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From Opposition to Constructive Attribution

In: B. A. Banathy, ed. Proceedings of the 43rd Annual Conference of the International Society for the Systems Sciences, Asilomar, CA, June 26 - July 2, 1999, 15 p.
Vitaly Dubrovsky

Following the "activity approach", this paper interprets duality as a fundamental logical principle of opposition, common to all historical times and cultures. Aristotle was the first to recognize the role of opposition in ontological construction and to formulate the main principles of opposition. Aristotle was also the first to make a giant step beyond opposition and create the method of ontological construction, which permitted him to develop his philosophy and which also paved the road for further development of philosophy and science. We call this method constructive attribution of opposites. Although Aristotle did not formulate the principles of constructive attribution, he did use the method repeatedly in his work. Normative reconstruction of constructive attribution is the main purpose of this paper.

Keywords: duality, opposition, intermediates, cross-attribution, same-side attribution, constructive attribution.

1. Introduction

The purpose of this paper is to reconstruct the Aristotelian method of ontological construction, which, we believe, made Aristotelian philosophy not just another step in the development of Greek philosophy following Plato, but which was itself a radically new way of thinking. Only with a radically new way of thinking was it possible to resolve what Windelband (1888) called "the great controversy" in pre-Aristotelian Greek philosophy: Being versus becoming (Parmenides versus Heraclitus), objective versus subjective (Socrates versus the Sophists), form versus matter (Pythagoras versus the Milesians), ideal versus real (Plato), etc. Typically, one side was proclaimed as the true and perfect reality, while the opposite side was false, imperfect, illusory. But even in those cases when both opposites were recognized as equally necessary for the World construction, there was an absolute, unbridgeable gap between the two. Resolving "the great controversy" Aristotle overcame the "two-world" ontological duality, basic to Greek philosophy including Plato, and built a "one-world" ontology (Zeller 1883/1928, p. 160; Solomon and Higgins 1997, p. 40). The new ontology was built upon a dualistic approach and thus was a more concrete representation of "the world" than the dualistic one (Coplestone 1962, p. 298); this required what Hegel called "ascending from abstract to concrete." In turn, the latter required a systematic method of ontological construction (Zeller 1883/1928, p. 168).

The duality in Greek philosophy was a direct result of opposition used by all the philosophers in their ontological constructs. Aristotle was the first who recognized the essential role of opposition as a principle of ontological construction. He radically changed the notion of opposition by formulating ontological and epistemological principles of the unity of opposites and introducing the third member of opposition--basis. Aristotle identified four types of opposition in Categories, Chapter 10. He discussed them in the context of ontological construction in Physics, Metaphysics and other works. In Topics, Book 6, Chapters 9 and 14, Aristotle analyzed the typical mistakes that people make in formulating definitions by opposition.

Before Aristotle, opposition was the only formal principle of ontological construction. Aristotle developed a new method that can be considered as the next stage of ontological construction following opposition. We call this method constructive attribution. The essence of this two-step method is the construction of intermediates between opposites followed by reinterpretation of the opposites in terms of the intermediates, which upgrades the entire construct to a more concrete level of ontological representation. Although Aristotle did not provide a detailed description of constructive attribution, as he did for opposition, this paper will show that he used the method repeatedly in his work. Normative reconstruction of constructive attribution is the main purpose of this study. Considering the complexity of this task, we will narrow the scope of analysis to a single unit, which is the primary and central unit of Aristotle's ontology -- "substance-form-matter".

In this study, we entertain a non-critical approach to Aristotle. We believe that any external critique of Aristotle's views would be irrelevant to the purpose of this study. If we want to learn from Aristotle his method of ontological construction, we have to accept his philosophical ideas as they are. Even an internal critique of self-contradictions, discrepancies, omissions, and incompleteness in Aristotle's works would be irrelevant. Metaphysics, the main material used in this analysis, according to a common view, was not written by Aristotle as a book to be published, but, most likely, is a collection of lecture notes of his students. The collection might be incomplete; it includes irrelevant fragments and repetitions, not all promises are fulfilled, and there are traces of repeated editing. We believe that for the purpose of this study, the most productive approach would be to view the entire forest of Metaphysics, along with the surrounding landscape of other books, and attempt to grasp its principle design and only then to look the at trees of individual statements.

Approaching Aristotle in this way, we make two assumptions. The first assumption is that Aristotle "was not a fool" (Coplestone, 1993, p. 299) and was the only one who had an intuitive grasp of his philosophy. Based  on this assumption, we consider Aristotle's statements that appear contradictory to be so only because of incorrect interpretation or editing. We have adopted the view advocated by Hegel that "Aristotle tended to approach every problem from many different perspectives, every time obtaining different results that did not contradict each other but rather complement each other" (according to Rozhansky, 1981, p. 19).

The second assumption of this study was that, in his ontological construction, behind the typical scene of Aristotle's dialectical inquiry, he consistently followed his principles of opposition and construction of intermediates. According to this assumption, we looked for evidence that Aristotle, "being constrained as it were by the truth itself", treated form and matter as polar species, opposed upon the same genus, even in those cases where he did not explicitly oppose them, and for the appropriate intermediate constructs.

2. Aristotle's Principles of Opposition and Construction of Intermediates

2.1. Principle 1: Primary Elements of Ontology Must Be Introduced by Opposition

As was mentioned above, Aristotle was the first who recognized the philosophical tradition of ontological construction using opposition:

All thinkers then agree in making the contraries principles, both those who describe the universe as one and unmoved (for even Parmenides treats hot and cold as principles under the names of fire and earth) and those who use the rare and the dense. … It is plain then that they all in one way or another identify the contraries with the principles. And with good reason. (Physics 188 a 19-28).

Aristotle believed that this tradition was objectively necessitated: "…for all of them identify their elements, and what they call their principles, with the contraries, giving no reason indeed for the theory, but constrained as it were by the truth itself" (Physics, 188 b 28-30). He felt himself as being constrained by the truth: "It is clear then that our principles must be contraries" (Physics, 189 a 10). The principle, according to which primary elements of ontology must be introduced by opposition, we consider the first Aristotelian principle of ontological construction.

