Bernard Bolzano: Study of science – Collections of representations

Bolzano's journey through characteristics of representations has reached the concept of characteristic itself. He really has no definition of the concept, except that a characteristic is something that an object has, no matter how temporary it is. This having, Bolzano thinks, has then no better explanation than being a relation of a thing to its characteristic (and not, say, possessing another thing, like when we say that I have money). It is then completely arbitrary, which of the two – characteristic or having – is taken as primary notion and which as defined, although Bolzano prefers having as the primary one. He also notes that spatial and temporal determinations are to not to be taken as characteristics, since in propositions they more conveniently characterise the subject position, while characteristics always fall to the predicate position.

Bolzano divides characteristics into internal and external or properties and relations. Of these, he insists, relation between things is actually a characteristic of the collection or the whole composed of the related things, for instance, the relation of three points forming an equilateral triangle is the characteristic of the collection of the three points, not of the points themselves, although we can say that the points have the (external) characteristic of being a part in a collection with such characteristic. Bolzano adds to his definition of relation that both the parts and the characteristic must be variable, because otherwise we would have to say that the primeness of number 13 is a relation, because it refers to the whole system of numbers.

Having defined relations and external characteristics, Bolzano can easily explain internal characteristics or properties as characteristics that are not external. From these definitions it easily follows that a relation between things is a property of their collection. Furthermore, Bolzano adds, an internal characteristic of even a simple thing can be seen as a relation, that is, between the thing and its characteristic (the having described earlier). He then briefly defines similarity or equality as a reciprocal relation, where objects have a same part in a characteristic belonging to the collection they form. A dissimilar or unilateral relation is then a relation that is not reciprocal.

Bolzano notes that with complex objects we can distinguish between their matter – the parts from which they are constituted – and their form – the manner in which the parts are combined. He notes that similar definitions can then be applied to representations of things, so that representation of their matter means representations showing constituent characteristics of the things and representation of their form means type of combination for these parts. Bolzano notes that the distinction between matter and form can be related to the distinction of internal and external characteristics. Matter of an object, he says, can always be determined as consisting just of internal characteristics, when the parts are thought as simple representations, but they can also be seen as external characteristics, if described by representations referring to other things: for instance, “not-human” consists of “not” and “human”, but also of “not” and “the most perfect type of living beings on Earth”. Then again, Bolzano thinks, some types of combinations in form can be represented only through relations.

We have already mentioned a couple of times the notion of a collection (Inbegriff). By this, Bolzano means simply a representation composed of other representations A, B, C…, where the order of these collected representations or parts of the collection is not yet considered: it might be relevant or irrelevant, depending on the type of collection. He also notes that we can either discuss this collection collectively – the whole formed of these parts – or distributively – each part of this collection (for instance, all players are a team, but each player is not). Bolzano also points out that sometimes we leave implicit whether the collection includes parts beyond those explicitly mentioned.

We just mentioned that the order of the parts might be irrelevant to the collection. In case it is explicitly so, Bolzano speaks of sets (Menge). Now, both in collections in general and in sets, the parts of parts are not usually parts of the collection or set – a set of people does not include their hands. Then again, Bolzano notes, there is an important type of sets – he calls them sums – where parts of parts are parts: lines are of this kind.

If the order of the parts does not matter in a set, a series is a collection where it does. Bolzano defines series through a law or rule, so that for any part or member M of the series can be found another member N, where either N is determined by the law from M or conversely. The N and M are then said to follow immediately one another, the determined member being later and the determining member earlier. Bolzano also defines internal members of a series as such that have both earlier and later members, while for external or limit members, either of them cannot be found. Limit members include the first or starting member that has no earlier member and the final or end member that has no later member.

