Last time, Fichte had ended with the concept of this (Dieses) that was empty or lacked all positive content and that was related to an equally empty this, and because they both lacked any content, they were not internally distinguished from one another. This concept, he continues, opens up a new field of thinking, where we have an infinite series of such “these” that have no internal, but only formal distinction and are thus unlimited in their similarity. Here, it is left expressly undetermined what internal relations the various “these” have to each other and whether they correspond or differ in some respect: they are just formally not same and are thus vanish in an infinity that is not separated by any content or qualitative difference. This being formally distinguished and qualitatively not distinguished, Fichte suggests, is the fundamental concept of quantity. Quantity, he adds, is the most formal or most abstract determination that still also leaves everything undetermined, since it does not yet point to any internally distinguishing quality.
Quantity is thus, for Fichte, the first of all proper categories or the most abstract manner of distinguishing beings. The basic characteristic of the quantity, he suggests, is the highest contradiction of abstraction where, on the one hand, we expressly affirm difference, but on the other hand, also expressly deny it again and resolve it into an unbroken, abstract similarity. This is the most formal level of thinking that does not yet determine anything, but still already tends toward determining and prepares for it the form of distinction. Fichte goes even so far as to suggest defining quantity as the unification or synthesis of formal distinguishing – indeed, of a possibility of infinite distinction – and of non-distinguishing, where internal distinctions are not permitted. To put it shortly, in quantity we can posit a limit, which is then immediately cancelled.
Fichte clarifies that what he has described here is especially the concept of pure quantity, which can then be regarded from different viewpoints, according to whether manifoldness or similarity is highlighted. This pure quantity, he suggests, should then be differentiated into determined quantities or magnitudes, which differ from pure quantity only insofar as they are results of determining quantity. In other words, magnitude still shares the general character of quantity that it is indifferent toward how it is determined. Therefore, Fichte explains, magnitude precisely negates the manner in which it is determined, as he thinks can be seen in the mathematical definition of magnitude: it is something that can be infinitely increased or diminished. Determined and pure quantities should thus contain the same contradiction that they are both determined and left undetermined.
Fichte reminds us that the universal meaning of all categories is to serve as fundamental determinations of the absolute. Thus, he notes, absolute could be defined in a very undeveloped manner as the pure quantity that infinitely comprehends or determines everything quantitative. While the pure quantity thus gives everything its quantity, it is not itself determined according to magnitudes or relations of quantity, but contains all of these as moments in itself. In other words, Fichte clarifies, the absolute is the unlimited that limits or measures everything else quantitatively, while itself it is measureless or infinite in the crudest sense of the word. He also suggests that we could give a more detailed meaning to this definition of absolute by relating it to the quantitative forms of intuition or space and time. Thus, Fichte continues, while absolute or God is thought as positing and filling space and time, as the universal essence it is not itself in space and time.
Fichte also suggests that we can anticipate here the notion of indifference that is the one of the emptiest determinations of the absolute. Thus, the absolute as pure quantity should already be the abstraction from everything finite, including both quantitative and qualitative distinctions. In other words, absolute in this sense is the universal sphere and internal limit for distinctions, but is itself indifferent to these distinctions. Yet, Fichte notes, this notion of indifference is still just an anticipation, since we have not yet consciously discovered anything qualitative.
After these preliminary considerations, Fichte goes on to study in more detail magnitude as the first and thus the most universal form of all thinking of quantity: everything that is quantitative is at first to be determined by a magnitude, but abstractly and not as magnitude of any kind (e.g. not as magnitude of space or time). Now, Fichte continues, there is no internal distinction that would form any proper limits to the magnitude, or if there is such, it is expressly ignored. Thus, this immediate form of magnitude grasped is an unbroken, inseparable series or a continuous magnitude. What this continuity means, Fichte explains, is internal similarity or negation of any distinction posited in the magnitude formally: it is an infinite manifoldness that is immediately again united and resolved into similarity. Hence, continuous magnitude contains manifoldness only as a possibility, which could still be actually distinguished and separated into further magnitudes.
Continuous magnitude contains no distinction, but everything in it melts into a similar togetherness of what is distinguished, although still distinguishable. Fichte thinks that all external limitations must therefore also seem indifferent to the continuous magnitude: within and without the continuous magnitude, there is nothing qualitative that could limit its continuity that always remains the same. Thus, he notes, continuity is outwardly unlimited or infinite in the sense that it is a series that could be indifferently lengthened, while inwardly it is endlessly distinguishable or divisible, since its internal similarity allows an infinite possibility of distinctions.
