–++–
SLE++++++++––––––––
IEI+–+–+–+––+–+–+–+
SEE++––++––––++––++
ILI+––++––+–++––++–
ESI++++––––––––++++
LIE+–+––+–+–+–++–+–
EII++––––++––++++––
LSE+––+–++––++–+––+

As for the didactic advantage of the “new variant” proposed by me, it consists in the fact that every beginner in socionics can obtain it independently, using a very simple algorithm and relying only on the “Jung basis” (which would better be called the Jung–Augustinavichiute–Reinin basis, since in a certain sense it contradicts Jung’s typology). This algorithm is described in detail in [10], but it can be guessed by examining Figs. 3 and 4 attentively.

Fig. 3. Coincidence of poles from the shortened list of the ART group (in the Jung–Augustinavichiute–Reinin basis) between neighboring TIMs in the new “quadra-wise” order in the 4×4 table.

   ILE —6(6)— SEI —14(7)— LII —6(6)— ESE
    |9(9)      |9(9)       |9(9)      |9(9)
   LSI —6(6)— EIE —14(7)— SLE —6(6)— IEI
    |11(13)    |11(13)     |11(13)    |11(13)
   SEE —6(6)— ILI —14(7)— ESI —6(6)— LIE
    |9(9)      |9(9)       |9(9)      |9(9)
   EII —6(6)— LSE —14(7)— IEE —6(6)— SLI

Legend: 6(6) — irrational/rational; 9(9) — logician/ethicist; 11(13) — intuitive/sensoric; 14(7) — extravert/introvert.

Fig. 4. Coincidence of poles from the shortened list of the group alternative to the ARTs (in the basis coordinated with the Jung–Augustinavichiute–Reinin basis) between neighboring TIMs in their “square-wise” order (cf. Fig. 3).

   IEE —6(6)— SLI —14(7)— ILE —6(6)— SEI
    |9(9)      |9(9)       |9(9)      |9(9)
   LII —6(6)— ESE —14(7)— LSI —6(6)— EIE
    |11(13)    |11(13)     |11(13)    |11(13)
   SLE —6(6)— IEI —14(7)— SEE —6(6)— ILI
    |9(9)      |9(9)       |9(9)      |9(9)
   ESI —6(6)— LIE —14(7)— EII —6(6)— LSE

Legend: 6(6) — aristocrat/democrat; 9(9) — detached/involved-1; 11(13) — internal/external-1; 14(7) — declatim/questim.

The double trait numbers figuring in the diagrams — the traits whose poles coincide between diagram-neighboring TIMs — correspond to the numbers in the tables considered earlier. In Fig. 3, connected with the “quadra-wise” division of the socion and the ART group, the first number corresponds to Table 1 and the one in parentheses to Table 3. In Fig. 4, connected with the “square-wise” division of the socion and the group alternative to the ARTs, the first number corresponds to Table 2 and the one in parentheses to Table 4. Note that the double numbers occurring in Figs. 3 and 4 are the same, and they occupy coinciding positions in the compared diagrams.

Let me give two more tables which are not only very similar to each other but will also recall the “Table of intertype relations after G. Reinin” from O. B. Karpenko’s article “The structure of the socion” [2]. Table 5, connected with the ART group, practically coincides with Olga Bogdanovna’s. The difference is that I have used the “new variant” of ordering the TIMs in the socion, while she uses the more customary Augustinavichiute–Liashkiavichius order. But this did not substantially affect either the structure of the table or the composition of its elements. The elemental composition of Table 6, however, is substantially different, though the general structure of the table is preserved. Of the “old” elements only ТО, ДУ, СЭ, ПО remain. Four other elements coinciding in name with the symmetric IRs per Augustinavichiute — ЗЕ, АК, КФ, КВ — have been replaced by another four: ДЕ, МИ, РО, ПД.

Table 5. Coincidence spectra, in pairs of TIMs, of the poles of the bipolar traits of the Augustinavichiute–Reinin group.

Rows and columns in the Table 1 (“new variant” quadra-wise) TIM order: ILE, SEI, LII, ESE, LSI, EIE, SLE, IEI, SEE, ILI, ESI, LIE, EII, LSE, IEE, SLI.

ILESEILIIESELSIEIESLEIEISEEILIESILIEEIILSEIEESLI
ILEТОДУЗЕАКIкIзμξСЭПОКФКВRкRзτω
SEIДУТОАКЗЕIзIкξμПОСЭКВКФRзRкωτ
LIIЗЕАКТОДУμξIкIзКФКВСЭПОτωRкRз
ESEАКЗЕДУТОξμIзIкКВКФПОСЭωτRзRк
LSIIкIзμξТОДУЗЕАКRкRзτωСЭПОКФКВ
EIEIзIкξμДУТОАКЗЕRзRкωτПОСЭКВКФ
SLEμξIкIзЗЕАКТОДУτωRкRзКФКВСЭПО
IEIξμIзIкАКЗЕДУТОωτRзRкКВКФПОСЭ
SEEСЭПОКФКВRкRзτωТОДУЗЕАКIкIзμξ
ILIПОСЭКВКФRзRкωτДУТОАКЗЕIзIкξμ
ESIКФКВСЭПОτωRкRзЗЕАКТОДУμξIкIз
LIEКВКФПОСЭωτRзRкАКЗЕДУТОξμIзIк
EIIRкRзτωСЭПОКФКВIкIзμξТОДУЗЕАК
LSERзRкωτПОСЭКВКФIзIкξμДУТОАКЗЕ
IEEτωRкRзКФКВСЭПОμξIкIзЗЕАКТОДУ
SLIωτRзRкКВКФПОСЭξμIзIкАКЗЕДУТО

The four asymmetric IRs “split” along the line democratism/aristocratism instead of the line irrationality/rationality: Iз, Iк, Rз, Rк → Dз, Dк, Aз, Aк. The coincidence spectra of ART poles in a pair of TIMs, denoted by Grigory Romanovich with Greek letters, turned out to be replaced by coincidence spectra of the poles of bipolar traits from the JMT group with analogous designations: ξ, μ, τ, ω → ν, λ, ρ, η.

