Hegel’s Logic: An Essay in Interpretation. John Grier Hibben 1902

Chapter IX Measure

We have seen how the category of being, when allowed to develop fully its own inherent nature, discloses the phases of quantity and of quality.

There now remains to be considered the relation which obtains between quantity and quality, and which in itself constitutes a distinct category.

It is an extremely abstract view of quantity which regards it as having no qualitative significance whatsoever. In the concrete which embraces the totality of elements which constitute the significance of a concept, there are some quantitative differences at least which must be regarded as having marked qualitative equivalents. For instance, the general size of any given species of animals is intimately associated with the complex of properties which form its qualitative determinants. This is true to such an extent that the element of magnitude ranks in itself as a qualitative characteristic. For instance, the size of an elephant is regarded as one of its determining qualitative marks; so also the size of a mouse is regarded as one of its essential properties. The idea of an elephant having the dimensions of a mouse, or a mouse bulking large as an elephant, would do violence to the essential features which constitute the concepts of these animals.

There is, of course, a margin of variation which is allowable, so that the difference in size within certain limits is to be regarded as an accidental property of an animal, having no specific significance whatsoever.

Beyond certain well-defined limits, however, this is not the case.

This relation of quantity to quality, which indicates for every quantitative change a corresponding qualitative value, Hegel calls measure (das Maass). The term is used in almost the same sense as the word standard, or type. To translate das Maass literally as measure does not convey the full significance of the term as it is used by Hegel. It would be better to translate it as the standard measure, or type. Illustrations of its meaning in the Hegelian sense are found throughout the organic world where a definite species is associated with a typical or a standard size. It finds abundant illustration also in the inorganic world wherein each element possesses its own definite specific gravity, so that the quantitative coefficient becomes in each case a distinctive mark of a definite group of correlated qualities which are constantly present with it. Thus, for instance, the specific gravity of gold is inseparably associated with all the essential properties of gold which give it the specific quality by virtue of which it is constituted as it is. The illustration which is the most perfect is found in the scale of relative differences in the two corresponding series, – on the one hand the variation in lengths of the chords in a musical instrument, and on the other the accompanying variation in differences of tone. The former represent purely quantitative differences, and the latter, qualitative. Between them there exists an exact correspondence. This may be further illustrated by the correlation which obtains between the wavelengths of light, and the corresponding differences in color. All these illustrations emphasize the essential relation which exists between a variation in quantity and the corresponding variation in quality.

In accordance with Hegel’s general method of procedure, it will be remembered, every phase in the progressive development of being is to be regarded as a manifestation of one of the various attributes of the Absolute. In this connection, therefore, the Absolute, or God, may be defined as das Maass, – that is, He is the absolute standard of measure, the ideal, or type, of all creation. This signifies that God must contain within His own nature the norm or standard of all things. This is essentially in accord with the Hebrew conception of God as One who has appointed to everything its proper bound and typical form, – to the sea, and land, to the rivers and mountains, to plants and animals, and also to man himself. In his description of wisdom, Job exclaims: –

“God understandeth the way thereof, and he knoweth the place thereof.
For he looketh to the ends of the earth, and seeth under the whole heaven; To make the weight for the winds; and he weigheth the waters by measure.
When he made a decree for the rain, and a way for the lightning of the thunder:
Then did he see it, and declare it; he prepared it, yea, and searched it out."[11]

Moreover, in the religion of the Greeks this idea is frequently expressed, especially in the doctrine of Nemesis, as Hegel points out. According to this conception there is a natural bound to all things, to riches and honor, to power and pleasure, even to pain; and when the definite measure allotted to each is exceeded, there must inevitably follow its corresponding opposite. It is characteristic of Hegel’s general method in this connection to gather from the ancient forms of religion, both an illustration and at the same time a justification of his own point of view.

The religious and philosophical teachers of all ages have in Hegel’s opinion touched upon important truths which it is his peculiar task to gather together in the unity of a philosophical system that will embrace them all.

Moreover, since there is some form and size which may be regarded as the standard or type for any given species, to take an illustration from the organic world, then this type may be departed from within certain limits without affecting the integrity of the species, as has already been pointed out. Variations from the type within such limits are to be regarded merely as natural departures from what Hegel calls the rule. The term “rule” (die Regel) is used to denote the standard form or size in reference to any given class. It has the same significance, in the Hegelian usage, as the term “mode,” which is employed to signify the prevailing type in curves showing the relative distribution of variations, the curve itself indicating the manner in which the variations in question are distributed about the type itself. In these curves the mode is represented by the maximum ordinate, the varying lengths of the other ordinates indicating the relative number of cases corresponding to the different variations.