Fichte notes that we can also emphasise the other side or multiplicity in the determination of magnitude or make distinguishability its prevalent characteristic. This leads us to the concept of a discrete magnitude. Discreteness, Fichte explains, is the formal separation of one (Eins) from another one, while this separation had vanished in the continuity. Fichte thus takes one as the fundamental element of concrete magnitudes. He also points out that discrete and continuous magnitudes are not two different kinds of magnitudes, but only complementing viewpoints on the same quantity. In other words, in magnitude taken as continuous, every distinction is extinguished into a similar, unbroken togetherness, while the same magnitude as discrete highlights multiplicity or infinitely distinguishable ones.
We have thus formally separated many ones, Fichte points out, but they also appear internally undistinguishable or similar. Thus, the moment of continuity is reproduced in discrete quantities, he thinks. Series of ones can be arbitrarily limited, but every limitation is again cancelled, just like in continuous magnitude. Difference between both notions of quantity is just that the one emphasises the internal multiplicity, while the other asserts the similarity, because multiplicity is just formal and not qualitative manifoldness.
Continuous and discrete magnitudes are, according to Fichte, only different viewpoints on quantity in general and on quantitative magnitudes in particular. Every quantity can thus be determined in this dual manner: on the one hand, we can grasp only its internal indistinguishability and make it a continuous quantity, on the other hand, we can highlight the possibility of infinite distinguishing and grasp it as discrete quantity splintered into an infinity of ones.
Fichte thinks that we can find a common expression for such a quantity that is from one respect similarity, from another respect distinguishability. This common expression, he suggests, is the number that flows into a continuity of endless multiplicity or an infinite series of similar ones, but also again collects these ones into discrete units in individual sets of ones. Number, Fichte describes, is the most comprehensible abstraction that formally emphasises distinction that at once becomes fully indifferent. Such a speculative category can exist, according to Fichte, only in the world of pure, abstract thinking. It is still the most effortless and easiest to handle, he adds, since it overlooks everything difficult and deep in thinking. Number encloses and governs every determination of thought and being, because it is the universal form of all determining and distinguishing. While we have not yet developed any internal distinction of things, Fichte emphasises, we can at least distinguish them according to numbers, and this opens up the road to the sphere of qualitative fundamental distinctions.
Fichte suggests that the principle of dialectics for numbers, leading to all numeric relations, is the opposition of continuity and discreteness that goes through everything quantitative and finds its most immediate reconciliation in numbers. Thus, all numeric relations appear from the double viewpoint, where numbers are regarded, on the one hand, continuous, on the other hand, discrete: either the multiplicity of internally similar ones can be again collected together and raised to a higher unity, or the ones are expressly fixated in their separation and enumerated as distinguishable.
In the further chapters, Fichte reveals, numbers will develop into more qualitative forms. As the common expression for all these further determinations of quantity, he explains, number can, despite its abstract position in the whole series of categories, still be a paradigmatic expression for properly qualitative relations or any determinations where it is not the question about merely quantitative. Thus, Fichte muses, if a symbol should be chosen to designate the eternal form of all determinations, the most fitting would certainly be the number, because it posits every distinction expressly as indifferent and can designate what is externally most formal in it.
Fichte returns from these general considerations of the nature of numbers to its further development. He points out that what was formerly designated as this (Dieses) is in its quantitative relation to others a mere one (Eins) related to other ones. This one, Fichte explains, is an empty abstraction that is still opposed to another, equally empty one. “One” is the simplest determination under the categories of quantity, he thinks, since everything in general can at least be called one, which can be thought only in relation to another one. Just like something (Etwas) was the fundamental concept of all determining, Fichte states, one as the quantitative expression of something is the fundamental element of numbers, which is determined only in relation to other ones.
With one, its relation to another one is already posited, Fichte continues: just like earlier developing the concept of something posited another, developing one leads to other ones. These other ones, Fichte explains, do not just appear contingently and form a plurality from an aggregate of externally collected units, but one is by its own nature comprehended in and beside other ones. Still, we at first see only the loosest, most external relation of ones to one another or an indeterminate, numeric multiplicity in general that can be increased and decreased. This plurality or “many”, Fichte emphasises, is the result of thoughtless not-counting or of unlimited and undetermined quantifying in general. Thus, it is the vaguest category of quantity.
Next, Fichte states, thinking proceeds to comprehend this empty manifold in allness: many are combined into a unity. One is thus comprehended not just in many ones, but in totality of ones that forms a synthesis to thesis of one and antithesis of many. Allness in in this sense also completely relative, Fichte thinks, since it is all just in relation to this particular set of combined similar ones. Therefore this relative allness is to be distinguished from absolute or conceptual allness, which, according to Fichte, we haven’t yet reached in relations of quantity.
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