2.2. Principle 2: Elements of Ontology Must Be Opposed as Polar Species upon the Common Basis of Their Genus

Aristotle should be credited with the introduction of the third member of opposition, a basis upon which the contraries must be opposed: "…it is clear that there must be something underlying the contraries, and that the contraries must be two" (Physics, 191a4-5). He defined opposites as two polar species of the same genus (Metaphysics, X, 4 and 8): "And the things in the same genus which differ most are contraries…" (Metaphysics, X, 4, 1055a, 27-28) and "… it has been shown that contraries, though they are completely different, are in the same genus.  ... Hence, all contraries differ as to species, not as to genus and are of the same category" (Metaphysics, 1058a, 10). This common genus then plays the role of the basis of opposition (Physics I, 6 and 7; Ross, 1923/1995, p. 66-68).

The principle of opposition of contraries upon the same genus was a formal representation of the ontological unity of opposites. The principle that opposites must be studied by the same science (Metaphysics, IV, 2 and Book XI, 3) was its epistemological counterpart. The principle according to which contraries as polar species must be opposed upon a basis of the common genus, we consider the second Aristotelian principle of ontological construction.

2.3. Principle 3: Elements of Ontology Must Be Opposed in Four Different Ways

Aristotle distinguished four types of opposition:

Things are said to be opposed to one another in four ways: as relatives or as contraries or as privation and possession or as affirmation and negation. Examples of things thus opposed (to give a rough idea) are: as relatives, the double and the half; as contraries, the good and the bad; as privation and possession, blindness and sight; as affirmation and negation, he is sitting--he is not sitting (Categories, 11b, 18-22).


Although the examples in the above quotation may give an impression that different things can be opposed in different ways, we will show below that in his ontological construction Aristotle opposed form and matter in all four ways. So we assert that the four types of opposition are not independent or optional, but are required stages of ontological construction, and, therefore, must be mutually congruent. We consider this as the third Aristotelian principle of opposition.

2.4. A Principle of Construction of Intermediates

In respect to intermediates, Aristotle formulated the following principle: "Clearly, then, intermediates are all in the same genus and intermediate between contraries and compounded out of the contraries" (Metaphysics, 1957 b 33-34; also 1057a 19-20). He did not discuss rules of composition of the intermediates, but introduced the intermediates through an ad hoc dialectical discourse.

According to our assumptions, we are looking in Aristotle's works for: (1) four layers of opposition of form and matter; (2) intermediates, constructed of form and matter, for the three first layers (since "contradictories accept no intermediates" (Metaphysics, 1057 a 33-35; also Metaphysics, IV, 7); and (3) definitions insuring congruence among the layers. Due to the constraints of length, in this paper we concentrate on the internal construction of the layers.

3. Sensible versus Intelligible Substances

For a correct understanding of Aristotle's ontology, one must keep in mind that, although Aristotle viewed reality, or "being", as objective and independent of human mind, he analyzed it as a subject matter of theoretical thought (Asmus, 1976). Another point necessary to keep in mind for a correct understanding of Aristotle is that all his logical and ontological doctrines were heavily influenced by the assumption that any statement about reality, essentially, is attribution of properties to things. This also accounts for the subject-predicate form of Aristotle's language (Losiyev 1975). Bambrough (1963, p. 36) combines these two points in the summarizing assertion that the main constituents of Aristotle's ontology "are all derived from a study of the ways in which language-as-we-use-it is applied to the world-as-we-know-it".

The above considerations are especially important in understanding the primary category of Aristotle's ontology, the category of substance. According to Aristotle, the objective, and independent of human mind reality of Being, must be categorically represented as a subject matter of human theoretical thought as Substance (Metaphysics, 1028b 2-4; Barnes, 1995). Unfortunately this primary category of Aristotelian philosophy is also the most controversial. Chanishev (1981, p. 294) called Aristotle's treatment of primary and secondary substances "the main contradiction of Aristotle's ontology". Barnes (1995, p. 67) characterized Aristotle's arguments related to substance "tortuous to the extreme" and without clear final view on the subject (see also Driscoll 1981; Woods 1967 and Owen 1965). We avoid discussion of this controversy at this point. We accept Aristotle's view that only an individual thing that exists independently in itself is a substance; it cannot be attributed to anything else, but itself can have attributes and properties. In a statement, it can play only the role of a subject to which names, properties, and definitions are attributed. While ontologically, being, or individual substances, exist objectively and independently and can be perceived directly, epistemologically, they are a subject matter of theoretical investigation, and are represented conceptually in terms of universals, species and genera, which can be grasped only by intelligence. Aristotle characterizes them respectively as logically primary (sensible) and secondary (intelligible) substances. "But as the primary substances stand to everything else, so the species and genera of the primary substances stand to all the rest: all the rest are predicated of these (Categories, 3a 1-3). While primary substance conveys "thisness"; secondary substance conveys "whatness", or "essence" of a thing (Ross, 1923; Losiyev, 1975). It seems that Aristotle reflectively expands his ontology by inclusion of mind and reason as constituents of being along with nature (Physics, 198 a 10-12). If this is correct, then Aristotle can be interpreted in the following way: although in the reality of nature, universals do not exist apart from the individual substances, in the actuality of mind, they are thought of as independent individual substances (species, or eidos).

4. Form and Matter

Form and matter are essential constituents of Aristotle's ontology that he inherited from his teacher Plato. However, Aristotle was dissatisfied with the way Plato treated the relationship between form and matter. He accused Plato of an absolute separation of form and matter and considered it the main source of problems in Plato's philosophy (Metaphysics, 1086a 30-1086b 13). The main problem was an inability to explain the observable motion of things, their changes, and their coming-into-being and passing away. The motionless forms of Plato could not account for the motion of their "copies", or things. This problem was the main preoccupation in Aristotle's dealing with Form and Matter (Ross, 1923).

The view of a individual substance as combination of form and matter proved to be essential in explaining how things come to be and cease to be and in explaining change and motion in general. We believe that this view was inspired by his observation of human activity, specifically of human cooperation: "The arts, therefore, which govern the matter and have knowledge are two, namely the art which uses the product and the art which directs the production of it… For the helmsman knows and prescribes what sort of form a helm should have, the other from what wood it should be made and by means of what operations " (Physics, 194 b 37-195 a 7). It was typical of Aristotle to draw his ideas and examples from the realm of human activity and then extend them to natural processes by a kind of metaphor (Bambrough, 1963).

