In developing the dialectical- and historical-materialist worldview, Marx and Engels found it necessary to test its appropriateness as a universally scientific methodology in the spheres of nature, society, and thought:

The fact that our subjective thought and the objective world are subject to the same laws, and, hence, too, that in the final analysis they cannot contradict each other in their results, but must coincide, governs absolutely our whole theoretical thought. It is the unconscious and unconditional premise for theoretical thought (Engels 1987b, 544).

Scientific activity represents the dialectical unity of theory and practice. One aspect of this activity is the theoretical description of the structural development of material systems (in the social, biological, and physical spheres). This, of course, includes the investigation of the laws governing the motion and development of the system on specific levels of organization. In their intensive research activities, scientists often introduce fundamental concepts intuitively, without the conscious appreciation of their dialectical nature. This paper will explore the various ways in which dialectical oppositions, for which we have the philosophical term contradictions, form the basis for the existence of structures and the processes of development that these structures undergo. Familiarity with the various ways in which contradictions enter into the stability and development of material systems can serve as an important methodological tool for further scientific investigation.

To discuss contradictions as a source of structure and development, it will be useful to start with a few comments about the relationships expressed by the term structure. According to Hörz et al. (1980, 47), by structure we understand the totality of essential and nonessential, general and particular, necessary and contingent relations among the elements of a system in a definite interval of time. The term structure is generally used to denote the stable aspect of a system. The stability is always relative, determined by the time interval over which the system’s elements and relations show no significant qualitative change. [1]

The formulation of Hörz et al. is by no means exhaustive, as is the case with any statement about philosophical categories. For example, there is a hierarchical aspect implicit in every material structure, and the theoretical description of structures must also embrace this aspect. Analysis, however, must start at some level of organization and integration of a material system, so that we can include among “elements” the various hierarchically organized substructures. Then we can say that systems are characterized by the complex of elements and the relations among them. Thus, fundamental to the characterization of a system is the characterization of its elements and the relations among them. The elements and relations are examined first in terms appropriate to a given level. The connections to higher and lower levels of organization then also have to be examined to extract the fuller essence of the relations.

The need to examine the dialectical interconnections that unite elements and relations is readily seen when one tries to probe the content of fundamental concepts. In Newtonian mechanics, the principal elements to which the laws of motion refer are approximations of physical bodies; in particular, they are point masses (or mass points). This reduction of physical bodies to point masses was not postulated explicitly by Newton, but follows from his laws of motion. Newton’s first law (the law of inertia) did not allow for a body wobbling or twisting as it underwent inertial motion. Newton’s law of inertia postulates certain space and time relations for these bodies. Newton accepted the a priori existence of absolute space and time independently of these bodies or elements. We know today that these postulations about space and time are devoid of physical content. Nevertheless, Newton’s laws of motion were of great scientific importance and are still an adequate representation of the behavior of physical systems for a wide range of practical situations. Therefore the space and time of Newtonian mechanics must have had a physical content that had not been recognized by Newton. Since these laws involve the concepts of space and time, which cannot have an a priori meaning, the physical basis of these concepts is established by the manner in which they enter the laws and the way the laws appropriate the properties of the physical world. In other words, the nature of the elements of a system and the relations among them cannot at all be embraced independently of one another. When we say that “a” stands in some relation to “b” (symbolically aRb), we are introducing two “objects” – the elements and the relations—neither of which can arise as concepts independently, that is, without one another. Elements are distinct from relations; but the concept elements cannot arise without the existence of relations. The existence of elements is conditioned by the existence of relations and conversely. Elements and relations are therefore mutually exclusive and mutually conditioning. Hence they constitute a dialectical unity. This unity arises on both the logical and material levels. The deeper logical and material content of the elements and the relations is expressed through the laws that embrace them. The fundamental laws of the natural and social sciences bring out the material content of the elements and relations when the laws are associated structurally with material systems in nature and society.