Another important concept Bolzano mentions is that of unity or unit (Einheit can be translated in both ways), which is simply something that has a certain characteristic A (in the concrete sense) or then a property that makes something a unit of type A (in the abstract sense). Plurality in the concrete sense is then, for him, a collection of concrete units of some type A, while plurality in the abstract sense is the property, by which something is a concrete plurality. Bolzano notes that we could go on defining twos and threes and so forth by determining that the plurality is to have a unit and then a unit etc., but turns then to define a concrete whole or all as a collection that has each object belonging to some representation A and nothing else; similarly allness in abstract sense is a property that makes a concrete whole into such. He also points out that when the expression “all A” is used to mean A in general, it is used distributively, but here it is used collectively.

Bolzano’s account of the representations of set and series is quite close to later logicist ideas of defining basic mathematical concepts, so it is no surprise that he next tackles magnitudes. Types of magnitudes, he says, are characterised by the property that no matter which two of them are taken, they are either equal or have the relation of one of them being greater, that is, a whole with a part equal to the other. With this definition, Bolzano notes, pluralities, wholes and units can be seen as magnitudes.

Bolzano has something to say even about the notions of finite and infinite. A plurality of finite magnitude, he defines, is any plurality of type A that appears as a member in a series, where two of As is the first member and next member is reached from the previous by adding a new A. Plurality of infinite magnitude, on the other hand, is a plurality of type A, where each finite plurality of A appears only as a part. Furthermore, Bolzano defines number as a member of a series, the first member of which is a unit of any type A and each next member is a sum of previous with a new unit. Every finite plurality, he points out, is a number, while infinite pluralities are innumerable.

From these novel considerations, Bolzano moves on to more traditional logical notions, first of which is what he calls an exceptive representation, that is, a collection from which certain objects are excluded, either by individually naming the excluded objects or through general characteristic, for instance, by discussing a collection of all A that do not have the characteristic b, although Bolzano is not certain whether to really call this latter an exceptive representation. The second traditional notion Bolzano discusses is the concept of negation or “no”, which he considers undefinable. He defines all representations having “no” as constituent to be negative, although since two negatives cancel one another, he delineates a stricter sense of negative representations, which do not have an even series of negations – other representations are then affirmative.

Bolzano divides quite traditionally negative representations into two kinds. First of these he calls purely or completely negative representations. These deny a certain representation A without requiring any other representation in its stead – not even the very indeterminate representation of something. Such purely negative representations include, Bolzano notes, at least the concept of nothing. The other kind is, then, those of partially negative representations. In these, Bolzano explains, negation is only one of its constituents, like in the representation of A that is not B.

Bolzano closes off this section with the notion of symbolic representation. Quite appropriately, this notion is defined by the form “representation that has a characteristic b”. Thus, all the various concepts described in this section are of such a kind. Furthermore, all the concepts described are what Bolzano calls real or objective symbolic representations, since there have been representations having the described characteristics. He notes that we could also delineate the notion of mere symbolic representation, which are completely imaginary in the sense of having no objects: a notion of a representation that is also a judgement would be of such kind.

Immanuel Hermann Fichte: Outline of a system of philosophy. Second division: Ontology – Limitation

The latest result of Fichte’s ontological studies has been the concept of limitation, by which he means a positive quality that appears only through negation, that is, in opposition to all other qualities that it complements. Thus, he thinks, all finite entities should limit one another and so determine their characteristics: they maintain themselves precisely through this mutual negating and by being absolutely inseparable from others. In this category, Fichte thinks, converge all the previous concepts that are summarised in it in a new and higher manner. Thus, all synthesis should have its proper truth in the limitation: everything determined is only in such a way that it is connected to infinity of others and thus asserts itself with a completely particular characteristic belonging only to it. All isolation, Fichte suggests, is simply cancelled and everything antithetical is in general resolved into synthesis, and even further, the synthesis itself is infinitely unifying: everything is absolutely linked with everything else.