Western translations use the term "form" for three different Aristotelian terms: "morphe", "eidos", and "logos". However, some translations use the term "idea" or "species" to translate "eidos" and "formula" or "definition" to translate "logos", leaving "form" for "morphe". "Aristotle used the terms 'form' (morphe) and 'species', or 'idea' (eidos) almost as synonyms. Strictly speaking, form is what makes a species distinctive and what is signified by the verbal definition (logos)" (Rozhansky, p. 563). Also, Aristotle used different terms related to matter: "sensible matter", "intelligible matter", "primary matter" and the number of meanings for matter is even greater (Ross 1923, pp. 173-179). It seems that the term "matter" (hyle) plays a unifying role for all the uses of matter and form (Barnes 1995, pp. 97-98).

4.1. Opposition of Form and Matter as State and Privation

Aristotle explicitly opposed form and matter as Definition and Privation-of Definition upon the basis of intelligible substance. “The primary contrariety is that between state and privation, not every privation, however (for ‘privation’ has several meanings), but that which is complete" (Metaphysics, 1055a, 33-35). In the "possession-privation" type of opposition, privation of one of the opposites plays the role of the other one (Physics, 191a 5-7). In the privation-possession type of opposition, form as Definition (logos) is opposed to matter as Privation-of-Definition: "… one is the form or definition; then the further its contrary, the privation (191a 9-14) and "one element is formula (logos) and one is matter (hyle)" (Metaphysics, 1058b 38 - 1059a 2).

Aristotle distinguished sensible and intelligible matter: "And some matter is sensible and some intelligible, sensible matter being for instance bronze and wood and all matter that is changeable, and intelligent matter being that which is present in sensible things not qua sensible, i.e. in the objects of mathematics" (Metaphysics, 1036a 8-11). He defined the basis of opposition of form-Definition and matter-Privation as intelligible substance (Physics, 191a 9-14).

"It is in studying becoming of things that the state of privation has to be recognized" (Ross, 1923/1995, p. 69).

The abstract opposition of form-Definition to " indefinite" and "unknowable in itself" matter-Privation was a too abstract one to permit explanation of how things come into being.

4.2. The Intermediates: Actuality and Potentiality

Aristotle solved the above problem by "the distinction of grades of being -- potentiality and actuality" (Ross, 1923/1995, pp. 68-69), or, in our terms, by constructing the intermediates of Potentiality (dynamis) and actuality (entelecheia) between form-Definition and matter-Privation. Although Aristotle did not explicitly characterize Actuality and Potentiality as intermediates between form-Definition and matter-Privation, he treated them as intermediates. First, Actuality and Potentiality are not primary opposites: since "in the primary sense potential is potential because it is possible for it to become actual" (Metaphysics, 1949 b 13-14), not everything that is not actuality is potentiality. This can be illustrated by a simple example: "A man in a state of deep sleep or coma is not actually thinking, but, being a man, he has the potentiality of thinking, whereas a stone, though it is not actually thinking, has no potentiality for thinking" (Copleston 1993, p. 310). Second, as it would be required for intermediates between form and matter, Aristotle characterized Potentiality and Actuality in the terms of these opposites: "Further, matter exists in a potential state, just because it may attain to its form; and when it exists actually, then it is in its form" (Metaphysics, 1050 a 15-16). Actuality and Potentiality are connected by the process of Actualization (energeia), in which matter capable of attaining a form actually attains it.

In our interpretation of Aristotle's terms we follow Losiyev (1975) and Rozahnsky (1963, p. 561): "Along with the term 'entelecheia', and even more often, Aristotle uses the term 'energeia', which has almost the same meaning, however, with a different emphasis. Energeia is a process or realization of potential, activity, an act; entelecheia is a result of this activity, i.e. the final state at which the process ends." In this paper, we have chosen to quote Aristotle according to the standard translation (The Complete Works of Aristotle, 1984). In our interpretations, however, we use the terms as we believe they should be used. Aristotle explains the relationship between the two terms in the following way:

The word "actuality " (energeia) which we connect with "fulfillment" (entelecheia), has, strictly speaking, been extended from movements to other things; for actuality (energeia) in the strict sense is identified with movement. (Metaphysics, 1047 a 30-32)… For the action is the end, and actuality is the action. Therefore even the word "actuality" (energeia) is derived from "action" (ergon), and points to the fulfillment (entelecheia). (Metaphysics, 1050 a 21-23).

4.2.1. Actuality

Aristotle suggested that the definition of Actuality should include both matter and form-Definition:

Obviously then some part of the result will pre-exist of necessity; for the matter is a part; for this is present in the process and it is this that becomes something. But do some of the elements of the formula preexist? Well, we describe in both ways what bronze circles are; we describe by matter by saying it is bronze, and the form by saying it is such and such a figure; and figure is a proximate genus in which it is placed. The bronze circle, then, has its matter in its formula." (Metaphysics, 1033 a 4-5) …And so, as there also a thing is not said to be that from which it comes, here the statue is not said to be wood but is said by a verbal change to be not wood but wooden…" (Metaphysics, 1033 a 17-19).

The definition should also reflect the process of Actualization:

Where, then, the result is something apart from the exercise, the actuality is in the thing that is being made, e.g. the act of building is in the thing that is being built and that of weaving in the thing that is being woven, and similarly in all other cases, and in general the movement in the thing that is being moved; but where is no product apart from the actuality, the actuality is in the agents, e.g., the act of seeing is in the seeing subject and that of theorizing in the theorizing subject and the life is in the soul (and therefore well-being also; for it is a certain kind of life). (Metaphysics, 1050 a 30 - 1050 b 1).

Since actualization means that matter that is potent to attain form-Definition does attain it, attribution of matter-Privation to form-Definition, i.e. material Form (I would prefer a verbal form "materialized Definition") can be used to formally characterize Actuality in terms of the opposites. This approach corresponds to Aristotle's subject-predicate form of language, so that everything in the world which is not a particular substance must be an attribute of such a substance (Bambrough, 1963). A wooden statue from the above quotation is the example. We follow the "attributive" approach in this paper.