Consider, for example, the physical property mass. In Newton’s laws, the magnitude of the mass is specified as the relationship between a force and the acceleration that results from the application of that force; but force, in turn, is that which causes a change in velocity. [2] Accelerated motion is thus placed in contrast with inertial (unaccelerated) motion, neither of which can be comprehended without the other, nor independently of the concepts of force and mass. Mass, therefore, enters Newtonian mechanics in the form of a dialectical unity of accelerated and unaccelerated motion as expressed in the first law (law of inertia) and the second law (force equals the product of mass and acceleration). Mass, force, uniform motion, and accelerated motion are thus found to be specialized categories of mechanics, and, as is the case with all philosophical categories, none of them can be defined independently of the other categories. As categories, these physical concepts and properties can only be understood through their mutually conditioned and mutually exclusive relationships to one another, which are disclosed in the process of investigation of the laws embracing them—and these laws not only embrace them, but arise together with them. In the case of mechanics, it was only after the discovery of non-Euclidean geometry by Lobachevsky and, independently of him, by Bolyai that it became apparent that Newton’s a priori notions of space and time had to be abandoned, and that, as Riemann’s work suggested, a physical basis for establishing an appropriate geometry is needed. Newtonian mechanics was a logically consistent theory because Newton, unknowingly, gave us the physical basis for a straight line: a straight line is the trajectory of a physical body produced by inertial motion (Marquit 1990b, 869). To the extent that Newtonian mechanics is an adequate approximation of physical reality, this criterion of straightness is also adequate. We have here an example of the deeply dialectical content of Newton’s laws, although Newton, despite his genius, was unable to recognize this content.

In political economy, Marx unraveled the mystery of the exchange value of a commodity. Here we have a case in which dialectical thinking was consciously applied in research and the clarity that resulted from this consciously dialectical approach is so remarkable that Marx’s Capital is still regarded as contemporary, and not simply historical, scientific literature. According to the law of value discovered by Marx, the exchange value of a commodity is determined by the socially necessary labor time embodied in its production. Marx pointed out that while a commodity is a product of the concrete labor of its producer, this concrete labor “ranks as, and is directly identified with, undifferentiated human labour,” and it therefore ranks as identical to any other sort of labor.

Consequently, although, like all other commodity-producing labour it is the labour of private individuals, yet at the same time, it ranks as labour directly social in character.... [T]he labour of private individuals takes the form of its opposite, labour directly social in form. (Marx 1996, 69)

The exchange value of a commodity finds its quantitative expression through the law of value. Its qualitative side finds expression both through the law of value and through its dialectical opposite, use value, without which no object can be a commodity. A commodity is produced because it can be exchanged. It is exchanged for other commodities because of its use value. In Marx’s words: “use value becomes the form of manifestation, the phenomenal form of its opposite exchange value” (1996, 66). At this stage of his exposition, Marx had not yet come to the discussion of the relationship between price and value. Actually it is not value, but price that is the phenomenal expression of exchange value. While price can be measured directly – by direct observation in the marketplace—exchange value, which, in general, is different from price, cannot be measured directly. What is being said here is in sharp contrast with various empiricist views asserting that fundamental properties are first established by observation (for example, in the form of operational definitions denoting the procedures by which the observation is to be carried out) and that the laws describing the relationships among these properties are then established by further observation and theoretical deduction.

At the basis of the usual logical structure of a hypothetico-deductive system is the postulation of the existence of elements and categories of relations among them. These are the fundamental notions or concepts of the system. The elements and relations are then combined in more specific form as axioms (or laws) from which the theorems are derived. When we are dealing with objectively existing material systems, or generalizations of them, the elements, relations, and axioms are not the result of arbitrary mental activity, but are reflections of the material characteristics of the system. Although in the logical structure of the system, the elements, relations, and the axioms embracing them form a hierarchy in that order, ontologically and epistemologically they are mutually conditioning, as our examples have shown, and therefore they arise together, as if lifting themselves together by a common bootstrap, rather than arising one after the other. Moreover, as we pass from one level to another, elements can go over into their dialectical opposites—that is, into relations—just as relations can pass over into elements (Uemov 1963, ch. 4). For example, in physics the field concept was introduced to describe a relationship between an object and the space in which it is located. Thus an electric field represents the force on a charged particle at a given spatial position. On another level, the field acquires all the attributes of physical matter: mass, momentum, relative localization, and so on—that is, it becomes a physical object.

The recognition that categories become transformed into their opposites as we go from one structural level to another is essential for the recognition of the hierarchical structure of systems. The role played by the economic basis of society in Marx’s basic law of social development cannot be understood without this recognition. Thus the level of development of the forces of production is the essential content of the stage of development of a given socioeconomic formation. The relations of production represent the form in which this content is put to work. This form, however, becomes the content in relation to the superstructure, the latter being the form in which the relations of production are maintained relatively stable as the productive forces develop. Marx used the term economic basis of society to distinguish the different categorical role of the relations of production in relation to the superstructure from their role in relation to the forces of production.