The conceptual level of limitation, Fichte thinks, should correspond to both position and negation. Thus, the beginning of limitation should somehow combine in itself both the determination (the beginning of position) and nothing or negativity (the beginning of negation). In other words, Fichte concludes, we should begin with a determination tainted with the negation of something else, which means, according to him, just a relation to this something else or other. The relation to others, he suggests, as the first and most immediate expression of the concept of limitation, means that everything is generally able to be determined by others. In other words, nothing is without any relation or nothing is isolated, and since it is determined or quantitatively and qualitatively limited, it is also open for receiving influences from others, but also has influence on these others. This concept, Fichte suggests, is the truth of both distinction and change, which could be thought as holding between absolutely isolated entities, while here we expressly understand that these entities are mutually determinable.

Relation to something else, Fichte argues, is the most comprehensive concept for the finite in general. Finite entities are in their determination still completely dependent and only moments for something else, thus, being for another or being determinable is the essential meaning of finite. Indeed, Fichte emphasises, this relation to something else is not accidental to the finite, that is, finite cannot fail to have it, but the quantitative and qualitative limit of the finite determination and therefore its fundamental character consists in being in its own being also only for something else.

The relation to something else means, firstly, Fichte suggests, the negation of the exclusive isolation of finite in general: finite is only for another. This concept of “for another”, he thinks, is here regarded abstractly, ignoring all the following categories complementing it. Then the finite exists only for another, but is nothing in itself and thus becomes only what seems to be for this other. The other, Fichte argues, must thus be called the true being or the thing in itself, while the existence of the finite is possible only by assuming a consciousness representing it. This idealistic insight could mean, he suggests, that the finite entities are real only in divine spirit, so that the creation of the world would be only a divine self-representation and perhaps also a partial representation of individual spirits. Fichte thinks that this theory is partially – but only partially – true, because it understands the notion of creation through the notion of divine consciousness. A second manner to understand the idealistic insight, Fichte continues, is that the concept of finity is limited only to natural things, while the spirits should be eternal and substantial realities: here, the sense world would be just delusion. Yet, both ways to grasp the idealistic insight, and indeed, all forms of idealism, Fichte insists, suffer from the mistake that they understand the concept of relation to others in an isolated fashion, ignoring the relative independence of the finite entities. Then again, what is true in them, according to Fichte, is the idealism of finite, according to which anything finite can exist only by letting the other shine through or realise itself in this finite.

Secondly, Fichte assures us, the concept of being for another retains also the positive meaning that in this outward limitation the finite also manages to confirm its own internal determination: the finite is related to or for itself or asserts itself. This does not mean that the relation to other would be completely unrelated, but instead, that this being creates its power to exist from its conflict with others. This self-relation or being for itself is therefore the same as the simple position, Fichte notes, but only unified with a relation to others that it complements. Self-assertion of something continuously reappears from threats to its independence that make it into a living activity.

The category of being for itself, in Fichte’s opinion, is the centre for all categories of quality. Just like simple determination changed into negative and just like from negativity appeared the absolute limited relation of everything to everything, all of these categories have now been collected in their proper result or in the infinitely self-reproducing assertion. Positive is not anymore just an abstraction without relation, but determined only in infinite relation to others. Furthermore, this relation is not external or quantitative, but internal reciprocal determinability. Finally, positive is not just a result of externally arriving determinations and nothing else, but it posits these determinations as appropriated and governed by itself. In conclusion, Fichte states that precisely by facing the infinite negation from others, the determined being receives its positive character, asserting permanently its place in the system of these negations.

The categories of relation to another and of self-assertion, Fichte continues, are now immediately combined: relation to another is the source of self-assertion, and the self-assertion again leads to infinite relation of everything to everything. This combination, he suggests, moves to a mediating unity of a position that is limited by an infinity of othera or asserts itself in infinity of reciprocal relations. According to Fichte, this synthetic concept of limitation is a new category of internal infinity that is distinct from the earlier externally endless process into infinity.

Fichte distinguishes within this internal infinity three moments. Firstly, every determined or finite being is in its self-assertion also for an infinitely other. In other words, each of the determined entities maintains itself against an infinity of others, while it also itself influences this infinity. Thus, both the self-assertion and the relation to others contain an infinity of moments that could be called the external side of the internal infinity. Fichte sees here embodied the proposition that every individual part of the universe is in connection with all others, being open to their influence and influencing them in turn. He notes that later we will see that the individual things are not externally connected into this system of reciprocal influence, but they themselves are derived from this infinity.

