|Dialectical Materialism (A. Spirkin)|
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The concepts of quality and property. In his practical activity and search for knowledge man selects from the multiplicity of surrounding phenomena "something" on which he concentrates. Philosophers call this an object. It may be a thing, a phenomenon, an event, a mental condition, a thought, a feeling, an intention and so on. An object can be singled out from the background of reality because it, as a fragment of existence, is delimited from everything else. Its limits may be spatial, temporal, quantitative or qualitative. If, for example, we are confronted with a plot of land of, say 20 sq m, these are quantitative limits. But this plot may also be a meadow as opposed to a forest, and this is its qualitative limit. Quality determines the kind of existence of an object.
The category of quality is an integral definition of the functional unity of an object's essential properties, its internal and external definiteness, its relative stability, its distinction from and resemblance to other objects. Quality is an existing definiteness, as distinct from other definitenesses. It is the expression of the stable unity of an object's elements and structure. Quality is at the same time the limits of an object within which it exists as that object and no other. This means that quality is inseparable from the object. In losing its quality any object ceases to exist as such.
The quality of the object is revealed in the sum-total of its properties. The unity of properties is, in fact, quality. Thus an overall definition of the quality of a thing or phenomenon is a definition of the thing as a system with a certain structure. The nature of a thing is revealed in its properties, which constitute the mode of the object's relationship with other things. It is thanks to their properties that things interact. A thing has the property of evoking one or another action in something else and of manifesting itself in its own way in relation to other things.
A property is the way in which a certain aspect of the quality of an object manifests itself in relation to other objects with which it interacts. A property is that by means of which something manifests its existence in relation to something else. To speak of the properties of a given thing out of connection with other things is to say nothing about these properties. A property of an object thus consists in its being able to produce this or that action in another object and reveal itself in its own way in this action. Moreover, the mode of its manifestation in acting on another object substantially depends on the properties or condition of the latter; a spark falling on a gunpowder store is far more dangerous than the same spark falling on damp ground, where it dies without a trace.
Properties not only manifest themselves, they may also change or even take shape in these relations. Just as matter cannot be reduced to the sum-total of its properties, so no object dissolves in its properties: it is their vehicle, their substratum. A thing should not be regarded, as it sometimes is, as a kind of hook on which its properties should hang. n object glows, as it were, with various aspects of its properties, depending on the context. For example, a person is seen in different qualitative lights by the doctor, lawyer, writer, sociologist, anatomist or psychiatrist. The properties of an object are conditioned by its structure, the internal and external interactions of its elements. Since an object's interactions with other objects are infinite, the properties of the object are also infinite.
Every property is relative. In relation to wood steel is hard, but it is soft in relation to diamonds. Properties may be universal or specific, essential or inessential, necessary or accidental, internal or external, natural or artificial, and so on. The concept of quality is often used in the sense of an essential property. The higher the level of organisation of matter, the greater the number of qualities it possesses.
Quantity. Every group of homogeneous objects is a set. If it is finite it can be counted. We may have, for example, a herd of 100 cows. To be able to consider each cow as "one", we must ignore all the qualitative peculiarities of these animals and see them as something homogeneous. One and the same number "100" is the quantitative characteristic of any set of 100 objects—cows, sheep, diamonds or whatever. Consequently, any quantity is a set if it can be counted, or a dimension if it can be measured.
Quantity expresses the external, formal relation of objects, their parts, their properties, their connections, number, dimension, set, element (unit), individual, class, degree of manifestation of this or that property.
In order to establish the quantitative aspect of an object we compare its constituent elements— spatial measurements, rate of change, degree of development, using a certain standard as a unit of computation or measurement. The more complex the phenomenon, the more difficult it is to study it by quantitative methods. For example, it is not so simple to count or measure phenomena in the sphere of morality, politics, aesthetic perception of the world, religion and so on. So it is no accident that the process of getting to know the real world both historically and logically takes place in such a way that knowledge of quality precedes knowledge of quantitative relations. Knowledge of the quantitative aspect of a system is a step towards deepening our knowledge of this system. Before a person can count, for instance, he must know what he is counting. Science proceeds from general qualitative estimates and descriptions of phenomena to exact mathematical laws of quantity.