With this brief discussion about the role of dialectical processes in the emergence of fundamental concepts associated with a system (or its reflection in theory), I can now proceed to questions related to stability and development. In particular, I shall consider the role of contradictions in the moments of motion, stability, growth, and transformation of a system. At first glance, it might seem that stability should precede motion in this discussion. It can be argued, however, that stability is subsumed under the concept of law-governed change (motion), just as rest in Newtonian mechanics is subsumed under the concept of uniform motion (constant velocity). Therefore stability and motion are not properly a set of objectively occurring dialectical opposites when we are dealing with the overall process of development. On the other hand, at a particular stage in the development of the system, stability and change do confront each other as opposites and their interpenetration must be examined dialectically.

Motion in physics

Aristotle expressed motion in its most general terms as the realization of the potential, that is, as the dialectical transition of the potential into the actual. Motion is thus seen in two different dialectical aspects: as the transition from a potential state of being into an actual state and as the passage from one state of being into another state of being. The latter can also be formulated as the leaving of one state and the entering into another. Here we face a new opposition, one between the existence of states and the transition between them. Fundamental to the dialectical worldview is the recognition that everything is in a continuing state of flux. Thus the dialectical view gives primacy to motion (that is, to transition), and looks upon states as being of a transitory nature. The dialectical view allows us to deal conceptually with the transitions between discretely separated states and still preserve the continuity of motion—for example, in the case of the radioactive decay of one isotope into another (Marquit 1978–79). The dialectical view contrasts sharply with the reductionist description of motion as a succession of states of rest (Salmon 1975, 41), the view, for example, held by Russell in his solution of Zeno’s paradox of the arrow. For the mathematization of certain motions such as a simple change of position in space, a view that reduces motion to a succession of positions (in essence, a succession of states of rest), gave us a powerful tool for the further study of motion of mechanical systems, but the recognition of its approximate character forced itself upon us as we descended into the microworld, where the quantum-mechanical representation of motion became necessary. The nature of the approximation embodied in motion as a succession of states of rest was, in effect, pointed out by Hegel when he wrote:

The difficulty is to overcome thought, for what makes the difficulty is always thought alone, since it keeps apart the moments of an object which in their separation are really united. (Hegel 1892, 274) [3]

Stability

The stability of a system is both absolute and relative, just as the boundary of a system is both relative and absolute. A system can be considered stable even when essential qualitative changes take place within it. In other words, some aspects of a system can remain stable while other aspects undergo transformation. A given chemical atom maintains its integrity even while taking part in various chemical reactions. A family retains its identity even with the birth and death of some of its members. The concept system is meaningless without the relative and absolute characters of the stability and boundaries of the system. If the relations among elements of the system had no stability whatsoever, then the elements would not have any relationship to one another at all, and one would be left with pure chaos – that is, elements without interconnections, the existence of which would violate the basic dialectical-materialist principle of universal interconnection. Stability is characterized by the essential structural elements remaining in qualitatively constant relations. The relative constancy of the relationship is what makes reduction possible as an approximation, that is, the separation of the system into parts for more detailed study. Every interconnection implies a relative separateness, for the very term interconnection denotes a bond between things that are separate. The nucleus of a cell has a stable relationship to the rest of the cell and, as a result, its characteristics can be studied, in part, separately from the cell as a whole. At the same time, a deeper comprehension of the nucleus requires restoration of its bonds with the rest of the cell so that its function in relation to the entire cell can be understood. The qualitative constancy of the relations does not imply quantitative constancy. Systems can have stability with or without quantitative change or relative motion. Systems that are stable without qualitative change are often said to be in equilibrium. Such equilibrium can have a relatively static character, such as a weight hanging motionless at the end of a spring. The sharing of state power by groups of finance capital in a given country, despite the conflict of interest among them, takes on the character of a static equilibrium over certain periods of time. Another type of equilibrium involves an oscillatory motion, such as a weight bobbing up and down at the end of a spring. Here we are dealing with motion without any qualitative change. This motion is not usually characterized as a state of equilibrium, but it is intermediate between static equilibrium and dynamic equilibrium. The latter occurs, for example, in the case of the population of a country when the number of deaths equals the number of births in, say, one year. Any system which repeatedly passes through the same state cannot be considered as undergoing growth or development over a period that goes beyond one cycle. Thus, concepts of qualitative change, growth, and development can have a relative character. In the life cycle of plants, the seeds germinate, the stalks grow, flower, and produce new seeds, yet unless the plant undergoes genetic change, we cannot speak of qualitative change (assuming constant environmental conditions) from generation to generation.