4.2.2. Potentiality

In every particular process of becoming, or act of creation, for example, creation of a bronze sphere from bronze, a lump of bronze, as potential bronze sphere, precedes the bronze sphere. At the same time, the actuality of a bronze sphere in general precedes the definition of a lump of bronze as a potential bronze sphere (Metaphysics, Books 9, Chapter 8). For example, before making a sphere out of bronze, an artist, according to his experience of making bronze spheres, determines that the lump of bronze is suitable for making a bronze sphere. In other words, he defines a lump of bronze, not just as privation, but as privation of sphere, or as definite Privation, "e.g. in bronze the privation of a particular shape" (Metaphysics, 1033 a 15). Similarly, in the objects of nature, matter must be in a definite state to have potentiality of attaining a certain form: "E.g. is earth potentially a man? No--but rather when it has already become seed, …the seed is not potentially a man; for it must further undergo a change in a foreign medium. But when through its own motive principle it has already got such and such attributes, in this state it is already potentially a man" (Metaphysics, 1049a 1-16). Thus Potentiality can be formally characterized in terms of the opposites by attribution of form-Definition to matter-Privation which produces definite Privation, or more generally, formal Matter.

The above attribution of matter-Privation to form-Definition producing "material Definition" and attribution of form-Definition to matter-Privation producing "definite Privation" prompted us to call the method of introduction of intermediates cross-attribution. (This English term was suggested by Dr. Emanuel Smikun.)

4.2.3. Concretizing Reinterpretation of the Opposites

After introduction of the intermediates, Aristotle reinterpreted each of the original opposites using a method, which we will call same-side attribution. We will first see how Aristotle reinterpreted form-Definition based on Actuality and then we will formally reconstruct the method. Aristotle characterized form-Definition as a pure and complete actuality, disassociated from any potentiality, and thus as a form, completely disassociated from any matter (Metaphysics, Book 12, Chapter 7). ). To comprehend pure actuality, one has to consider a special type of actualization ("actuality" in the quotation): "but where is no product apart from the actuality, the actuality is in the agents, e.g., the act of seeing is in the seeing subject and that of theorizing in the theorizing subject" (Metaphysics, 1050 a 30 - 1050 b 1). This type of actualization in turn has a special subtype ("action" in the quotation) "in which the end is present is an action. E.g. at the same time we are seeing and have seen, are understanding and have understood, are thinking and have thought…(Metaphysics, 1048b 22-24). Now let us imagine activity of self-thinking "thought of thought", which is continuously theorizing and thus have theorized and the result of theorizing is already in the thought itself. In other words, thought of thought is a continuous process of self-actualization containing its actuality, and thus, is continuous pure actuality. Aristotle identifies thought of thought as God (Metaphysics, Book 12, Chapters 7 and 9).

We suggest the following formal reconstruction of the same-side attribution. First Aristotle attributed Actuality to form-Definition, "subtracting", however, from its characteristic as "material Definition" the attribute "material" (because opposites "do not involve one another in their composition") thus characterizing form-Definition as pure actuality. But because attribution of matter to definition in actuality reflects the process of actualization, Aristotle had to demonstrate how pure actualization without any potentiality, and therefore, without matter, is possible.

On the opposite side, in the same manner, Aristotle attributed potentiality to matter-Privation, "subtracting" the attribute "definite" from "definite Privation", thus characterizing matter as a pure, or indefinite potentiality, which never becomes actual, but underlies actualization of all things (Metaphysics, Book 9, Chapter 7; Physics, Book 1, Chapter 9). Aristotle illustrates this in the following way: "The matter comes to be and ceases to be in one sense, while in another it does not. As that which contains the privation, it ceases to be in its own nature; for what ceases to be--the privation--it contained within it. But as potentiality it does not cease to be in its own nature, but is necessarily outside the sphere of becoming and ceasing to be" (Physics, 192 a 25-29).

Thus, Aristotle bridged the gap between form-Definition and matter-Privation by introducing the intermediates, Actuality as material Definition and Potentiality as definite Privation constructing them by cross-attribution of the opposites. He then reinterpreted the initial opposites, attributing to them additional properties by means of same-side attribution, thus ascending the entire system to a more concrete level. At this level, Aristotle represented becoming and creation as actualization--the process in the course of which potentially existing things become actual. Cross-attribution and same-side attribution are the two steps of the method of ontological construction that we will call constructive attribution.

4.3. Form and Matter As Contraries

Aristotle did not directly oppose Form and Matter as contraries, but introduced them along with an intermediary, a "concrete thing".

Now the substratum (hypokeimenon) is that of which other things are predicated, while it is itself not predicated of anything else. And so we must first determine the nature of this; for that which underlies a thing primarily is thought to be in the truest sense its substance (oysia). And in one sense matter (hyle) is said to be of the nature of substratum, in another, shape (morphe), and in a third sense the compound of these. By the matter I mean, for instance, the bronze, by the shape the plan of its form, and by compound of this (the concrete thing) the statue (Metaphysics, 1028 b 35 - 1029 a 6).

However, actually, Aristotle treated Form (eidos, morphe) and Matter (hyle) as contraries upon the basis of sensible, or primary Substance (oysia). First, like in the above quotation, Aristotle always introduced form and matter first, and only then he mentioned "the compound of these"--a concrete thing. Second, according to Aristotle, "contraries do not involve one another in their composition " (Metaphysics, 1057 b 23). Correspondingly, Aristotle never used form or matter in composing one another. Third, according to Aristotle, opposites are always polar species of the same genus and intermediates also belong to the same genus. Correspondingly, "both the matter and the form and the compound are substance" (Metaphysics, 1035 a 1-2). and, thus, the Substance plays the role of the basis for opposition of Form and Matter (Metaphysics, Book 10, Chapter 4). Fourth, "if intermediates are in the same genus, as has been shown, and stand between contraries, they must be composed of these contraries" (Metaphysics, 1057 b 1-3). Correspondingly, Aristotle describes an intermediate, "the concrete thing", as a compound of form and matter. Finally, Aristotle treats Form and Matter as principles, and therefore, as pre-existing of creation or coming to be of any particular substance or thing (Metaphysics, Book 7, Chapter 9). They also are imperishable after a particular thing is destroyed or perishes (Metaphysics, Book 8, Chapter 1; Book 10, Chapter 10; Physics, Book 1, Chapter 10). For example, although this particular bronze lump changes in the process of becoming a sphere, a sphere as form (morphe) stays unchanged. Likewise, the bronze as matter of the bronze sphere does not change either; it stays bronze throughout the entire process of formation.

4.4. The Intermediates: Thing and Element

Since Aristotle opposed Form and Matter as contraries, he had to define intermediates between them. One intermediate--Thing--he introduced along with the contraries. The other intermediate is Element.

