The result of the previous chapter was that the limitation of magnitudes was seen to depend on the qualitative contents measured by the magnitudes, or as Fichte also puts it, quality was shown as the source of quantitative. Thus, we are not anymore dealing with the empty continuity of counting formal, indifferent units into infinity nor with a positive or negative relation of magnitudes measured by this mutual relation. Instead, Fichte emphasises, the content forms the foundation of limits and relations of a magnitude that is derived from this content.
The first form of this magnitude, Fichte says, is an extensive magnitude. Often by an extensive magnitude, Fichte admits, is meant simply any limited quantity in general. Yet, he is here using the term in a special meaning, where the content is recognised as the foundation of this limitation: the content alone extends itself into a determined quantity against other contents and does not just receive a limit from outside. Thus, the content is by its own nature extended and limited from others.
Extensive magnitude is limitation, Fichte clarifies, but only with the distinction that it is the qualitative determination that limits itself and divides into a manifold of quantitatively distinguishable parts. There are thus two aspects, outward and inward, in any extensive magnitude. Outwardly, Fichte begins, extension is related to something else, since limitation implies in general an opposition. Here the opposition is not anymore formal opposition of different amounts, but a determined opposition, where the content itself determines its own extension opposed to other similar extensions (you might picture here a sort of force field). Just like earlier, we might speak of the relations that the numeric expressions of these extensions have to one another.
Inwardly, Fichte adds, extension is an infinitely divisible or distinguishable manifold sharing a continuous, unified quality. Here we meet again the opposition of continuous and discrete magnitude, but now finally balanced. Thus, Fichte notes, we have a similarly continuing extension, and if we formally ignored the content that determines the limits of this extension, it would seem to be able to continue in infinity. Such a return to earlier stages of quantity, Fichte explains, is caused by the one-sidedness of the concept of continuity. Conversely, the extension as a magnitude in general is an internally distinguishable, discrete manifold. Just like with continuity, taking this discreteness one-sidedly would lead us to an infinity – this time to infinite divisibility. Yet, Fichte points out, both continuity and discreteness are by themselves untrue and presuppose one another or their common unity. This unity, he says, is just the extensive magnitude or the determined content quantifying itself and giving itself its own extension and thus showing itself as both a continuous quantity and a discrete plurality of parts.
Fichte notes that an extensive magnitude appears to also contain the opposed conceptual moment of intensity. He begins his argument from the notion of extension as a limited and determined continuous quantity that rejects from its extension everything opposing its determination. In other words, Fichte suggests, the outward limitation of the determination of the extensive magnitude is necessarily connected with a positive self-assertion of this determination within these limits. Now, at the level of quantity, this self-assertion must also have a measure, which is then its force or intensity, in opposition to mere extension or outward limitation.
The intensive magnitude, Fichte continues, is the simple, undivided determination, not yet as a pure quality, but as a quantitative measure. In other words, it is still a magnitude, but not a manifold of parts (that would be an extension). It is more like the grade of the content, designating its inner energy or its strength and weakness. The grade, Fichte suggests, is a simple measure of a simple content, but it can be designated through the general expression of all quantities, that is, through number. Thus, the increase or decrease of intensity can be expressed through determined numbers, but these numbers do not designate any sum of individuals or no amount of grades. Instead, Fichte says, a numerically expressed grade shows a certain position in a scale of grades.
It shouldn't be surprising that Fichte manages to again introduce here the opposition of continuous and discrete. While intensity remains same as to its content, he says, it can be thought as continuously strengthening or weakening in infinity, whereby the grade of intensity seems indifferent. In other words, the content itself should remain the same, no matter how great or small of an intensity it has.
In addition to the indifferent continuum of strengthening or weakening in infinity, Fichte says, the intensity also contains the aspect of discreteness as a quantitative determination. In other words, an intensity has a determined grade and is locked within certain limits of strengthening and weakening, but only in a series of other grades that give the continuum of strengthening and weakening internal distinctions that reproduce the moment of discreteness. The measure of intensity, Fichte thinks, is only in relation to others, and a determined intensity can be called great or small and strong or weak only when it is compared to other similar intensities, and so the same grade can appear at the same time great and small according to different comparisons and relations. Grade, Fichte concludes, is thus the highest mediation of the oppositions of quantity.
The intensity, Fichte notes, on the one hand, limits itself outwardly in relation to other intensities by having a different grade than them. On the other hand, it also limits itself internally by allowing the determination of its content remain the same within the limits of strengthening and weakening. This means, Fichte suggests, that intensity must give itself an equally determined extension, which leads us to the mediation between extension and intension. This mediation, in Fichte’s opinion, is a particular application of the more general principle that qualities must also have a quantitative determination.
The result of Fichte’s investigation has been that extensive and intensive magnitudes are reciprocally conditions of one another. Since both thus by themselves move to the other, their truth is only their unity, which is then also the truth of the third stage of quantity. This unity of both, Fichte suggests, is the quantitative determination appearing from qualitative content that gives itself an appropriate and specific quantity with determined intensity in itself and in determined extension toward other self-quantifying qualities. In relation to itself, such self-quantifying quality can be increased or decreased, but this changeability remains locked within determined limits. Beyond these limits, the content itself changes, and thus this qualitative determination can be thought only within a series of such determinations and limited by them. At the same time, Fichte notes, the concept of quantitative is thus raised to a new and higher meaning, since it receives a qualitative sense.
The mere formal continuity of infinite increase and decrease of magnitude, Fichte thinks, has received a limit and a deeper meaning by becoming an expression of the content. On the other hand, the content has its specific, fundamental character in a series of magnitudes, within which it can grow or diminish, but beyond which it will immediately become something else. Mere quantitative difference has thus become qualitative, and continuity of quantitative increasing and decreasing is thereby limited: what is just quantitatively changed in an unremarkable fashion suddenly leaps over the limit of its changeability and becomes qualitatively different, breaking the series of quantitative graduality. Quantitative in general, Fichte suggests, is absorbed by qualitative and assimilated as a mere moment in it. Quantity is nothing in itself, but only the expression of qualitative and even in its formal limitation it shows itself as dependent and subsumed to the content that places in these quantitative limits qualitative distinctions.
Fichte concludes with a summary of the development of the concept of quantity. Its journey began with the notion of this (Dieses) that was formally, but not really distinguished from other these. This first concept of quantity developed into the notion of a limited quantity or magnitude, which was expressed or determined as a countable number, as a measure, and finally, as a determined grade of extension and intensity. Through this development of quantity, the notion of qualitative determination protruded more and more forcefully: something has to be qualitatively determined or has to have a content, in order to be quantified. In other words, Fichte states, quantity presupposes in general the quality as determining and governing it. Transition into quality, he adds, is, like every dialectical step forward, also a return to more essential or a conscious highlighting of an implicit presupposition. Quality is therefore not deduced from quantity, since this would mean deriving more full and real from the empty and abstract. Instead, Fichte insists, the new concept appears, when something hidden in the earlier conceptual context is raised to consciousness by showing how the earlier concept in its purity and isolation leads to the next concept. Because of this isolation, Fichte ends the chapter, the new thought is at first still the negation of the previous, until the following conceptual level mediates both and collects them in a common higher expression.
Ei kommentteja:
Lähetä kommentti