Since systems are always confronted by some state of motion, externally and internally, stability can never be understood in isolation from change, but must be comprehended as stability in face of change. The stability of a system has to be investigated by considering the opposite tendencies at work that give rise to the stability while tending to disrupt it. In fact, a frequently used method to investigate the stability of a system is to introduce a disturbance and examine its consequence. In the absence of qualitative change, the result is often an oscillation, which is another reason for considering an oscillating system to be in equilibrium.

In the general case, the condition of equilibrium resulting in stability is generally not an equal balance of opposites in every sense. It is not unusual for one tendency to play the qualitatively decisive role, even though the quantitative equality necessary for equilibrium implies a qualitative equality in some sense. For example, in the case of a mass suspended motionless from the end of a spring the active role in establishing the equilibrium is the force of gravity pulling downward on the mass, while the opposing tendency is the elastic force upward that arises from the stretching of the spring. As mechanical forces, both tendencies are quantitatively and qualitatively equal, while as elastic and gravitational forces they are qualitatively different. The possibility of a dominance of one tendency in an equilibrium situation is strikingly clear when one considers the capitalist socioeconomic formation. The dominance of the capitalist class over the working class in the superstructure ensures the relative stability of the capitalist relations of production. It may be argued that this illustration is not a suitable one, since we are in reality dealing with a system undergoing development. However, the fact that the system is undergoing development does not imply the absence of equilibria responsible for stability. I have already stressed that some aspects of every system remain stable as the system changes; otherwise there would be no sense in speaking about structure.

Growth

In considering the growth of a system, we can immediately discern two characteristic situations. In the first we are dealing with a system in which the relative strength of the principal contradictions that ultimately constitute the basis for the existence of the system changes quantitatively with a general unidirectional tendency. Hydrogen and helium stand in opposition to each other in the process of thermonuclear combustion that occurs in the sun. The hydrogen fuel is consumed in the production of helium. The combustion process results in the release of radiative energy that exerts sufficient outward pressure to prevent the inward collapse of the sun under the influence of the gravitational forces. In the maintenance of this equilibrium, the hydrogen is steadily depleted until a point is reached where the attractive gravitational forces become stronger than the repulsive forces and the system rapidly collapses—that is, it undergoes a rapid qualitative transformation. The unidirectional character of growth processes is also relative, and one or more reversals are possible at various stages of development. For example, in the case of the formation of the sun, the gravitational forces are believed responsible for the initial accretion of hydrogen in sufficient quantity for the thermonuclear combustion process to begin. Similarly, the accumulation of capital provides the material basis for the use of force by a capitalist state to preserve capitalist relations of production in the face of the resistance of workers to these relations. As capital accumulates, the relative strength of the working class also undergoes change and eventually becomes powerful enough to effect a change in the relations of production despite zigzags in the course of historical development and fluctuations in the relative strength of contradictions. Superimposed on these fluctuations are law-governed tendencies of quantitative changes that arise from the character of development of the system. These are the changes that lead to qualitative transformation of the system.

A second situation arises in which a secondary contradiction grows quantitatively to the point where it comes into conflict with the primary contradiction. In this case the further development of the system takes place as a result of the quantitative development of the new struggle of opposites. Under feudalism, the principal contradiction was between feudal lord and serf. It was not, however, the superior strength of the serfs in Europe that led to the breakup of the feudal order, but the strength of the growing capitalist sector, which, in turn, came into class conflict with the feudal sector.

The alliance between the bourgeoisie, the working class, and the feudal peasantry under the leadership of the bourgeoisie increased the strength of the antifeudal forces to the point where successful revolutions against feudalism were possible. In the formation of the chemical molecules the principal opposition arises between the negative charge of the electrons and the positive charge of the nucleus, mediated by the laws of quantum mechanics. Moving electric charges always give rise to magnetic fields, but these magnetic fields play a minor role in determining the structure of the lighter chemical atoms and molecules. As we build up atoms of increasing complexity, we reach a stage where the magnetic interactions resulting from certain electron configurations in the atoms become strong enough to be decisive for the molecular structures formed from the atoms. In other words, the interactions between opposite electric charges give rise to interactions between opposite magnetic polarities. These latter can grow in significance and finally dominate the behavior of the molecular system.