The basis of quantitative thinking is the objective discrete ness of things and processes. Quantity is expressed by number, which has two main meanings: the measure of generality of the elements when put together; the divisibility (real or putative) of an object, its properties and relations, into homogeneous elements relatively independent of its quality. For example, we form the number 5 in the process of counting, thus turning this five into a simple quantity. Five people are not simply a formal unit of five human beings, they are not something singular but a specifically divisible unity of five elements. Any number is a relatively independent, integral assembly of a certain set or a divisible unity of quantity. Moreover, quantity is not identical with number. One and the same quantity as a dimension—length, for example—may be expressed in different scales of measurement (metres, centimetres) and therefore in different numbers.
Besides discreteness, which serves as the real premise for the concepts of quantity and number, it is important for an understanding of the objective basis of mathematics to realise that discrete things, their properties and relations, are united in sets.
Measure. For centuries people have said, "everything has its measure". The reasonable person has a sense of measure in everything: behaviour, dress, eating, taste, and so on. Loss of the sense of measure, of proportion, is a bad sign and takes its revenge by putting the offender in a comic and sometimes tragic situation. Not for nothing do people dislike exaggeration, the superfluous. The perfect is something that has no defects of proportion. The imperfect can never be the measure of anything. Measure is the quantitative limit of a given quality. Quality cannot be more or less than that limit. The whole history of philosophy from ancient times to the present day is permeated with the idea of measure.
Measure is thought of as a perfect whole, a unity of quantity and quality. The concept of measure is used in various senses: as a unit of measurement, volume, as proportion of the parts to the whole, as the limit of the permissible, the legitimate, as law, as unity of quantity and quality, as their perfect wholeness, integration (a molecule of ordinary water must have two atoms of hydrogen and one of oxygen), and as a self-developing system. Measure is also a certain stage in the historical development of something.
Measure expresses unity of quality and quantity. For example, the atoms of various chemical elements are only distinguished from each other by the fact that their nuclei contain various quantities of protons. If we change the number of protons in the nucleus, we change that element into another. Every colour has its wavelength and corresponding frequency of oscillation. Every drug has its measure: its good or bad effect depends not only on its quality but also its quantity. One and the same chemical substance in various doses may stimulate growth or inhibit it. Measure is proportion. It may embrace certain normative features: in morality a knowledge of measure in everything, moderation, modesty; in aesthetics, symmetry, proportion. Gracefulness, for example, is freely organised harmony, proportion in motion. Rhythm, melody and harmony in music are based on the strict observation of measure. Measure is the zone in whose limits a given quality may be modified or varied by virtue of changes in the quantity of certain inessential properties while retaining its essential ones.
The transformation of quantity into quality and vice versa. The path of development in nature, society and consciousness is not a direct line, but a zigzag. Every turn signifies the appearance of new laws that hold good for that particular leg. The limits of these laws are by no means always clearly fixed, sometimes they are conditional. Who can determine the exact limits showing where childhood ends and adolescence begins, where youth begins and when it enters the quality known as "young person"?
The transition from an old to a new quality involves a leap—a break in the gradualness of development. The process of development combines a unity of the continuous and the discontinuous. Continuity in the development of a system indicates relative stability, its qualitative definiteness. Discontinuity in a system's development indicates its transition to a new quality. Figuratively, one may compare this process with the action of a spring and cogwheels in a clock: the spring operates continuously, but thanks to the regulating effect of the cogwheels the energy transmitted by the spring is converted into rhythmical work. The world is not a steady stream, nor is it a stagnant pond, it is a combination of relatively stable and changing systems. Systems develop rhythmically and every stroke of the "clock of the universe" signifies the birth of the new. This is where the law of the transformation of quantity into quality and vice versa reveals itself. This law has an objective and universal character admitting no exceptions.
Quantitative changes show themselves in various ways: as changes in the number of elements of an object, the order of their connection, their spatial dimensions, their velocity, degree of development, and so on. In short, any change in quantity amounts to a change in the elements of a system. The degree of difference between an old and a new quality depends on what quantitative changes have taken place in them. For example, water is heated (increase in the speed of its molecules), but it remains water although it is much hotter or perhaps very hot. Only some of its properties have changed. This change is gradual or phased, a movement from one state to another. But then comes the critical boiling point. The agitated water molecules start bubbling to the surface and leave it in the form of steam. From its liquid state water passes into steam. Basically the appearance of a new property means the appearance of a new object with new laws of existence, with a new measure possessing a different quantitative definiteness. Moreover, the degree of qualitative change may differ. It may confine itself to the level of the given form of motion or it may go beyond this level. Thus measure expresses a unity of quality and quantity in relation to objects for which simple transformation is characteristic, that is to say, change within the limits of the given form of motion of matter, as, for example, in the case of the transformation of water into steam or elementary particles into each other. But measure also expresses the limits of transition from one level of a system's organisation to another, for example, the emergence of the animate from the inanimate. On the threshold of the new, measure grows old and this is the sign of the necessity for transition to another measure.
