Bernard Bolzano: Study of science – Kinds of characteristics

The final section of Bolzano’s study of representations concerns relations representations have to other things, although Bolzano notes many of them have to be left later, when these other things are treated specifically. Still, he begins by defining a correct representation of an object simply as a representation that truly is a representation of that object and similarly an incorrect representation of an object as one that is not. Bolzano points out that correctness and incorrectness are only external characteristics or relations of representation to a certain object, so that we cannot speak of correct or incorrect representations in isolation, although he does make the exception that imaginary representations can be always called incorrect, because they are not representations of any object.

Bolzano continues by noting that a correct representation of an object can be complete in the sense that any characteristics of the object can be derived from the proposition stating that the object is represented by the representation and truths recounting the characteristics of the representation – other representations are then incomplete. He explains further that a complete representation does not need to contain all the characteristics of the object as its constituents – indeed, he adds, there would be an infinity of such characteristics. Bolzano points out that a representation of an individual object is always a complete representation: otherwise, some characteristics of the object could not be derived from this representation, so that we could have another object without these characteristics fitting the representation, which would then not be a representation of just this individual object. This means, he argues, that all intuitions are complete representations.

Furthermore, Bolzano notes, if there are no two actually existing objects with the exact same characteristics, all complete representations must be singular representations, because a representation with multiple objects would have to leave some of their individual characteristics undetermined. He also adds that just like with the notion of correctness, we cannot say from a representation by itself whether it is complete, but this requires comparison with the object: the same representation can be complete for one and incomplete for another object. Bolzano will go on to note the same thing for nearly all notions studied in this chapter, and indeed, it is rather obvious, since he is dealing with notions inherently dependent on relations of representations to other things.

Bolzano moves on to discuss especially notions related to characteristics. Characteristics as such are, of course, not representations, but features of objects, thus, he underlines in many places that we are here actually speaking of representations of characteristics: despite the importance of difference for explaining the inclusion of these notions in a discussion of representations, we can usually just ignore it and just speak of characteristics directly.

Bolzano begins simply by defining a correct characteristic as such that belongs to an object corresponding to a certain representation (other characteristics are, of course, incorrect). A more interesting notion is that of an essential characteristic, which he defines as characteristic that is correct for an object of a pure concept (other characteristics are then inessential). Evidently, the less objects there are in the concept chosen, the more the object has essential characteristics. Thus, Bolzano argues, for a singular and therefore complete concept, all the characteristics of the object are essential. He also suggests that if a characteristic can be expressed by a pure concept, it will be essential for some pure concept (for instance, the concept of something that has this characteristic).

Bolzano defines as absolutely proper or exclusive characteristic as one that belongs to this object and no other and contextually proper or exclusive characteristic as one that belongs to this object and no other in some kind, to which the object belongs. Characteristics that do not fit even the definition of contextually exclusive characteristic are then common or shared characteristics. Bolzano notes that for an exclusive characteristic, the representation “something that has this characteristic” is a complete representation of the object, since it represents only this object.

Bolzano goes on to point out that absolutely or contextually exclusive characteristics can be used for recognising the object that has them and could then be called its distinguishing feature (Kennzeichen). Such a distinguishing sign can then consist of several characteristics, which he calls marks, defining them as characteristics that at leas in connection with others are suitable for recognising an object. If a collection of such marks are enough for recognising the object, Bolzano states, they should be called sufficient marks, while otherwise they are object: if a single mark is sufficient by itself, it is then also a distinguishing sign.

Bolzano also divides marks into immediate and mediate marks, where a mediate mark is essentially a mark of a mark: for instance, speaking is an immediate mark of reason and thus a mediate mark of humanity, he explains. Furthermore, Bolzano defines affirmative mark as a characteristic that does not belong to all things of a kind, but to some of them, and negative mark or condition as a characteristic that belongs to all things of a kind, but not exclusively to them. The meaning of these definitions lies in that a presence of positive mark can always reveal that an object belongs to the kind, but its absence does not guarantee that an object does not belong to it, while conversely the absence of negative mark shows that an object does not belong to a kind, while its presence does not guarantee that an object belongs to the kind. In this sense, distinguishing signs of some kind can then be called both affirmative and negative.

Bolzano defines original or constitutive characteristic as such that its representation is already a constituent in the representation describing the object – other characteristics of the object are then called derived or consecutive. He notes that if the representation in question is a pure concept, an original characteristic is essential to that concept. Then again, Bolzano assures the reader, an original characteristic need not be internal, because some representation of an object can concern only its relations: Bolzan’s example is the representation of the middlemost rose on his window.