The second moment that Fichte emphasises is that every finite being contains this infinity in itself ideally: each is the middle point of infinite radii converging in it. He points out that this notion of internal infinity was already expressed in the Leibnizian idea that a monad reflects in itself the whole universe. Furthermore, Fichte recognises this notion also in the early Schellingian philosophy, which asserted the presence of an actual infinity or reason in the most individual and smallest details of the world. Fichte also thinks that if this thought would have been dialectically developed to its proper conclusion, it would have led to the insight that this absolute reason can only be an absolute spirit or the highest personality.

The second moment unites infinity immediately with determination that arises from its relation to a system of infinite determinations related to each other. Thus, Fichte suggests, the concepts of relation to another and self-assertion are fully balanced: in asserting itself, an individual retains and asserts also its other, and conversely, the infinite system of relations simply ascertains the self-assertion of each individual. Each determinate individual points, according to Fichte, over itself to an infinitely creative, but also ordering and harmonising power.

This creative and harmonising power is, for Fichte, the third and highest moment in the concept of infinity. The finite determinations can be thought only as comprehended in the infinite that always surpasses them by having more finite entities to be related to each other. Here we find again a case of external infinity, and Fichte admits it is a necessary part of this concept, but only as regulated by the internal infinity. Indeed, he insists, this externally infinite system can only exist through a positive comprehension or relating of finite to an infinity of others, whereby the finite is both destroyed and also retained.

Fichte takes this infinity that actively creates and relates finite entities as the first proper definition of absolute. It contains, in Fichte’s opinion, the previous definitions that the absolute is quantifying and qualifying, and the unity of these previous definitions is precisely the concept of an infinite, qualitatively determining and also qualities relating power. This absolute negates the finite, but also posits it at the same time. Thus, Fichte emphasises, although finite both is necessarily opposed to others and also itself becomes something else, in addition, the finite is also affirmed through the infinite or absolute. In other words, the finite has as its basis a determined original quality going through all its facets, which is provided by the absolute in inserting this finite into the system of reciprocally related determinations. This original quality remains one and the same both in being related to others and in becoming itself something else.

Fichte considers the just developed principle of an infinite qualification by the infinite absolute as the mediation of all previous categories and thus as the true internal infinite. The absolute creates infinitely many finite original positions and orders them into a system of reciprocally complementing, but therefore itself changing relations that assert themselves as essential and as necessary members of this reciprocal system. Earlier, Fichte reminds us, these original positions were called finite, but this has now been shown to be only a negative designation. Finite is to be recognised as finite, that is, as negative, he states, only in regard to its external distinctions and changes. Yet, both distinction and change just require complementing from the positive relation and the self-assertion. From an absolute or positive viewpoint, Fichte states, finite is infinite, firstly, because infinity of positive relations converge in it, and secondly, because even in becoming something else it still always remains the same. Fichte calls this the true or positive finity, because as positive it carries in itself also the moment of infinity.

Fichte thinks that the concept of positive finity fills a gap in the category of becoming or change. It solves a contradiction that pure becoming involved both an identity remaining same and an otherness distinguished from itself. The positive, unchangeable original determination, Fichte states, is the principle of unity that remains the same throughout the changing relations to other determinations and that still changes its characteristics and so involves also the opposed principle of changeability. This unity combines the otherwise separated moments of otherness into becoming, so that what does not otherwise become can in another sense become (Fichte thinks that Hegel’s notion of becoming lacks this unity and is thus the most contradictory of all concepts).

Fichte suggests that we have found the correct and the highest mediation between the infinite and finite. Finite is not anymore the merely negative or eternally disappearing moment in infinite, which would make infinite into a mere formal or negative process of such eternally posited and eternally disappearing moments. This negative process is, according to Fichte, the high point of Hegelian philosophy that does not expressly recognise the principle of an infinite qualification in finite. Speaking against Hegel, Fichte insists that the absolute should be the creator of infinite original positions that it also orders into a system of relations. In other words, the absolute posits a finite as originally determined against others, but also again cancels its mere finity and sustains it as enduring in change.

