The Logic of Hegel

by Georg Wilhelm Friedrich Hegel

106.] The two sides of the ratio are still immediate quanta: and the qualitative and quantitative characteristics still external to one another. But in their truth, seeing that the quantitative itself in its externality is relation to self, or seeing that the independence and the indifference of the character are combined, it is Measure.

Thus quantity by means of the dialectical movement so far studied through its several stages, turns out to be a return to quality. The first notion of quantity presented to us was that of quality abrogated and absorbed. That is to say, quantity seemed an external character not identical with Being, to which it is quite immaterial. This notion, as we have seen, underlies the mathematical definition of magnitude as what can be increased or diminished. At first sight this definition may create the impression that quantity is merely whatever can be altered:—increase and diminution alike implying determination of magnitude otherwise—and may tend to confuse it with determinate Being, the second stage of quality, which in its notion is similarly conceived as alterable. We can, however, complete the definition by adding, that in quantity we have an alterable, which in spite of alterations still remains the same. The notion of quantity, it thus turns out, implies an inherent contradiction. This, contradiction is what forms the dialectic of quantity. The result of the dialectic however is not a mere return to quality, as if that were the true and quantity the false notion, but an advance to the unity and truth of both, to qualitative quantity, or Measure.

It may be well therefore at this point to observe that whenever in our study of the objective world we are engaged in quantitative determinations, it is in all cases Measure which we have in view, as the goal of our operations. This is hinted at even in language, when the ascertainment of quantitative features and relations is called measuring. We measure, e.g. the length of different chords that have been put into a state of vibration, with an eye to the qualitative difference of the tones caused by their vibration, corresponding to this difference of length. Similarly, in chemistry, we try to ascertain the quantity of the matters brought into combination, in order to find out the measures or proportions conditioning such combinations, that is to say, those quantities which give rise to definite qualities. In statistics, too, the numbers with which the study is engaged are important only from the qualitative results conditioned by them. Mere collection of numerical facts, prosecuted without regard to the ends here noted, is justly called an exercise of idle curiosity, of neither theoretical nor practical interest.

107.] Measure is the qualitative quantum, in the first place as immediate,—a quantum, to which a determinate being or a quality is attached.

Measure, where quality and quantity are in one, is thus the completion of Being. Being, as we first apprehend it, is something utterly abstract and characterless: but it is the very essence of Being to characterise itself, and its complete characterisation is reached in Measure. Measure, like the other stages of Being, may serve as a definition of the Absolute: God, it has been said, is the Measure of all things. It is this idea which forms the ground-note of many of the ancient Hebrew hymns, in which the glorification of God tends in the main to show that He has appointed to everything its bound: to the sea and the solid land, to the rivers and mountains; and also to the various kinds of plants and animals. To the religious sense of the Greeks the divinity of measure, especially in respect of social ethics, was represented by Nemesis. That conception implies a general theory that all human things, riches, honour, and power, as well as joy and pain, have their definite measure, the transgression of which brings ruin and destruction. In the world of objects, too, we have measure. We see, in the first place, existences in Nature, of which measure forms the essential structure. This is the case, for example, with the solar system, which may be described as the realm of free measures. As we next proceed to the study of inorganic nature, measure retires, as it were, into the background; at least we often find the quantitative and qualitative characteristics showing indifference to each other. Thus the quality of a rock or a river is not tied to a definite magnitude. But even these objects when closely inspected are found not to be quite measureless: the water of a river, and the single constituents of a rock, when chemically analysed, are seen to be qualities conditioned by quantitative ratios between the matters they contain. In organic nature, however, measure again rises full into immediate perception. The various kinds of plants and animals, in the whole as well as in their parts, have a certain measure: though it is worth noticing that the more imperfect forms, those which are least removed from inorganic nature, are partly distinguished from the higher forms by the greater indefiniteness of their measure. Thus among fossils, we find some ammonites discernible only by the microscope, and others as large as a cart-wheel. The same vagueness of measure appears in several plants, which stand on a low level of organic development,—for instance, ferns.