4.4.1. Thing

Aristotle observed that "different things must have their matter different, e.g. a saw could not be made of wood" (Metaphysics, 1044a 27-9). A particular matter, suitable for creation of a certain kind of thing, Aristotle called proximate matter. In congruence with the previous "form-Definition -- matter-Privation" layer, proximate matter of a thing can be characterized as a matter potent of attaining the form. Aristotle explains: "E.g. a casket is not earthen not earth, but wooden, for wood is potentially a casket and is the matter of casket, wood in general of a casket in general, and this particular wood of this particular casket" (Metaphysics, 1049a 24-25). Although according to the Greek belief, wood is made of earth, earth is not potentiality of a casket, and therefore, is not its proximate matter. Thus Thing is an intermediate by definition: (1) it is a substance, i.e. in the same genus as Form and Matter; (2) as a species, it is intermediate between these contraries; and (3) it is composed of Form and proximate Matter. Aristotle explains that the essence of a particular thing which is composed of bronze and sphere is not "bronze and sphere", or "spherical bronze", but "bronze sphere", "because its coming to be implies change in that from which it comes, and not permanence. For this reason, then, we use this way of speaking" (Metaphysics, 1033a 21). Thus formally, proximate matter (bronze) is attributed to form (sphere), producing an individual Thing (a bronze sphere). The formal act of attribution reflects the actual process of the Thing's formation. If in the specific terms of sphere and bronze a thing is defined as a bronze sphere, then in general terms of Form and Matter, Thing can be defined as material Form. The act of attribution of Matter to Form reflects the process of Formation in general.

4.4.2. Element

Because many things can be made of bronze, we can view it as a metal with all its properties and characteristics independent of any particular thing that can be made of bronze. In other words, we can view a lump of bronze as a particular substance in its own right, a thing, which has its form and matter. This is exactly how a metallurgist views it. And we can ask "of what is bronze made?" or "what is the matter of bronze?" The same question can be asked regarding any particular substance. And the same question can be asked iteratively regarding a hierarchy of matters: "And there come to be several matters for the same thing, when the one matter is matter for the other, e.g. phlegm comes from the fat and from the sweet, if the fat comes from the sweet; and it comes from bile by analysis of the bile into its ultimate matter" (Metaphysics, 1044a 20-23). So the question arises: what is the first matter that each thing can be reduced to? Aristotle answered this question according to the Greek tradition, which maintained that all things are made of different combinations of four simple bodies, fire, air, water, and earth: "all bodies are composed of all the simple bodies" (On Generation and Corruption, 335 a 22). Note that every matter in the hierarchy including simple bodies is a proximate matter for the previous substance. Now, what are simple bodies as substances? What is their form and matter?

Aristotle explains that the form of each simple body is constituted by a coupling of two non-opposite "elements" out of the existing four: hot, cold, dry, and moist. "Hence, it is evident that the couplings of the elements will be four: hot with dry and moist with hot, and again cold with dry and cold with moist. And these four couples have attached themselves to the apparently simple bodies (Fire, Air, Water, and Earth) in a manner consonant with theory" (On Generation and Corruption, 330 a 33 - 330 b 2). Simple bodies under certain conditions can be transmuted into one another. For example, under heat, water may become air, and air may become fire. The substance that underlies all these and other transmutations, staying unchanged itself, Aristotle called prime matter. So one peculiarity of simple bodies is that they do not have definite proximate matter. Another peculiarity is that their combination determines the form of the substance that they, as a proximate matter, compose. These peculiarities clearly distinguish simple body from Thing and suggest categorization of simple bodies as formal Matter. The attribution of Form to Matter reflects the process of transmutation of a simple body from one form into another. Thus, along with Thing, Aristotle introduced another intermediate substance between Form and Matter--Element.

4.4.3. Concretizing Reinterpretation of the Contraries

As in the case of form-Definition and matter-Privation, Aristotle reinterpreted the original opposites Form and Matter according to the same-side attribution of the intermediaries. On one side, Aristotle attributed being a Thing (material Form), to the Form, of course, "subtracting" the attribute "material" from "material Form", and defining it as pure, i.e. disassociated from any matter. According to Aristotle, as a thing's constituent, form is preexisting to thing's formation and imperishable after its destruction. He absolutely extended this characteristic on the pure form and attributed it with being eternal. However, somehow he had to make-up for the loss of the process of formation, which was reflected in the act of cross-attribution of Matter to Form. Aristotle pointed to the already familiar to us thought of thought as a thing, or a particular substance, which he characterized as a pure "form of forms": "Thought is itself thinkable in exactly the same way as its objects are. For in the case of objects which involve not matter, what thinks and what is thought are identical; for speculative knowledge and its object are identical." (On the Soul, 430 a 3-4) and "for as the hand is a tool of tools, so thought is the form of forms" (On the Soul, 432 a 2). This view of Form is in complete congruence with the view of form-Definition.

On the other side, according to the same-side attribution, Aristotle attributed being an Element to Matter, but "subtracting" the attribute "formal" from "formal Matter", thus characterizing matter as a pure, or prime matter--an ultimate substratum of all transmutations of elements. Unknowable in itself, existing only in conjunction with some form, prime matter can only logically, by abstraction, be separated from form (Metaphysics, Book 9, Chapter 7; Copleston, 1946; Asmus, 1976). As an element, prime matter does not need to reflect the process of transmutation in its definition, because it does not change in any transmutation.

Thus, Aristotle, bridging the gap between contraries Form and Matter, introduced the intermediates, Thing and Element, by means of cross-attribution. Then using the same-side attribution, he extended Thing and Element onto same-side opposites, attributing to them additional properties, thus ascending the entire system to a more concrete level. At this level, Aristotle represented creation and change as formation and transmutation of elements.


4. 5. Form and Matter as Relatives

Aristotle introduces the category of cause for the purpose of explanation of motion and change in terms of form and matter (Asmus, 1976). As in the case of contraries, Aristotle does not oppose form and matter as relatives directly, but introduces all four causes, Material, Formal, Efficient, and Final in the course of historical-philosophical analysis (Metaphysics, Book 1).