Bolzano considers the question whether an original characteristic can be used as a distinguishing sign of the object. He notes that if we are dealing with an original characteristic connected to a general representation, the answer is negative, since then the characteristic cannot be exclusive to the object in question. Then again, if we are dealing with a singular representation, Bolzano ponders, the question hinges on whether any of the original characteristics could be used to derive the others. He ends the discussion of original characteristics by pointing out that although representation of each characteristic of an object belongs to constituents composing the representation of the object, we cannot say that each constituent of its representation is original or even expresses characteristic of the object (a simple example is a representation of not-red that has red as its constituent, which still is not characteristic of the object).

Bolzano ends the discussion of representations with the notion of a difference between two objects by defining it as a characteristic that belongs to one, but not to the other object. Like all characteristics, he notes, differences can be divided into internal and external, essential and inessential, shared and proper, and original and derived. Furthermore, Bolzano differentiates a numeric difference between individual things from a specific or generic difference between kinds and quantitative differences involving difference of quantities from all other, which he calls qualitative differences.

Bolzano also considers the question whether all two objects (that is, not just two representations of the same object) differ by some characteristic. He notes the obvious answer that the characteristic of being this object and not the other does the trick, but then specifies the question to ask for internal differences and not mere relations. Bolzano himself believes, like Leibniz, that this is true of actually existing objects. He argues for this by asking the reader to picture two completely identical objects: in order to be identical, they would have to be surrounded by exactly identical things and experience the exact same events – otherwise, these things and events could change their features from one another – which all is extremely improbable. In any case, Bolzano concludes, the Leibnizian principle seems to be true about at least most things.

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

Fichte has arrived at the concept of negation that he describes as a simple denial, difference or opposition and thus in general a more abstract expression for the concept of qualitative relation. In other words, because something is precisely a specific this, it is not something else, which similarly is not the first something: by being distinctly determined they at the same time mutually deny one another and are thus generally related, although at first only in a negative manner. The concept of relation has reappeared, Fichte notes, although it had seemed to disappear in the simple determination of quality. In fact, he emphasises, nothing qualitatively determined and characterised can subsist or be thought in such a simplicity or it must be distinguished from something else. Finite determinations move away from their isolation and take part in negation. Furthermore, Fichte continues, just like nothing positive is possible without being tainted with negation, it will be also shown that denial has positive as its necessary counterpoint and both concepts move then to the common third concept of relation in general.

At first, Fichte begins, this negation or “nothing” (Nichts) is to be grasped only as a negation of some determination or as a determined nothing that is related to the denied determined quality. Such a denial is found in another positive: every positive is at the same time the denial of another and every denial is itself something positive. The negativity or determined nothing is then, Fichte thinks, one of the most comprehensive categories, since it goes through all qualitative determinations as a hidden moment that taints everything.

Secondly, Fichte continues, the nothing can be understood as a negation of all qualities or as purely undetermined and not-qualitative. This is the most abstract meaning of nothing, which, according to Fichte, characterises all categories before quality, which could be collectively designated as not yet qualitative or nothing. This means, he explains, that these previous categories are contradictory in that they are supposed to be sustained by themselves and still are nothing in themselves, but only as related to something qualitatively determined. Thus, they are not unrelated to quality, but demand and presuppose a qualitative principle that could take them beyond the contradiction of their emptiness. The nothingness in general is, hence, only the most general expression for the contradiction of the lacking dialectical complement, Fichte suggests, and every abstraction sinks constantly to nothing. Indeed, he emphasises, the whole field of categories consists only of forms for reality, but is nothing in itself. Real could then be partly defined as the negation of this mere nothingness of forms, he suggests, but partly it is a positive filling or a creative principle behind these formalities. Thus, Fichte concludes, only in the original reality or in absolute can be found both the principle of this formal nothingness and also its eternal cancellation of nothing.

Thirdly, Fichte states, the nothingness or negativity implies a relation to something else. In other words, what is finite is nothing or negative, because it is only in a negative relation connecting it to something else: finite is finite, because it is otherwise than anything outside it or because it can be distinguished from everything else. Determined nothing, Fichte suggests, can therefore be expressed as distinction or difference (Unterschied), which means qualitative, reciprocal negation of something else or qualitative non-identity. Everything finite is then partly different from others, but partly is itself other to these others. Because this reciprocal negating continues infinitely, Fichte argues, distinction is an infinitely continuing separation and relation of finite entities or infinite negative relativity, and this distinction is the truth of negation or nothing. Thus, Fichte says, in the very concept of finite lies an infinite relation to everything else.