108.] In so far as in Measure quality and quantity are only in immediate unity, to that extent their difference presents itself in a manner equally immediate. Two cases are then possible. Either the specific quantum or measure is a bare quantum, and the definite being (there-and-then) is capable of an increase or a diminution, without Measure (which to that extent is a Rule) being thereby set completely aside. Or the alteration of the quantum is also an alteration of the quality.

The identity between quantity and quality, which is found in Measure, is at first only implicit, and not yet explicitly realised. In other words, these two categories, which unite in Measure, each claim an independent authority. On the one hand, the quantitative features of existence may be altered, without affecting its quality. On the other hand, this increase and diminution, immaterial though it be, has its limit, by exceeding which the quality suffers change. Thus the temperature of water is, in the first place, a point of no consequence in respect of its liquidity: still with the increase or diminution of the temperature of the liquid water, there comes a point where this state of cohesion suffers a qualitative change, and the water is converted into steam or ice. A quantitative change takes place, apparently without any further significance: but there is something lurking behind, and a seemingly innocent change of quantity acts as a kind of snare, to catch hold of the quality. The antinomy of Measure which this implies was exemplified under more than one garb among the Greeks. It was asked, for example, whether a single grain makes a heap of wheat, or whether it makes a bald-tail to tear out a single hair from the horse's tail. At first, no doubt, looking at the nature of quantity as an indifferent and external character of Being, we are disposed to answer these questions in the negative. And yet, as we must admit, this indifferent increase and diminution has its limit: a point is finally reached, where a single additional grain makes a heap of wheat; and the bald-tail is produced, if we continue plucking out single hairs. These examples find a parallel in the story of the peasant who, as his ass trudged cheerfully along, went on adding ounce after ounce to its load, till at length it sunk under the unendurable burden. It would be a mistake to treat these examples as pedantic futility; they really turn on thoughts, an acquaintance with which is of great importance in practical life, especially in ethics. Thus in the matter of expenditure, there is a certain latitude within which a more or less does not matter; but when the Measure, imposed by the individual circumstances of the special case, is exceeded on the one side or the other, the qualitative nature of Measure (as in the above examples of the different temperature of water) makes itself felt, and a course, which a moment before was held good economy, turns into avarice or prodigality. The same principle may be applied in politics, when the constitution of a state has to be looked at as independent of, no less than as dependent on, the extent of its territory, the number of its inhabitants, and other quantitative points of the same kind. If we look e.g. at a state with a territory of ten thousand square miles and a population of four millions, we should, without hesitation, admit that a few square miles of land or a few thousand inhabitants more or less could exercise no essential influence on the character of its constitution. But, on the other hand, we must not forget, that by the continual increase or diminishing of a state, we finally get to a point where, apart from all other circumstances, this quantitative alteration alone necessarily draws with it an alteration in the quality of the constitution. The constitution of a little Swiss canton does not suit a great kingdom; and, similarly, the constitution of the Roman republic was unsuitable when transferred to the small imperial towns of Germany.

109.] In this second case, when a measure through its quantitative nature has gone in excess of its qualitative character, we meet, what is at first an absence of measure, the Measureless. But seeing that the second quantitative ratio, which in comparison with the first is measureless, is none the less qualitative, the measureless is also a measure. These two transitions, from quality to quantum, and from the latter back again to quality, may be represented under the image of an infinite progression—as the self-abrogation and restoration of measure in the measureless.

Quantity, as we have seen, is not only capable of alteration, i.e. of increase or diminution: it is naturally and necessarily a tendency to exceed itself. This tendency is maintained even in measure. But if the quantity present in measure exceeds a certain limit, the quality corresponding to it is also put in abeyance. This however is not a negation of quality altogether, but only of this definite quality, the place of which is at once occupied by another. This process of measure, which appears alternately as a mere change in quantity, and then as a sudden revulsion of quantity into quality, may be envisaged under the figure of a nodal (knotted) line. Such lines we find in Nature under a variety of forms. We have already referred to the qualitatively different states of aggregation water exhibits under increase or diminution of temperature. The same phenomenon is presented by the different degrees in the oxidation of metals. Even the difference of musical notes may be regarded as an example of what takes place in the process of measure,—the revulsion from what is at first merely quantitative into qualitative alteration.