We call a cause (1) that from which (as immanent material) a thing comes into being, e.g. the bronze of the statue and the silver of the saucer, and the classes which include these. (2) The form or pattern, i.e. the formula of the essence, and the classes which include this (e.g. the ratio 2:1 and number in general are causes of the octave) and the parts of the formula. (3) That from which the change or the freedom from change first begins, e.g. the man who has deliberated is a cause, and the father is a cause of the child, and in general the maker is cause of the thing being made and the change-producing of the changing. (4) The end, i.e. that for the sake of which a thing is, e.g. health is the cause of walking. (Metaphysics, 1013 a 24-34)

According to our hypothesis, although Aristotle did not directly oppose Material and Formal causes or construct Efficient and Final causes as the intermediates, he was "constrained as it were by the truth itself " to treat them as such. First, in every listing of the four causes, Aristotle mentioned Material and Formal causes first and Efficient and Final causes next.

Second, "Aristotle inclines to reduce the four causes to two, namely, the formal cause and the material cause" (Copleston, 1961/1993, p.314). Asmus (1976, p. 281) was even more specific: "After establishing in this way four causes of everything which happens, Aristotle asks which of them are main and irreducible and which can be reduced to others. As a result of his analysis, Aristotle comes to the conclusion that, out of four causes, two are main and irreducible and the other two can be reduced to the first two. These main and irreducible causes are 'form' and 'matter'."

Third, as irreducible to one another, form and matter are opposite principles if they are belong to the same genus, or in other words, are opposed upon a common basis. Aristotle identified Nature as a genus for Material and Formal causes and as an underlying substance: "It is plain then that nature is a cause, a cause that operates for a purpose" (Physics, 199 b 32). …"This then is one account of nature, namely that it is the primary underlying matter of things which have in themselves a principle of motion or change. Another account is that nature is the shape (morphe) or form (eidos) which is specified in the definition (logos) of the thing" (Physics, 193 a 28-31).

Fourth, according to Aristotle's actual treatment of Formal and Material causes, they were opposed by him as relatives, since one cannot be considered without the other. For example, if the purpose of a saw is to cut wood, then the saw should be made of iron rather then of wood (Metaphysics, 200 b 4-7). In this example, it is the form of saw, which determines certain material; and it is iron which "determines" that a saw can be used according to its purpose.

Fifth, since Aristotle did not start with the opposition of Formal and Material causes upon the basis of Nature, but introduced them along with Efficient and Final causes, he did not explicitly construct the latter two as the intermediates. Instead, he identified the intermediates by what in the literature is called their "reduction" to Material and Formal causes. We should not be misled by the English term "reduction", which was not used by Aristotle. Aristotle simply called different causes identical: "The last three often coincide; for the what and that for the sake of which are one, while the primary source of motion is the same in species as these" (Physics, 198a 25-26). The interpretation according to which Efficient and Final causes can be reduced to the Formal and Material ones contradict Aristotle's assertion that "there are several causes of the same thing, and in no accidental sense" (Metaphysics, 1013 b 5-6). It also contradicts the following statement: "Now, the causes being four, it is the business of the student of nature to know about them all, and if he refers his problem back to all of them, he will assign the 'why' in the way proper to his science--the matter, the form, the mover, that for the sake of which." (Physics, 198 a 21-24)

Aristotle explained that depending on the type of one's question, one should emphasize different causes: "In investigating the cause of each thing it is always necessary to seek for what is most precise (as also in other things); thus a man builds because he is a builder, and a builder builds in virtue of art of building. This last then is prior; and so generally" (Physics, 195b, 22-25). Moreover, Aristotle explains in which particular cases Efficient and Final causes would be the "most precise" ones:

And why are certain things, i.e. stones and bricks, a house? Plainly we are seeking the cause. And this is an essence (to speak abstractly), which in some cases is that of the sake of which, e.g. perhaps in the case of a house or a bed, and in some cases of the first mover; for this also is a cause. But while the efficient cause is sought in the case of genesis and destruction, the final cause is sought in the case of being also. (Metaphysics, 1041 a 25-32)

In the above quotation Aristotle gives us the clue for understanding the "reduction" of Efficient and Final causes to the Formal one, or "essence". If we speak abstractly (i.e. on the level of opposition) then the cause is form (essence, or "what it meant to be"). Often such abstract explanation is sufficient. But, depending on the type of question, more concrete explanation is needed; and one should look for the Final cause ("for the sake of which") or the Efficient cause. Thus we suggest that Aristotle's "reduction" of the Final and Efficient causes to the Formal and Material ones simply means that the first two causes are the intermediates between the latter two.

4.6. The Intermediates: Final and Efficient Causes

If our previous statement is correct, then Aristotle had to view the intermediates, Final and Efficient causes, as being constructed of the Formal and Material causes.

4.6.1. Final Cause

One important contribution of Aristotle is the introduction of the notion of immanent and objective finality or purpose (Copleston, 1961/1093). According to this notion, natural things, "which have in themselves a principle of motion or change", are said to "objectively" attain their own purpose, or finality. For example, according to Aristotle, each of the four elements has a natural movement towards its own proper place (fire goes up) and this characteristic belongs to the element's form. "Objects do not obtain an imposed on them, or prescribed from outside, purpose, but inside of themselves objectively possess their purpose. This purpose is realization, or actualization of their "form", or essence, hidden inside of them (Asmus 1976, p.282). This objective, or material embodiment of purpose in natural things (e.g. a seed grows into a tree because from the beginning it has the form of the tree somehow embedded in its material) is what Aristotle meant under final and formal causes being the same (Asmus 1976). In formal terms, this means that Final cause is a latent objective representation of the Form in the thing's matter as the thing's purpose. According to the principle of cross-attribution, this can be formally represented as material-Formal cause. The attribution of Material cause to Formal cause, thus, reflects the process of representation of the Formal cause in the thing's matter.

4.6.2. Efficient Cause

According to Aristotle, a natural thing that internally possesses its purpose (Final cause), strives to fulfill the purpose (Efficient cause), or to attain the form, and under certain conditions actually does it. Suppose we observe water turning into steam. Steam comes not merely from water that has a form of cold-and-moist (material cause), but from water which has been heated to a certain degree and "strives" to become steam (efficient cause) that has the form of air, i.e. is moist-and-hot (Final cause). Similarly an artist can be considered the efficient cause of the creation of a statue out of marble, if he has a form of statue in his soul (final cause) and is "striving", or is intending to make a statue. These examples show that the matter, in order to strive to attain a certain form (final cause), has to be in a certain state, or potentiality. Thus, according to the principle of cross attribution, it can be formally characterized as the formal-Material cause. The attribution of Formal cause to Material cause reflects the process of the matter's changing into the condition of "striving" to attain the form. Thus efficient cause is congruent with Potentiality (definite Privation) of a proximate matter in relation to the form: "Therefore the proper definition of the primary kind of capacity will be a source of change in another thing or in the same thing qua other" (Metaphysics, 1020 a 4-6).