It is a significant fact, however, that the range of possible deviation from the prevailing type is necessarily limited, so that if it is departed from in any way the type itself is so far changed as to constitute an essentially new type, or a distinct species. It appears, therefore, that there may be a continued alteration of quantity by increasing or decreasing the given magnitude up to a certain definite limit, and the various changes will have no appreciable effect upon the corresponding quality. Thus, while the quantity may be regarded as a variable, the quality nevertheless remains a constant. But in this process of variation some point must always be reached at which a quantitative change begins to produce a qualitative change as well. Hegel illustrates this by calling attention to the fact that the temperature of water seems to be quite independent of its qualitative state of liquidity, but as we increase the temperature through a wide range of variation there nevertheless is reached finally a degree of heat which marks a decided qualitative change as the liquid becomes transformed into vapor; and at the other limit, where the freezing-point is reached, the liquid of course changes into the solid state. Between these limits the various changes of temperature seem to have no qualitative significance whatsoever; and, as Hegel remarks, in the approach toward either limit, the advance is made without any accompanying circumstances to anticipate it as far as our observation goes, so that the point which marks the beginnings of a corresponding qualitative change is reached, as it were, by stealth. The illustration of Hegel’s in reference to the variations in the temperature of water may be further supplemented in the following manner, which may possibly shed some additional light upon Hegel’s exposition. It is a well-known phenomenon of physics that before reaching the freezing-point, at 2degF, the decreasing temperature causes a proportional decrease of bulk in the water. This decrease in bulk is continuous to about 9degF. At this point, however, a decided change is noticeable, for the bulk of water now begins to expand instead of contracting as before, and so continues until the fluid passes into the solid state at the freezing-point. This change seems to be a warning note which is sounded to indicate that even a more radical change may be anticipated.

The points which mark in a series of continuous changes the beginnings of a qualitative corresponding to a quantitative difference, Hegel calls the “nodes,” or “nodal points,” – a term. which he has borrowed from astronomy. The line which may be conceived as indicating the continuous changes which may occur between these points without effecting any qualitative difference he calls, “the line of nodes.” To understand this reference, it may be well to give the technical definition of a node, which Hegel, of course, has adapted to his purposes. The node as used in astronomy is one of the points at which any celestial orbit cuts the plane of the ecliptic, the latter being a great circle of the heavens in the plane of the earth’s orbit. The node, therefore, is a point having a double significance by virtue of its being the intersecting point of two circles, and therefore it may be conceived first as belonging to one and then to the other. This idea of a point having a twofold significance, Hegel has seized in order to indicate that particular point in quantitative variation which has at the same time a qualitative significance as well.

Such a point possesses the combined characteristics which constitute both its qualitative and its quantitative features, just as a point which is common to two circles possesses the characteristic features of each.

Between these nodes, however, or beyond them in either direction, the various quantitative differences seem to have no significance whatsoever as far as producing any change of definite qualitative nature. Whenever, therefore, quantitative changes possess no qualitative significance, they cannot be regarded as constituting any standard or type of measure, for the magnitude which they represent has no quality or complex of qualities corresponding to it. Such magnitudes Hegel designates as measureless (Maasslos), – that is, lacking the essential characteristics of a standard or a type. Thus it will be seen that the concept of quantity in itself does not determine qualitative differences, inasmuch as some magnitudes have no corresponding qualitative characteristics at all. The category of quantity, therefore, proves unsatisfactory as an ultimate explanation of qualitative differences. Inasmuch as it falls, as it were, of its own weight, it seems to necessitate by its very inefficiency some additional category which can satisfactorily explain the relation between quantitative and qualitative variations.

A similar situation has developed at every stage of progress in the evolution of the thought processes from the simplest beginnings in mere being to the present condition under discussion. Throughout, each category that has been reached in the progress of thought has proved insufficient to explain itself and all which have gone before, and has laid upon thought the necessity of proceeding to some further stage of development in order to supply its defects and complete its meaning. This is essentially the Hegelian dialectic movement of thought.

We have seen that the idea of mere being carried with it the necessary implication of a complex system of attributes designated as the quality of determinate being.

This concept in turn has been found to necessitate the idea of oneness of being, – that is, being-for-self, an individual separate in a sense from all others. This idea of the one, the individual, was then found to suggest by necessary implication the idea of the many, – a purely quantitative concept.

Starting then, with the idea of quantity, its highest expression was reached when it was regarded as correlated with the idea of quality.

Thus the quantity-quality relation which Hegel calls measure, or better the standard measure, would seem to be the consummation of the entire process.

The relation however being unstable, – that is, existing for certain quantitative values and not existing for others, – the thought is consequently constrained by the very nature of its own processes and its own demands to press onward to a further stage of development, and to ask the question, What is it which underlies these various relations of quantity to quality, rendering them significant at certain coincidental points, the ‘nodes’ according to Hegel, and at others attaching to them no significance whatsoever? This category of a standard measure is by its very limitations a challenge to thought, that it produce something of a more ultimate nature as its underlying ground. That which is demanded is some satisfactory explanation of the various distinct types which are found in nature, each determined according to its own definite standard of measure.

The most complete expression of the category of being, and the final term in the development of that idea, the concept of standard measure, has been found wholly insufficient to rank as a self-contained and self-explaining category. This last term, therefore, can no longer be regarded as a last term; it suggests rather additional terms in the process of development which will form its natural complement and explanation.

The immediately complementary term in the line of the logical unfolding of the universal reason is that of essence (das Wesen), which forms the second main division of the Logic. The category of essence is to be regarded as the ground which underlies the various changes which characterize the progressive development of the idea of being. What being is in its essence determines its qualitative characteristics and correlates them with certain definite quantitative changes by the fundamental law of its own nature. The magnitude does not determine the quality, nor does the quality determine the magnitude, but the roots, both of the quantitative and qualitative elements in being, lie deeply concealed in the fundamental essence. Hegel expresses this in his epigrammatic manner, “Essence is the truth of being.”