Transformation

Quantitative changes in processes of growth eventually lead to qualitative changes. In fact, any quantitative change is capable of producing a qualitative change. For example, a control system with a sufficiently sensitive detector can be triggered to produce a certain sequence of events that changes the quality of systems for any arbitrarily chosen quantitative change. Every qualitative change is a negation of the previous state – that is, what existed before exists no longer. Yet since we are not dealing with pure chaos, some connection remains between the old and new states. In other words, a thread of continuity unites the old with the new. We thus have a system transformed, that is, some degree of integrity is preserved, while its quality is negated. Hegel used the German term aufheben to describe this process of dialectical negation. In English we generally translate this as sublate, which in its Latin origin denotes both lift up and take away or annul, as does the German expression aufheben. Every qualitative change, therefore, has the character of sublation. The character of the negation can, of course, be quite different from case to case. As we go from the level of a gas as a system of molecules to the thermodynamic level, we go from a discrete structure to that of a continuous medium. The physical processes responsible for this transition are, of course, the proper subject matter of physics.

In the transition from capitalism to socialism, the dominance of the bourgeoisie over the working class is negated by the dominance of the working class over the bourgeoisie. The relations of domination and subordination are replaced by relations of cooperation and mutual assistance, again a clear negation into opposites. On the other hand, in the transition from feudalism to capitalism the relations of domination and subordination persist, since this transition is between one form of exploitative relations of production and another. It is not always the quantitative changes associated with one side of the principal contradiction characterizing a system during its entire existence that determine the further course of development. New contradictions can emerge and grow in significance, as I have already discussed in connection with the transition from feudalism to capitalism. What is obviously involved here is a change in the identity of the principal contradiction – from that between lord and serf to that between the capitalist mode of production and the feudal mode of production. The former contradiction remains important for the characterization and very existence of the socioeconomic formation, but it is no longer the contradiction that determines the nature of the qualitative changes that will follow. For this reason, the law of spiral development cannot be considered to be a unique consequence of the law of the negation of the negation. The negation of the negation does not always lead to the reappearance on a higher level of characteristics that occurred previously.

The nonexploitative relations of production in early communal societies were indeed negated by the emergence of exploitative relations of production. With the transition to socialism the nonexploitative relations emerge on a higher level. Here we are dealing with spiral development. This does not mean, however, that society is then doomed to the reemergence of exploitative relations. With the vanishing of the exploitative relations on a level of high technological development, the basis is laid for the vanishing of the very institution of private property. Although relations between people will continue to develop new forms, these developments will not involve property relations as such. The reemergence of previously occurring characteristics cannot be asserted as a general philosophical principle. Whether or not such reemergence occurs must be investigated within the individual sciences. This is what Marx did when he investigated the process of transition from capitalism to socialism, the results of which he then cited in his well-known passage in Capital:

Centralisation of the means of production and socialization of labour at last reach a point where they become incompatible with their capitalist integument. This integument is burst asunder. The knell of private property sounds. The expropriators are expropriated.

The capitalist mode of appropriation, the result of the capitalist mode of production, produces capitalist private property. This is the first negation of individual private property, as founded on the labour of the proprietor. But capitalist production begets, with the inexorability of a law of Nature, its own negation. It is the negation of the negation. (Marx 1996, 751)

As another example of a succession of negations, let us consider the cooling of a gas, first, to the liquid phase and then cooled further until it forms a solid. In the first (or gas) phase, the individual molecules interact with each other during the brief moments of collision and otherwise move about independently of one another, although they are affected as a whole by the results of the numerous collisions, in the sense that the energy is distributed among the molecules in accordance with well-known statistical laws. In the liquid phase, the interaction with neighboring molecules dominates the physical behavior of the system, negating the relative independence of the molecules of the gaseous phase. The molecules, however, are not constrained to a fixed range of spatial relationships with their neighbors, and neighbors continually change partners. In the solid phase, the behavior is still largely conditioned by the interaction with neighbors, but the freedom of motion relative to the neighbors is negated and replaced by fixed spatial relationships to neighbors. The invoking of spiral development here is not appropriate. What then is the significance of the concept of spiral development in connection with the law of the negation of the negation? The concept of spiral development is a means of stressing that in the process of development of a system, certain essential characteristics, including the principal contradictions, can reappear; this reappearance does not indicate a circular process, but a process of progressive development in which the characteristic features of the system reemerge on a qualitatively different level. The law of the negation of the negation is the assertion of directional, that is, progressive, development. Spiral development, on the other hand, describes some processes, but does not have universal applicability and therefore should not be considered to be a law.