4.6.3. Concretizing Reinterpretation of the Relatives

It appears that, according to Aristotle, the main mechanism of any change has two components: (1) Final (material-Formal) cause, which moves by generating attraction to the Form which is reflected in it and (2) Efficient (formal-Material) cause which is moved by desire to attain the Form. As in previous cases, Aristotle reinterpreted the original relatives Formal and Material causes according to the same-side attribution of the intermediaries. On one side, he attributed being Final cause (material-Formal cause) to Form, subtracting the attribute "material", thus extending the characteristic of attraction of Final cause onto Form itself. After an elaborate dialectical analysis, Aristotle came to the conclusion that there must be the first, or supreme mover that causes change without being changed itself, and therefore is eternal (Metaphysics, Book 12, Chapter 7). Aristotle attributes these qualities to God, who moves the world by inspiring absolute attraction, love, and desire, thus being a perfect Final cause and perfect Form. "That for the sake of which is found among the unmovables is shown by making a distinction; for that for the sake of which is both that for which and that towards which, and of these the one is unmovable and the other is not. Thus it produces motion by being loved, and it moves the other moving things" (Metaphysics, 1072 b 1-4). In congruence with previous layers of opposition, Aristotle identifies God with the perfect form of forms, which is a perfect activity of speculative thought, which has a perfect object--thought itself  (Metaphysics, Book 12, Chapter 9).

On the other side, Aristotle attributes Efficient cause to Matter-Nature. Asmus (1976) summarized reinterpreted relationship between Form and Matter in the view of the intermediaries, Final and Efficient causes: "Just existence of the supreme 'form' in itself is sufficient to cause 'matter' to desire to attain the 'form.' This is why, according to Aristotle, God is the purpose of the world and the entire universal process" (Asmus 1976, p. 287). Thus at this level Aristotle offers the causal mechanism of change in the world. It is comprised of a hierarchy of objects that are moved by desire and movers moving by attraction. God or the supreme mover is at the top of this hierarchy while the prime matter is at the bottom.


4.7. Form and matter as contradictories

As contradictories, things are opposed as affirmation and negation. Aristotle distinguished between facts which are affirmed or negated and affirmation or negation as statements about these facts (Categories, Chapter 10). So far we have made statements about form and matter opposing the two in different ways upon the bases of different substances. Now we shift our attention to the statements themselves. The subject matter of ontological construction in terms of form and matter is substance, and statements unique to substance are definitions: "Clearly then only substance is definable" (Metaphysics, 1031a 1). A definition is a formula of the essence of a thing (Metaphysics, 1030a 6) and only species (eidos) can have an essence (1030a 13). Therefore, a statement we are interested in is a definition (horismos).

A definition has a specific structure: "There is nothing in the definition except the first-named genus and the differentiae" (Metaphysics, 1037 b 29-30). Aristotle concluded that a definition constitutes unity, and that neither genus (Metaphysics, Book 7, Chapter 12) nor differentiae (Metaphysics, Book 8, Chapter 2) exists apart from the species:

If then the genus absolutely does not exist apart from the species which it as genus includes, or if it exists but exists as matter (for the voice is genus and matter, but its differentiae make the species, i.e. the letters, out of it), clearly the definition is the formula which comprises the differentiae. (Methaphysics, 1038 a 5 - 8)

In the physical world, in nature, form does not exist apart from matter, like in primary substances, things, and elements. However, since intelligence (thought of thought) may exist apart from nature, form, or species, exists apart from "real" matter, because it has its own intelligible matter--genus. Definition of species (e.g. man is "a two-footed animal") cannot be divided into differentiae (two-footed) and genus (animal). The reason is that the definition of man is not a man. The definition as a whole (genus and differentiae) defines man as a species, so in the definition of man "animal" cannot exist apart from "two-footed." The same genus may be used as a part of a definition of more than one species; for example, "animal" is also a genus in a definition of horse as a "four-footed animal". Then "animal" as such, taken out of the context of the definitions, would constitute a negation of the species.

Evidently, therefore, with reference to that which is called genus, none of the species which belong to the genus is either the same as it or other than it in species (rightly so, for the matter is indicated by negation [of form], and the genus is the matter of that of which it is called the genus, not in the sense in which we speak of the genus of Heraclidae, but in that in which we speak of a genus in nature)…" (Metaphysics, 1058 a 21-24)

Thus form-Species (eidos) and matter-Genus are opposed as contradictories and as such they do not allow any intermediates: "Among opposites, contradictories admit of no middle term; for contradiction is this--an opposition, one or other side of which must attach to anything whatever, i.e. which has no intermediate" (Metaphysics, 1057 a 33-35).

According to Aristotle, only individual substances comprised of Form and Matter really exist. Aristotle had to show that the supreme mover, removed from the material world, really exists as a particular substance. This is exactly what Aristotle did at the level of contradictories. As a definition, "thought of thought" defines a species of perfect thought and consists of the genus "thought in general" and the differentiae "of thought". So "thought in general" plays the role of the matter for the "perfect thought". This closes the circle of mutually congruent definitions of Form for all four layers of opposition of Form and Matter. Similarly Aristotle insured mutual congruence of definitions of Matter on all four levels of opposition and the intermediates on the first three levels.