At first, Fichte says, the distinction or difference between the finite entities is just an abstract, simple non-identity (Verschiedenheit): a finite entity just formally differs from everything else, without any regard to its particular content. As Fichte notes, this most abstract or formal distinction is valid everywhere, but it is still a superficial category, just like the categories of abstract determination and negativity. Indeed, the abstract difference unites both abstract determination and abstract negativity as a determination that negates everything else by being distinguished from them. Thus, the relation of difference does hold between all finite entities and therefore continues in infinity. Still, Fichte points out, such an abstract difference remains only at the surface of qualitative distinction, since it does not make explicit how nor how much the finite entities differ.

Abstract difference requires conceptual development, Fichte states, since the different moments related to one another are not just formally different from each other. Similarly, he notes, sameness or similarity expresses also just formally the negation of a distinction between related moments. According to Fichte, difference and sameness are only concepts that can be permuted with one another: same qualities a and b can in one specific regard be similar or same and still also dissimilar or different. The concepts of sameness and difference are just external and completely relative determinations, and the most inessential fact that can be asserted of two things is that they are similar or dissimilar with one another. Such a statement leaves completely undetermined their essential characteristic, and Fichte suggests that superficial comparing of individual things springs from one-sided application of the formal sameness and difference.

Mere difference therefore becomes opposition, Fichte insists. In other words, every determined entity is not just formally distinguished from something else, but this other has also a different determination: what a is, it is only in negative relation to b and vice versa, or both are opposed to one another. True distinction consists thus only in reciprocal negative relation to one another. The opposition, Fichte argues, is therefore never simple, but has in itself the double aspect that each side of the opposition can be only negatively toward what the other is positively and both are thinkable only in relation to one another and not as isolated moments or indifferent to one another.

The third moment of distinction after abstract difference and opposition, Fichte states, is specific difference. This means that something qualitative receives its own determination only in internal opposition to other determinations. Hence, Fichte thinks, qualitative determination is not just dissimilar to other determinations, but it is posited as this qualitative determination only through its opposition to others. Reciprocal negation of qualitative determinations therefore is not just external exclusion, but also their reciprocal positing in their mutual opposition, that is, each determination receives its own character only from its relation to other determinations. Abstract opposition has thus become a specific, self-determining distinction, which should be the truth of all previous categories of negation. Determinations are therefore to be thought as specific differences against others, that is, in both negative and positive relation to them within a system of related distinctions, all of which assert their character at this determined place in relation to others.

All determination is thus inseparable from the concept of specific difference, which completely removes the notion that there could be any isolated finite determination, Fichte insists. Instead, finite determinations need a system of qualities mutually bounding and thus determining each other. Fichte adds that the specific difference is not just the truth of negative categories, but has also a positive meaning, since it produces the positive side of negation, just like earlier positive determination transformed into a negative characteristic. Here both the opposite sides are at first fully united, he thinks, and the negative-positive character of each determination in a system of qualities is emphasised. Fichte makes the comparison that just like in the sphere of quantity the abstract relation of magnitudes became a determined and therefore specific magnitude, the concept of quality has finally developed itself into a specific difference within a system of qualities.

The negative relation between entities developed into a specific difference, Fichte continues, and now it will turn back to each of these finite entities. In other words, the character of otherness is common to all of the finite entities, and they resemble each other by being completely governed by it and only through otherness their similarity should be reproduced. This means, Fichte insists, that a finite entity is not other just outwardly or in relation to something else, but also toward itself: it is now this, but can also become something else.

We have thus arrived at a new concept of change or becoming. Fichte points out that what he refers to as becoming (Werden) is not the unity of being and nothing, like in Hegelian philosophy, but refers to the more developed thought of a transition from something to something else or other. In this becoming, something changes, but also remains the same, thus, Fichte suggests, what becomes should also be thought as not becoming, but being unchangeably. Becoming or changing therefore immediately combines the opposed and formally contradicting moments of sameness and distinction. Without similarity, the becoming would shatter into absolutely separated and external opposites and would not anymore be becoming. Furthermore, without true change between different moments, we would have just a rigid lack of movement that would not even be a unity, but just the former abstraction of empty something.

The becoming, defined as the formal identity of opposed moments of unity and non-unity or similarity and non-similarity, Fichte states, seems to be a contradictory concept. Even more, he adds, it is the highest expression of contradiction in the categories of negation. The contradiction in general, according to Fichte, is a form of negation and should thus be handled here. Earlier we found apparently contradictory insights that the positive carries in itself also the opposite or negation and that the determination is in another context the nothing. Now, the contradiction seems greatest in the concept of becoming, which as the formal identity of similarity and non-similarity is itself the absolute contradiction. Thus, Fichte argues, contradiction must be meaningful, even if not in the concrete actuality, still at least in the ontological consideration of pure concepts.