Fichte calls this process the truthful unity of infinite and finite, which is not just a formal unity, where the opposites would be balanced only dialectically. Instead, the infinite is the real, all fulfilling presence in finite, and the unity of both has appeared from the notion of the infinity of finite itself, since negating the finite negates only its negative side. Thus, Fichte says, the finite is not just endlessly vanishing, but an image of infinite. He explicitly opposes Hegel’s negative philosophy, according to which there is nothing finite, in which does not lie a contradiction that cancels it. In opposition to this standpoint, Fichte insists that contradiction or negativity means only one-sided formality, while the finite and limitation is internally infinite, since it is positive, original determination and not tainted with the contradiction, but sustained by the divine harmony and unity.

In these final concepts, Fichte thinks, the mediation of thesis and antithesis has found a completely new and higher expression. Earlier it might have seemed, he explains, as if the synthesis resulted only from a combination of the previous members, but here the case is completely opposite: the synthesis is the most original, creative and comprehensive, through which and in which the opposites only exist. Thus, the synthesis is the absolute that creates the opposites and relates them to one another, and here particularly it creates and orders the infinity of original positions. This opens up for us a new field of investigation, Fichte suggests. Earlier we were involved only with simple concepts that did change into one another and were related, but only in an external manner. Here, on the other hand, for the first time the concept is duplicated in itself into a higher or comprehensive and a lower or comprehended member. Thus, Fichte gives an example, the finite is only in the infinite that is a power positing and governing it. He suggests calling the relation between infinite and finite the original or absolute relation, since all further relations will be only further development of it.

The first part of ontology has thus led into a second part investigating relational concepts. Fichte considers this transition important, because it moves ontology from mere preliminary concepts to the proper task of speculation. Thus, the earlier fundamental determinations of absolute were always in opposition to predicates of finite, and it meant unmistakably a conflict between both conceptual spheres, if we designated the absolute as being without quantity, but also as quantifying everything, as indifference, but also as comprehending all finite differences or as identity, but as governing all finite distinctions. Fichte notes that it was earlier a problem how these two sides of the absolute could be combined, but it had to be passed over, because it could only be dealt in the sphere of relational concepts. The earlier definitions were then only provisional and elementary, while here, on the other hand, the principle of distinction has been found in the absolute itself: the second member or the created, finite world has appeared from it, which expresses the original relation of absolute to itself that the ontology tries to establish.

Before moving to this new field of investigation, Fichte summarises the first part. The task of ontology was to solve the question what actuality means or what are its universally valid forms. We began with the Ur-categories, which showed a paradigmatic structure for all categories: a thesis is possible only in relation to antithesis and both are comprehended in a synthesis as the true, perfect form of actuality, while thesis and antithesis are only its moments, parts or members, without any truth or meaning by themselves. Thus, everything actual was revealed to be a this (Dieses), absolutely mediating these oppositions, but because it was at first just empty this, it could be determined only quantitatively. Quantity was hence the first category or the most abstract form of actuality, with no particular content, but expressly grasped as an independent concept. The further divisions of quantity – number, measure and grade – were only in relation to other quantities, which led to the synthesis of all comprehending quantitative infinity: every number, every measure and every grade existed only in a system of infinite mutually determining quantitative relations.

The whole level of quantity refuted itself, Fichte continues summarising, and quantity was revealed to be a mere form of a quality. This simply qualified determination is the finite, which again was positive only antithetically or in opposition to another and in changing its characteristics to something else. Thus, this position inevitably had a negative side both in distinctions and in changeability. Although seemingly threatened with annihilation, it still maintained itself through a true synthetical relation, where the finite is grasped as really positive or as internal infinity, which in change appeared as the presence of a stable reality. These negative concepts are thus completed by a mutually affirming relation, and from this positing of limited original positions appeared as the highest result in this circle of categories the concept of truly creative infinite or absolute, in which and through which alone the finite is.