5. Conclusion: Principles of Constructive Attribution

We believe that the above discussion demonstrates the correctness of our assumption that Aristotle consistently followed both the rules of opposition and of construction of intermediates he formulated. For different reasons, Aristotle neither explicitly opposed form and matter as contraries and relatives, nor explicitly constructed Actuality and Potentiality and Final and Efficient causes as intermediates. However, as we have demonstrated, he treated the opposites and the intermediates as such. On this basis, we conclude that Aristotle did oppose Form and Matter in all four ways, which he prescribed: as possession and privation, as contraries, as relatives, and as contradictories. As Aristotle prescribed, each of the first three oppositions was defined upon the appropriate basis, or genus, common to the opposites as polar species of the genus. As he prescribed, for each of the first three oppositions, he constructed intermediates composed of the corresponding opposites. The fourth opposition as contradictories does not allow intermediates. The composition of intermediates can be formally characterized as cross-attribution: for each opposite, interpretation of one opposite as an attribute of the other one. We have demonstrated that this pattern was consistently used for all three layers. We have discovered that Aristotle, in all the three layers where intermediates were composed, consistently used another method, same-side attribution, for reinterpretation of the opposites in light of the intermediates, although Aristotle did not mention this requirement in his works. In each layer, construction of the intermediates by means of the cross-attribution and reinterpretation of the opposites by means of the same-side attribution, created a more concrete level of conceptualization compared with opposition. As we mentioned in the Introduction, in this paper we have focused on the ontological construction within one layer of opposition, leaving detailed analysis of how Aristotle ensured congruence among the layers for the future. Nevertheless, we have offered several examples, which demonstrate that Aristotle did take into account congruence.

This study suggests that, according to Aristotle, every ontological unit consists of five layers, one layer of categorical definitions and four structural levels, corresponding to the four types of opposition. Two levels constitute each of the first three layers: a lower, two-member abstract level of opposition and (2) a higher, four-member concrete level (Figure 1). Accordingly, the formal scheme for construction of an ontological unit includes five stages:

1.       Categorical definitions of an ontological unit with reference to empirical evidence and historical-problem analysis.

2.       Construction of the layer of possession-privation.

3.       Construction of the layer of contraries.

4.       Construction of the layer of relatives.

5.       Construction of the layer of contradictories.

(In later stages, care of congruence with previous layers must be taken.)


Figure 1: Five layers of Ontological Unit According to Aristotle.

Construction of the first three layers (stages 2-4) includes two steps: opposition that results in the most abstract definition of the ontological unit and constructive attribution, which creates a concrete definition of the unit. In turn, constructive attribution includes two phases: cross-attribution and same-side attribution. Figure 2 depicts the formal structure of the constructive attribution. In this figure A and B are opposites; bA and aB designate cross-attribution of B to A and A to B, respectively. I1 and I2 are intermediates while A(I1b) and B(I2a) stand for reinterpreted opposites A and B by means of same-side attribution of I1 to A and I2 to B, respectively; "b" after, not before, I1 in A(I1b) means that the attribute "b" is "subtracted" from I1 in the reinterpretation of A, "a" after I2a in B(I2a) has the same meaning. The "link" stands for the ontological relationship between the opposites determined by the phenomena being explained, e.g. change, motion, creation, and destruction.


Figure 1. A Structure of an Ontological Unit's Layer

Before Aristotle, Greek philosophy and science had been stuck at the level of opposition which was too abstract to explain change and motion observed empirically. Aristotle was the first to make a step beyond opposition, the first to perform the act of what Hegel called ascending from abstract to concrete. The concrete ontological constructs permitted Aristotle to be the first to conceptually represent change and motion, creation and destruction, and thus to pave the way for future development of philosophy and science. We believe that constructive attribution was the essential method of Aristotelian ontological construction, which he used, we claim, not only for the ontological unit of the substance-form-matter, but for all units of his ontology.

We believe that the Aristotelian method of ontological construction has more than historical interest. Aristotle's method was built upon the achievements of his predecessors; likewise, contemporary science is also based on previous achievements. Aristotle reinterpreted, modified, and formalized the method of opposition; likewise, we must reinterpret and modify his method in the light of post-Aristotelian developments, if any. In a previous paper, we illustrated a successful use of the method of opposition to solve logical problems of the concepts of norm and deviance in contemporary social sciences (Dubrovsky, 1996). We believe that the method of constructive attribution can be applied as effectively as that of opposition.

Even in its current interpretation, the method described in this paper can be effectively applied to the theoretical problems of contemporary science. The application should follow two stages. In the first stage, it can be used as a formal scheme, or an abstract systematizing framework, for the organization of the theoretical concepts of a theoretical problem. The formal scheme itself should never be viewed as sufficient in itself. The Aristotelian method requires a thorough classification of the empirical material and historical-problematic analysis of the relevant theoretical concepts. One advantage of the formal scheme is that it specifies the level of abstraction one should maintain for the analysis, so one will not be drawn into, the insignificant for ontological construction, detail. As the result of the first stage, we should have all the empirical material relevant to the problem classified, concepts systematized, and the problem formulated. In the second stage, the formal framework should permit us to formulate, in abstract categorical terms, the way to solve the problem, formulated at the previous stage. Likewise, it should permit specification of empirical investigation that should fill the "gaps" of factual knowledge identified in the previous step

As a final note, we should mention that Hegel's method of ontological construction--dialectics, with its "magic number 3" (thesis , antithesis, synthesis) is widely used in contemporary science. We believe that the Aristotelian counterpart with its "magic number 4" has, at the very least, higher resolution power. While Aristotle's method offers two cross-attributed intermediates between opposites, dialectics offers only one synthetic construct, which actually equates the two intermediates of Aristotle. Since Hegel uses the same "attributive" language for his synthetic constructs, this difference can be easily verified by the reader. We believe that the Aristotelian method of ontological construction can be used as an effective methodological tool in contemporary theoretical science, indeed more effectively than some of the methods presently being used.

6. References

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Bambrough, R. 1963. "Introduction," in The Philosophy of Aristotle: A New Selection (R. Bambrough, ed.) New York: A Mentor Book, pp.11-39.

Barnes, J (1995). "Metaphysics," In The Cambridge Companion to Aristotle (J.Barnes, ed.), Cambridge University Press, pp. 66-108.

Copleston, F.C. 1961/1993. A History of Philosophy, Volume 1. New York: An Image Book.

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Dubrovsky, V. 1996. "Duality: The Third Approach," In M.L.W. Hall, Ed., Proceeding of The Fortieth Annual Meeting of The International Society for The Systems Sciences (ISSS), Louisville, July 14-19, (235-246).

Gibbs, J.P. 1990. “The sociology of deviance and social control.” In Social Psychology: Sociological Perspectives. (M. Rosenberg and R. Turner, eds.). Transaction Publishers, New Brunswick, pp. 483-522.

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Ross, D (1923/1995). Aristotle. London and New York: Routledge

Rozhansky, I.D. 1981. "Notes", in Works of Aristotle, Volume 3 (I.D. Rozhansky, ed.) Moscow: Mysl', pp. 559-598.

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