Table 6. Coincidence spectra, in pairs of TIMs, of the poles of the bipolar traits of the group alternative to the ARTs.

Rows and columns in the Table 2 (square-wise) TIM order: IEE, SLI, ILE, SEI, LII, ESE, LSI, EIE, SLE, IEI, SEE, ILI, ESI, LIE, EII, LSE.

IEESLIILESEILIIESELSIEIESLEIEISEEILIESILIEEIILSE
IEEТОДУРОПДDкDзνλСЭПОДЕМИАкАзρη
SLIДУТОПДРОDзDкλνПОСЭМИДЕАзАкηρ
ILEРОПДТОДУνλDкDзДЕМИСЭПОρηАкАз
SEIПДРОДУТОλνDзDкМИДЕПОСЭηρАзАк
LIIDкDзνλТОДУРОПДАкАзρηСЭПОДЕМИ
ESEDзDкλνДУТОПДРОАзАкηρПОСЭМИДЕ
LSIνλDкDзРОПДТОДУρηАкАзДЕМИСЭПО
EIEλνDзDкПДРОДУТОηρАзАкМИДЕПОСЭ
SLEСЭПОДЕМИАкАзρηТОДУРОПДDкDзνλ
IEIПОСЭМИДЕАзАкηρДУТОПДРОDзDкλν
SEEДЕМИСЭПОρηАкАзРОПДТОДУνλDкDз
ILIМИДЕПОСЭηρАзАкПДРОДУТОλνDзDк
ESIАкАзρηСЭПОДЕМИDкDзνλТОДУРОПД
LIEАзАкηρПОСЭМИДЕDзDкλνДУТОПДРО
EIIρηАкАзДЕМИСЭПОνλDкDзРОПДТОДУ
LSEηρАзАкМИДЕПОСЭλνDзDкПДРОДУТО

If one looks at the structure of the socion exclusively “from the standpoint of group theory,” as Olga Bogdanovna proposes, then I, for one, cannot quite see in what way the “quadra-wise” division of the socion is better than the “square-wise” one. Comparison of Tables 1, 3, 5 with the corresponding Tables 2, 4, 6 points to a certain mutual symmetry of these two coordinated divisions of the socion (after all, it was one and the same ring of the socion that was being divided). But each of these divisions possesses a certain “one-sidedness,” with the result that, using only one of the two groups of bipolar traits, one cannot build a full-fledged theory of IRs.

Nevertheless these two groups of bipolar traits can complement each other, combating the “splitting” of IRs that is observed if one tries to consider the relations from the standpoint of one group alone. The complementarity of the two alternative groups of bipolar traits is written about in more detail in [11].

In connection with what has just been said, I propose that henceforth the phrase “IRs per Reinin” with his Iз, Iк, Rз, Rк, ξ, μ, τ, ω (and, correspondingly, “IRs per Minaev” with my Dз, Dк, Aз, Aк, ν, λ, ρ, η) not be used. For what is at issue is simply sets (or spectra) of traits whose poles coincide in the pair of TIMs under consideration. In one case the ART group is used, and in the other the alternative group proposed by me, which corresponds to a greater degree to Jung’s typology but does not allow one to reach the fours so important for socionics — the quadras. And by means of the ARTs one cannot obtain the squares — fours whose significance, in my view, has yet to be grasped in full. That is why I titled Tables 5 and 6 “Coincidence spectra…” rather than “Intertype relations per…,” and why in Tables 1 and 2 one of the columns is captioned “Designation of the coincidence spectrum…” rather than “Relations preserving the given trait” (as with Olga Bogdanovna).

That the designations of some “coincidence spectra” are the same as those of IRs is, in my view, no great trouble. What is important to stress is that the bipolar traits falling into a “coincidence spectrum” are not independent. Therefore there is no need whatever to check all 15 traits of a given group (by the 16th, neutral trait all TIMs are alike). It suffices to compare the poles by the four basis traits. This gives an unambiguous answer as to which “coincidence spectrum” is at issue. If it turns out that the designation of the “coincidence spectrum” recalls the asymmetric IRs, then from this designation one can say at once which IRs hold in the pair of TIMs under consideration. With the symmetric IRs there are likewise no problems. If a spectrum results that is designated by a Greek letter, one must turn to the second (alternative but complementary) group of bipolar traits. The whole trick is that for the two groups of traits we have considered, Greek letters as designations of the “coincidence spectra” will not result simultaneously (in a fixed pair of TIMs). On this remarkable fact is based the practical algorithm replacing the memorization of the IR table. It is described in [11].

Conclusion

I sincerely hope that this article will put a full stop (despite my love of the process) to my polemic with S. I. Churyumov concerning the uniqueness of the group of bipolar traits (not only the ART group is possible). The recognition of the existence of the group of bipolar traits which Semyon Ivanovich and I called for brevity the “JMT group” (Jung–Minaev traits) gives hope for interesting substantive results from a more detailed investigation of the group I have proposed. And this means that a new field of work opens up both for theorists and for experimenters. I, for example, would like in subsequent articles to disclose the role of the squares in the relay of the quadras.

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The article was received by the editors on 04.08.2014.

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