The concept of finite proves its own dependence in all instances, Fichte states, and it finds its truth only when raised in the synthetical unity. Thetic this, limited quantity and qualitative determination have all refuted themselves in isolation, but at the same time they have also refuted the negation or antithesis of their own levels. Present in everything, Fichte concludes, is the positively filling and also infinitely relating absolute, and the former categories have all appeared as mere forms of actualisation of the absolute. Thus, when the finite is thought in isolation or when someone wants to isolate it, it remains contradictory in the true sense of the word, but this attempt to isolate refutes itself: the finite is not at all by itself, but only in absolute.

It is thus possible to distinguish two results in the first part, Fichte suggests. Firstly, concerning the formal side, at all stages we have advanced from abstract to concrete, and every individual conceptual moment has been more concretely determined than the previous one. The beginning or something was the emptiest notion, Fichte reminds us, and we have raised ourselves to the concept of absolute, which is not just the most concrete concept possible in this sphere of ontology, but in general the principle of everything concrete. Secondly, concerning the content, the performed synthesis, that is, the complete thinking of all antithetical relations has refuted all the forms of finite (thesis-antithesis) and shown them as mere moments of infinite that actualises itself in them. The original synthesis or the absolute has appeared from all these opposites as the only true and actual, but also infinite being, which according to thus far investigated forms of actuality could even be called both quantitatively and qualitatively infinite. This absolute is not just a formal, empty actuality, which would make it again just a quantity, Fichte insists, because everything merely formal has always refuted itself. Instead, the absolute has appeared as a principle of reality that, on the one hand, is beyond the confines of ontology, but on the other hand, has forms that can be fully investigated by the ontology and that are in essential parts already known, although how or as what absolute actualises itself remains completely inaccessible to ontology.

Fichte states that he has already provisionally confirmed the basic characteristic of his ontology that it considers an absolute, which in itself is not merely formal, only in regard to its forms. Indeed, he thinks to have shown that in the self-realising act of the absolute is to be found the principle of these forms. This leads us to a higher concept of absolute as infinitely self-realising and self-forming: absolute is not anymore just a lifeless infinite being, but a living, creative unity that gives itself both infinite form and actuality. This completely new concept can be designated at first and in most general manner only as essence, which means defining the absolute as the infinite essence.

Immanuel Hermann Fichte: Outline of a system of philosophy. Second division: Ontology – Position

Fichte’s set of categories consist of many pronouns. He began with something (Etwas), then noted it was this (Dieses) distinguished from others, and while at first this distinction seemed just quantitative, now something has been revealed as internally determined or such (Solches), which is opposed to others that are not similarly determined (not-such). Fichte summarises this development with the rather bad German pun that Et-was must be Was, in other words, we have to be able to say of any something what it is. In other words, the formerly quantitative distinction has been shown to be qualitative. Just like quantity was the first of the proper categories, Fichte suggests, quality is its essential complement and therefore necessarily the second in the series of categories. This means, he adds, that individual stages of quality complement the individual determinations of quantity. Unlike quantity, Fichte explains, quality is a source of a true and not merely formal distinction between something and something else. As signifying what something is, he adds, quality is to be still separated from the notion of reality or actuality: even if we know how something would be determined, we still do not know whether such something exists.

Just like at the beginning of the stage of quantity, Fichte considers how the new notion could be used in defining the absolute. From the standpoint of quality, he suggests, this means that the absolute or God comprehends in itself all possible determinations of content or realities, as they were traditionally called, and could thus be called the most real being that also grants to each existent its determined quality. In the case of quantities, absolute grants all beings their quantitative measures, but has no particular quantity itself. Similarly, Fichte thinks, absolute can be ascribed no individual quality, just because it comprehends all qualities in itself. Indeed, the absolute should be purely indifferent and without any properties, and thus the concept of most real being turns into an empty negation. This does not reveal just how abstract and unsatisfying for determining the absolute these first categories are, Fichte says, but also more importantly it shows that all determinations, even in God, are inseparable from negation: absolute or God cannot be just the most universal being, but it must also be a completely determined individual. If we only look at the first viewpoint of universality, he notes, nothing is said about God when they are called the most real being, but this concept can have a positive meaning, when understood as a creative source of qualitative oppositions.

