Quantity and Quality -|- Educational Philosophy Theory

Quantity and Quality

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Everything can be seen from two points of view—quality and quantity. The fact that the world consists of a sum total of processes which are constantly changing does not mean that real things do not have a definite form of existence, an identity. However much an object changes, it remains, within certain limits, a qualitatively distinct form of existence, different from another. It is this qualitative definiteness which gives things stability, differentiates them, and makes the world so rich and boundlessly varied.

The properties of a thing are what make it what it is. But this quality is not reducible to its separate properties. It is bound up with the object as a whole. Thus, a human being is not just an assemblage of bone tissue, blood, muscles, etc. Life itself is a complex phenomenon which cannot be reduced to the sum total of its individual molecules, but arises from the interactions between them. To use the modern terminology of complexity theory, life is an emergent phenomenon.

The relation of whole and parts was dealt with at length by Hegel, who wrote: "The limbs and organs, for instance, of an organic body are not merely parts of it: it is only in their unity that they are what they are, and they are unquestionably affected by that unity, as they also in turn affect it. These limbs and organs become mere parts, only when they pass under the hands of the anatomist, whose occupation, be it remembered, is not with the living body but with the corpse. Not that such analysis is illegitimate: we only mean that the external and mechanical relation of whole and parts is not sufficient for us, if we want to study organic life in its truth." (Hegel, Logic, p. 191-2.)

It is interesting to note that the latest ideas which have caught the imagination of an important section of the scientific community—the theories of chaos and complexity—were anticipated long ago by Hegel, and, in many respects, received a much more comprehensive treatment in his hands. A case in point is his explanation of the transformation of quantity into quality, whereby an accumulation of small changes brings about a sudden change in quality.

In addition to the quality which defines the essential features of an object, all things possess quantitative features—a definite magnitude, number, volume, speed of its processes, degree of development of its properties, and so on. The quantitative side of things is that which permits them to be divided (actually or mentally) into their constituent parts and put together again. In contrast to quality, changes in quantity do not alter the nature of the whole, or cause its destruction. Only when a definite limit is reached, which is different in each case, do changes of quantitative character cause a sudden qualitative transformation.

In mathematics, the quantitative aspect of things is separated from their content and regarded as something independent. The extremely wide field of applicability of mathematics to spheres of natural science and technology with very different contents is explained by the fact that it deals purely with quantitative relations. Here, it is claimed, it is impossible to reduce quality to quantity. This is the fundamental error of which Marx and Engels referred to as the Metaphysical mode of thought, and which nowadays is termed reductionism. There is nothing in the real world that consists only of quantity, just as there is nothing which is pure quality. Everything in reality consists of the unity of quantity and quality, which Hegel called Measure.

Measure is the organic unity of quantity and quality. Every qualitatively distinct object, as we have seen, contains quantitative elements which are mobile and variable. Living organisms grow at a certain rate. Gases and liquids are affected by variations in temperature. The behaviour of a water droplet or a heap of sand is determined by its size, and so on. These mutations, however, are necessarily bounded by definite limits, which are different in each case, but in practice can usually be discovered. Carried beyond this limit, quantitative changes bring about a qualitative transformation. In its turn, the qualitative change brings about a change in its quantitative attributes. There are not only changes of quantity to quality, but also the opposite process, where a change in quality causes a change in quantity. The critical points of transition from one state to another are expressed as nodal points in Hegel’s nodal line of measurement.

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