The process of radical change of quality, the breakup of the old and the birth of the new is what we mean by a "leap".
A leap is a spontaneous discharge of mounting tension, a resolving of contradictions. The passage of a phenomenon from one qualitative state to another is essentially contradictory, it is a unity of destruction and renewal, existence and non-existence, negation and affirmation.
A leap includes the moment of cancellation of the previous phenomenon by the new. The transformation of one phenomenon into another is a unity, an interaction of quantitative and qualitative changes, which pass through a number of intermediate phases. Moreover, different phases of change in a given quality signify changes in the degree of the given quality, in other words a quantitative change.
The big leaps in the development of objective reality were the formation of stars, particularly the solar system and its planets, the origin of life on earth, the origin of man and his consciousness, the formation of new species of animals and plants and the emergence and replacement of socio-economic formations in the history of human society, the great landmarks in the development of science, art, and so on. The social revolution is a special kind of leap, characteristic of social development.
We sometimes use the concept of "evolution" to denote continuous changes, that is to say, gradual changes in quantity and changes of certain properties within the framework of a given quality. However, in the wider sense this term is used to mean development in general, for example, in relation to cosmogony (evolution of stars), and to biology, the evolution of the vegetable and animal worlds.
As a rule, two basic forms of leap take place in the process of development. A leap may be momentary in time, that is to say, a sharp transition from one quality to another, and it may also be a process of a certain duration. A leap may last for a billionth of a second, as in microprocesses, for example, for billions of years, as in cosmic processes, and hundreds of thousands of years, as in the formation of animal species. A distinctive feature of the leap is the fact that the emergence of a new quality puts an end to the former pattern of quantitative changes. Leaps of the first kind have sharply defined frontiers, great intensity, and high velocity in the process of transition; they signify an all-embracing reorganisation of the whole system at a single stroke. Such transformations are to be found in the atomic explosion or the political revolution in society. But political and particularly social revolutions rarely take place in the form of a one-off destruction of the old and construction of the new. The transition may not necessarily be clearly expressed, there may be intermediate stages combining the old and the new.
Assuming the nature of quality as a system of properties, one should distinguish individual or particular leaps associated with the appearance of new particular properties, and general leaps associated with the transformation of the whole system of properties, that is, the quality as a whole.
Changes in quantity and quality are interconnected, a change in quality also involves quantitative change. This is generally expressed in the fact that as the level of organisation of matter rises the rate of its development accelerates. Every level of organisation of matter has its specific laws of quantity. A new, better adapted animal species yields a progeny whose greater power of survival guarantees wider opportunities for it to spread.
The law of the transformation of quantitative into qualitative changes and vice versa places a number of methodological demands on cognition. It allows and requires us to study an object from the standpoint of quantity as well as quality. Study of the quantitative aspect of things has enormous significance in science, technology, and everyday practice. Access to the deep-going problems of science, including biology and social research, demands extremely refined mathematical methods.
Until quite recently, biology, physiology, linguistics, psychology, and many other sciences made little or no use of mathematics, but now they are forging ahead largely due to the application of mathematical methods. Cybernetics has opened up particularly tempting opportunities for their use in modern science. The degree to which mathematics may be used in the study of this or that science is determined by the degree to which quantity may be abstracted from quality. In every specific case this abstraction has its limits.
In scientific research the application of mathematical methods always presupposes a profound knowledge of the subject. Scientists need mathematics not only for computations and calculations—although, of course, this role of mathematics in science is highly important—but as an effective heuristic technique, and also for developing the rigour and discipline of logical thinking. The followers of Pythagoras assumed that universal order was based on the harmony of numbers. Later thinkers suggested that numbers indicate how the world is governed. The reasonable approach is to make sure that quantitative definitions do not over shadow the qualitative definiteness of facts and laws. We can fully understand the essence of an object only by considering both quantity and quality in their unity, their interconnection.