Intensive magnitude or Degree is in its notion distinct from Extensive magnitude or the Quantum. It is therefore inadmissible to refuse, as many do, to recognise this distinction, and without scruple to identify the two forms of magnitude. They are so identified in physics, when difference of specific gravity is explained by saying, that a body, with a specific gravity twice that of another, contains within the same space twice as many material parts (or atoms) as the other. So with heat and light, if the various degrees of temperature and brilliancy were to be explained by the greater or less number of particles (or molecules) of heat and light. No doubt the physicists, who employ such a mode of explanation, usually excuse themselves, when they are remonstrated with on its untenableness, by saying that the expression is without prejudice to the confessedly unknowable essence of such phenomena, and employed merely for greater convenience. This greater convenience is meant to point to the easier application of the calculus: but it is hard to see why Intensive magnitudes, having, as they do, a definite numerical expression of their own, should not be as convenient for calculation as Extensive magnitudes. If convenience be all that is desired, surely it would be more convenient to banish calculation and thought altogether. A further point against the apology offered by the physicists is, that, to engage in explanations of this kind, is to overstep the sphere of perception and experience, and resort to the realm of metaphysics and of what at other times would be called idle or even pernicious speculation. It is certainly a fact of experience that, if one of two purses filled with shillings is twice as heavy as the other, the reason must be, that the one contains, say two hundred, and the other only one hundred shillings. These pieces of money we can see and feel with our senses: atoms, molecules, and the like, are on the contrary beyond the range of sensuous perception; and thought alone can decide whether they are admissible, and have a meaning. But (as already noticed in § 98, note) it is abstract understanding which stereotypes the factor of multeity (involved in the notion of Being-for-self) in the shape of atoms, and adopts it as an ultimate principle. It is the same abstract understanding which, in the present instance, at equal variance with unprejudiced perception and with real concrete thought, regards Extensive magnitude as the sole form of quantity, and, where Intensive magnitudes occur, does not recognise them in their own character, but makes a violent attempt by a wholly untenable hypothesis to reduce them to Extensive magnitudes.
Among the charges made against modern philosophy, one is heard more than another. Modern philosophy, it is said, reduces everything to identity. Hence its nickname, the Philosophy of Identity. But the present discussion may teach that it is philosophy, and philosophy alone, which insists on distinguishing what is logically as well as in experience different; while the professed devotees of experience are the people who erect abstract identity into the chief principle of knowledge. It is their philosophy which might more appropriately be termed one of identity. Besides it is quite correct that there are no merely Extensive and merely Intensive magnitudes, just as little as there are merely continuous and merely discrete magnitudes. The two characteristics of quantity are not opposed as independent kinds. Every Intensive magnitude is also Extensive, and vice versâ. Thus a certain degree of temperature is an Intensive magnitude, which has a perfectly simple sensation corresponding to it as such. If we look at a thermometer, we find this degree of temperature has a certain expansion of the column of mercury corresponding to it; which Extensive magnitude changes simultaneously with the temperature or Intensive magnitude. The case is similar in the world of mind: a more intensive character has a wider range with its effects than a less intensive.
104.] In Degree the notion of quantum is explicitly put. It is magnitude as indifferent on its own account and simple: but in such a way that the character (or modal being) which makes it a quantum lies quite outside it in other magnitudes. In this contradiction, where the independent indifferent limit is absolute externality, the Infinite Quantitative Progression is made explicit—an immediacy which immediately veers round into its counterpart, into mediation (the passing beyond and over the quantum just laid down), and vice versâ.
Number is a thought, but thought in its complete self-externalisation. Because it is a thought, it does not belong to perception: but it is a thought which is characterised by the externality of perception.—Not only therefore may the quantum be increased or diminished without end: the very notion of quantum is thus to push out and out beyond itself. The infinite quantitative progression is only the meaningless repetition of one and the same contradiction, which attaches to the quantum, both generally and, when explicitly invested with its special character, as degree. Touching the futility of enunciating this contradiction in the form of infinite progression, Zeno, as quoted by Aristotle, rightly says, 'It is the same to say a thing once, and to say it for ever.'
(1) If we follow the usual definition of the mathematicians, given in § 99, and say that magnitude is what can be increased or diminished, there may be nothing to urge against the correctness of the perception on which it is founded; but the question remains, how we come to assume such a capacity of increase or diminution. If we simply appeal for an answer to experience, we try an unsatisfactory course; because apart from the fact that we should merely have a material image of magnitude, and not the thought of it, magnitude would come out as a bare possibility (of increasing or diminishing) and we should have no key to the necessity for its exhibiting this behaviour. In the way of our logical evolution, on the contrary, quantity is obviously a grade the process of self-determining thought; and it has been shown that it lies in the very notion of quantity to shoot out beyond itself. In that way, the increase or diminution (of which we have heard) is not merely possible, but necessary.
(2) The quantitative infinite progression is what the reflective understanding usually relies upon when it is engaged with the general question of Infinity. The same thing however holds good of this progression, as was already remarked on the occasion of the qualitatively, infinite progression. As was then said, it is not the expression of a true, but of a wrong infinity; it never gets further than a bare 'ought,' and thus really remains within the limits of finitude. The quantitative form of this infinite progression, which Spinoza rightly calls a mere imaginary infinity (infinitum imaginationis,) is an image often employed by poets, such as Haller and Klopstock, to depict the infinity, not of Nature merely, but even of God Himself. Thus we find Haller, in a famous description of God's infinity, saying:
Ich häufe ungeheure Zahlen,
Gebirge Millionen auf,
Ich sesse Zeit auf Zeit
Und Welt auf Welt zu Hauf,
Und wenn ich von der grausen Höh'
Mit Schwindel wieder nach Dir seh:
Ist alle Macht der Zahl,
Vermehrt zu Tausendmal,
Noch nicht ein Theil von Dir.
[I heap up monstrous numbers, mountains of millions; I pile time upon time, and world on the top of world; and when from the awful height I cast a dizzy look towards Thee, all the power of number, multiplied a thousand times, is not yet one part of Thee.]