Processes of qualitative change have minor, as well as major, consequences for the system as a whole. A qualitative change can even result in the necessity for a redefinition of the system. A geological formation in a plain can grow and become, for example, a mountain range. Another formation can grow and then later erode, literally vanishing as a system in the rain and wind. Both processes are forms of dialectical negation. In the latter case, however, the boundaries of the system require modification if the continuing progress of development is to be followed. One part of the eroded formation, for example, could have been transformed into sediment in a riverbed and another part into desert sand, each, in turn, entering new geological systems. A proton and antiproton can give rise to the atom-like system called protonium. But instead of being stable like the hydrogen atom formed by a proton and an electron, this system is very short-lived, for in some fraction of a second the proton and antiproton annihilate each other and the products of the annihilation are radiated in different directions. Although the law of conservation of energy is not violated in the process, so that the energy of the system before annihilation is equal to the energy of the system immediately after annihilation, it makes no sense to speak of a system once the products of the annihilation are absorbed into other systems. History is full of examples where nation-states have been absorbed into other states and the populations assimilated or single states divided into two or more states that then follow separate historical paths.

In Marxist literature dealing with the social sphere, the terms antagonistic and nonantagonistic contradictions are often encountered. The contradiction between capitalists and workers is characterized as an antagonistic contradiction, since the resolution of the contradiction takes place through the destruction of the capitalist relations of production and therefore the capitalists vanish as a class. The contradiction between the peasantry and the workers is characterized as a nonantagonistic contradiction, since the resolution of the contradiction is not through the elimination of the peasantry as a class, but through the formation of a class alliance between the peasantry and the working class. The private property of the peasantry is gradually transformed into the property of the people as a whole through a number of intermediary stages (which can vary from country to country), but sooner or later through the formation of cooperatives or state farms. The distinction between antagonistic and nonantagonisitic contradictions in the social sphere can serve as a guide in the formation of social policies.

It is tempting to try to apply these concepts to the physical world, say, by treating the electron’s negative charge and the proton’s positive charge as a nonantagonistic contradiction – leading to the formation of chemical atoms—while treating the proton – antiproton contradiction as an antagonistic contradiction, since it leads to the annihilation of both (that is, to the transformation of both into something entirely different). This distinction adds nothing to our scientific knowledge but can only be made on the basis of knowledge already acquired. Similarly, the philosophical characterization of the relationship between certain biological species as antagonistic and nonantagonistic would be of no epistemological value. One could be tempted to apply these terms to symbiotic and parasitic relationships. The difference between the two relationships is more clearly expressed by the biological terms and with greater subtlety than the terms antagonistic and nonantagonistic. Thus the characterization of contradictions as antagonistic and nonantagonistic is not a distinction that carries over to the general philosophical level, but is specific to a specialized science.

In the foregoing discussion on transformation we see that we are dealing with a wide range of qualitative changes, some of which can have a minor effect on further development of the system and others that affect the deepest foundations of the system structure, even to the point of forcing a redefinition of the system. There have been proposals by Kharin to divide these into three groups: sublation, transformation, and destructive negation. (1981, 155–58) In the discussion above, arguments were made that all processes of dialectical negation have to be considered as sublation. Nevertheless, it could be useful to pursue Kharin’s attempts to develop further a classification of qualitative changes.

The value of dialectical materialism as a methodological tool in the individual sciences is not only that it provides a consistent philosophical framework for the formulation of scientific theory, but also that it stimulates the investigator to ask what processes might occur. These questions have to be given specific form within the particular field, based on extensive knowledge of that field. A philosophical characterization of processes of qualitative change can then be an initial, and important, step in the lengthy and detailed process of scientific investigation.

NOTES

1. For more detailed discussion, see Marquit 1980.
2. See Definition IV in Newton 1934, 2.
3. Engels’s paraphrasing in Anti-Dühring (1987a, 111) of Hegel’s “resolution” of Zeno’s paradox of the arrow led to a long-lasting, still persevering, and ideologically damaging illusion among many Marxists that dialectical contradictions could also be logical contradictions. See detailed discussion of this in Marquit 1990a.

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