The first stage of quality, Fichte begins, is position: a simple, in itself determined quality. In order to grasp this first stage in its abstraction, he says, all further relations to others should be ignored, and these relations should then be developed from this simple beginning. Fichte reminds us that categories of quality should complement those of quantity, thus, position should correspond to the category of magnitude as both are the starting points of their own series. Hence, he suggests, position could also be designated as qualitative magnitude, which really means nothing else than that the further relations of this qualitative position must be set aside.

Position is thus at first a mere simple quality or determination (Bestimmtheit) without any further relation, or if it is related to something else, Fichte adds, this is seen as something external and contingent. This determination is therefore an affirmation (thesis) of a completely simple and unrelated quality. Fichte calls it one of the poorest categories, because it is only a transitional moment for future concepts. All distinctions and especially all quantitative limitations or magnitudes have been cancelled, as this pure, abstract quality should be still just the direct negation of the previous level: it is the qualitative one or atom of Herbartian philosophy. Furthermore, Fichte continues, the concept of simple determination corresponds also formally with the concept of identity: what is completely determined is similar only to itself. This category could then be stated in the form of an isolated proposition: A = A or the fundamental proposition of identity. Fichte notes that just like the category of simple determination, the proposition of identity is only one-sided and immediately connected to the opposing proposition of contradiction.

A determination can remain simple, Fichte insists, only because it is immediately distinguished from everything else. In other words, just like quantitative one was only in relation to other ones, so a qualitatively determined one is such, because it is externally related to otherwise determined ones: quality of one is its own characteristic (Beschaffenheit). This characteristic, Fichte explains, means otherwise the same as determination, but with the added consciousness that in the determination lies a moment of being distinguished from others. The simple determination is thus at least externally driven outside itself, at least to being beside others with different characteristics.

The simple determination or characteristic becomes qualitative restriction, Fichte insists: we have a series of characteristics or qualities, each of which acts as a boundary to others. Furthermore, he adds, only this qualitative restriction can make anything determined or characterised, thus, the determinations are qualitatively restricted or finite. The concept of finiteness brings forth even more the negative side of determinations. Indeed, finite is only negatively related to anything else that is also finite or they exclude one another in complete isolation, Fichte suggests. Therefore, from the standpoint of the other finite ones the first finite one simply would not be – or at least it would be something else.

Finite asserts itself or sets up boundaries against others, but these boundaries are immediately cancelled, because they are not recognised by the other finite beings. The concept of finite implies thus also its own self-negation, Fichte suggests, and the finite contains an implicit connection to not-finite. Finite and non-finite or infinite are at first only opposed moments that exclude one another: finite is such that cannot be raised to infinity, while the infinite cancels the finite. In this sense, Fichte thinks, finite is the internal boundary of quality, which appears to be governed by something else that turns the finite into its own opposite or lets alteration devour the finite from within: determinations appear, but they also vanish. Finite is thus something contradictory, since while it seems to assert itself, it also negates itself.

The concept of finite with its relation to infinite points to a further progression that should solve the fundamental contradiction involved with finite, Fichte continues. Finite disappears, only to lead into an endless series of further finite beings. This notion of endless seems the only infinite we have here, although Fichte identifies it with what Hegel called mere negative infinity: the finite ones vanish in this endless and infinite abyss, and thus infinite appears as a blind fate that allows everything to be both generated and destroyed. Instead of this negative infinity, Fichte insists, the proper truth of the previous developments is the concept of negation. What is finite goes beyond itself just because it is seemingly isolated and thus negated by the others. The finite ones are thus not just externally related to one another, but they are in a state of reciprocal negation, which is the following stage of quality.