The fundamental proposition of contradiction, Fichte reminds the reader, asserts the absolute non-actuality of contradictions: contradictory cannot exist. He asserts that contradictory should not be defined as the unthinkable, since in order that we can assert it as not thinkable, it must be actually thought. Instead, Fichte makes the correction, contradictory as self-cancelling should not be thought as actual, because the self-cancellation is precisely the denial of actuality. Showing contradiction in our thoughts can mean two things, Fichte adds. Firstly, the contradictory might lack a moment that is necessary for its actuality and then its concept is not perfect and therefore also not actual: this he calls formal contradiction. Secondly. it could contain a moment that does not allow the actuality of the asserted concept, that is, positively cancels it: this he calls material contradiction.

If we stop at the general result that the contradiction in the formal or material sense designates in general a non-being, Fichte suggests, the ontology has to exclusively do with contradictions of the formal kind, since such a formal contradiction points to the lack of moments that are necessary for existence of something. The nearest solution of this ontological contradiction is then adding what is lacking and continuing to search for these necessary complements, until the contradiction is resolved and the concept is complete and able to be actual. Fichte suggests that this resolving of contradiction, which he has earlier called the negative dialectics, goes through the whole ontology, since every subordinate category can be brought to contradiction, because they require being complemented through the following concept. Indeed, he adds, even more generally the whole world of categories falls prey to contradiction, because it cannot be actual in itself, but only in the reality complementing it. This means, Fichte thinks, that contradictions have only ontological and not real validity, which gives ontology its characteristic position that it has to transition into a speculative discipline that will give ontology its truth. Ontology itself does not yet fully resolve contradictions insofar as its categories and concepts as a whole are tainted with self-negation, which makes it necessary to complement them through actuality.

Returning to the notion of pure becoming, Fichte notes that it is one of those contradictory concepts and even the most contradictory of all that we have seen thus far, since the opposition of position and negation condenses here to its sharpest expression. Its contradiction means just that pure becoming must be denied any actuality, that is, we still require other ontological and real moments, in order to be able to think what is becoming as actual. It is the task of ontology to find the ontological conditions for this, Fichte explains, and it is the task of the gradual process through the following categories to perfect this concept ontologically. At the same time, he adds, ontology also demonstrates negatively which real moments the becoming still lacks and what therefore still remains for real philosophy to do, in order that we can think this concept as actual.

Changeability means continuing self-negation or transition from one moment to another, thus, Fichte argues, it splinters into opposed moments of generation (Entstehen) and destruction (Vergehen) or beginning and end. He immediately adds that the isolated opposition of these two concepts is one-sided and untrue: beginning is already end and generation is also destruction. In other words, we can distinguish beginning and end only by arbitrarily separating one moment in the flow of unbounded becoming, where this isolated moment can be regarded as the end of the previous moments, just as well as the beginning for the following. Generation or beginning is a completely relative concept, Fichte suggests, or there is no absolute beginning in the continuity of becoming that always remains the same. Similarly destruction or end breaks the series of becoming, but this break just transitions to something new and the supposed end is actually a beginning.

The separation of the beginning by itself and the end by itself is untrue and one-sided, Fichte insists: same moment of change is both a beginning to what appears from it and an end to what lies behind it. He notes that it has been one of the easiest and one of the earliest known ontological propositions that generation and destruction, abstractly understood, belong only to what seems. In other words, ontologically regarded nothing is generated and nothing is destroyed, but something continually becomes something else. Then again, Fichte adds, each determined entity is just a finite moment of this infinite becoming and these finite moments are both generated and destroyed. Thus, he concludes, we must join the two, each other complementing propositions – nothing is truly generated and nothing is truly destroyed – with the third proposition that everything determined is both generated and destroyed.

The changeability flows out into an endless series of individual moments of varying determinations. Fichte notes that this endless series corresponds with what Hegel called the bad infinity, although Fichte suggests calling it the external infinity. What is properly true and remains the same in this changeability, he adds, is the omnipresent, infinite relation of all these individual moments to one another. Every finite individual from the series of becoming is driven over their isolation to a positive relation with everything else. Such an individual is not just negatively related to the others, Fichte explains, as happened in the earlier relation of infinite otherness. Instead, the becoming of a moment from and to other moments makes their interrelation more positive, and Fichte calls this positive mutual bounding of the finite entities limitation.