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Remark 1: Examples of This Identity
§ 483
In everyday use we distinguish extensive and intensive magnitudes “as if some objects had only intensive, others only extensive magnitude.” As well, the natural sciences consider certain properties as either extensive or intensive, for example,
density, or the specific filling of space, for example, must essentially be understood not as a certain aggregate and amount of material parts in a quantum of space, but as a certain degree of the space-filling force of matter.
§ 484
Both intensive and extensive magnitudes pertain to force, but this will be elaborated later.
§ 485
Extensive and intensive magnitudes are contained in each other; hence
every existence exhibits its quantitative character just as much as an extensive as an intensive quantum.
[Compare to Bergson who says that intensive magnitudes are not contained within each other. Time and Free Will §2; §3]
§ 486
Number itself is both intensive and extensive:
It is an amount in so far as it is an extensive magnitude; but number is also one, a ten, a hundred, and as such it is on the threshold of transition into an intensive magnitude, seeing that in this unity the plurality has become simple.
Even the number one has intensive parts, its 10th part for example, that is, it’s 10th internal degree.
§ 487
This is why a circle, although whole, consists of different degrees.
§ 488
Concrete objects also display both extensive and intensive magnitudes, as they are considered in their internal and external determinations.
for example, a mass as weight is an extensive magnitude, in so far as it constitutes an amount of pounds, hundredweights, etc., and an intensive magnitude in so far as it exerts a certain pressure; the magnitude of the pressure is a simple number, a degree, which is specified by its place in a scale of degrees.
§ 489
Although heat is a degree and hence an intensive magnitude, it is also present as an extensive magnitude when it expands the mercury of the thermometer that reads its intensive magnitude. In other words, heat has both an intensive magnitude, its degree of energy, and an extensive magnitude, the length of expansion of the heated object.
§ 490
Intensive and extensive magnitudes show their dual character in many other ways. When a musical note is intensively at a higher degree of pitch, its vibrations are of a greater extensive quantity, (and inversely its wavelengths are of a lesser extensive quantity). A note with a greater intensive degree of volume is audible in a larger space.
A color at a greater intensive degree of brightness can be seen at a greater distance.
§ 491
In the spiritual sphere, if one has a high intensity of character, talent, or genius, one’s influence may reach farther distances of the globe. And the most profound idea has “the most universal significance and application.”
[Other Entries in the Hegel Science of Logic Series]
From the original text:
Remark 1: Examples of This Identity
§ 483
Extensive and intensive quantum are usually distinguished in the ordinary conception of them as kinds of magnitude,as if some objects had only intensive, others only extensive magnitude. In addition, we have the conception of a philosophical science of Nature in which what is a plurality or extensive — for example, in the fundamental property of matter to occupy space, and in other concepts too — is converted into something intensive, meaning thereby that the intensive aspect as dynamic is the true determination; density, or the specific filling of space, for example, must essentially be understood not as a certain aggregate and amount of material parts in a quantum of space, but as a certain degree of the space-filling force of matter.
§ 484
There are two kinds of determinations to be distinguished here. In what has been called the conversion of the mechanical into the dynamic point of view, there occurs the concept of separately existing, independent parts,which are only externally combined into a whole, and the concept of force which is distinct from this. In the occupation of space, what is regarded on the one hand as only an aggregate of atoms external to one another, is on the other hand regarded as the expression of an underlying simple force. But these relations of whole and parts, of force and its expression, which here stand opposed to each other, do not belong in this section; they will be considered in their proper place later on. But this much may be remarked here, that though the relation of force and its expression which corresponds to intensive magnitude is in the first instance truer than that of whole and parts, yet this does not make force, as intensive, any less one-sided; also expression, the externality of extensive magnitude, is equallyinseparable from force; so that one and the same content is equally present in the two forms, both in intensive and in extensive magnitude.
§ 485
The other determinateness which occurs here is the quantitative as such, which, as extensive quantum, is sublated and transformed into degree, the supposedly true determination; but it has been shown that degree equally contains the former determinateness, so that the two forms are essential to each other; consequently, every existence exhibits its quantitative character just as much as an extensive as an intensive quantum.
§ 486
Consequently everything, in so far as it manifests a quantitative character, serves as an example of this. Number itself necessarily has this double form immediately within it. It is an amount in so far as it is an extensive magnitude; but number is also one, a ten, a hundred, and as such it is on the threshold of transition into an intensive magnitude, seeing that in this unity the plurality has become simple. One is in itself an extensive magnitude, it can be represented as an arbitrary amount of parts. Thus the tenth, the hundredth, is this simple, intensive magnitude which has its determinateness in the plurality lying outside it, that is, in extensive magnitude. Number is a ten, a hundred and at the same time the tenth, hundredth, in the system of numbers; both are the same determinateness.
§ 487
In the circle the one is called degree because the determinateness of any part of the circle derives essentially from the many parts outside it; that is, it is determined as only one of a fixed amount of such ones. As a mere spatial magnitude, the degree of the circle is only an ordinary number; taken as degree, it is intensive magnitude which has a meaning only as determined by the amount of degrees into which the circle is divided, just as number generally has meaning only in the number series.
§ 488
The magnitude of a more concrete object exhibits its dual aspects of being extensive and intensive, in the dual determinations of its real being, in one of which it appears as an outer being but in the other as an inwardness. Thus, for example, a mass as weight is an extensive magnitude, in so far as it constitutes an amount of pounds, hundredweights, etc., and an intensive magnitude in so far as it exerts a certain pressure; the magnitude of the pressure is a simple number, a degree, which is specified by its place in a scale of degrees. As exerting pressure, mass is manifested as a being-within-self, as a subject to which belongs a difference of intensive magnitude. Conversely, that which exerts thisdegree of pressure is capable of displacing a certain amount of pounds, etc., and its magnitude is measured by this.
§ 489
Again, heat has a degree; this degree, whether it be the tenth, twentieth and so on, is a simple sensation, something subjective. But this degree is equally present as an extensive magnitude, as the expansion of a fluid, of mercury in a thermometer, of air, or sound, and so on. A higher degree of temperature expresses itself as a longer column of mercury, or as a narrower sound cylinder; it heats a larger space in the same way as a lower degree heats only a smaller space.
§ 490
The higher note is, as more intensive, at the same time a greater number of vibrations, and a louder note, to which we ascribe a higher degree, is audible in a larger space. A larger surface can be coloured with a more intensive colour than with a weaker colour used in the same way; or again a brighter object (another kind of intensity) is visible at a greater distance than one less bright, and so forth.
§ 491
Similarly in the spiritual sphere, high intensity of character, of talent or genius, is bound up with a correspondingly far-reaching reality in the outer world, is of widespread influence, touching the real world at many points. The profoundest Notion also has the most universal significance and application.
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