Distinction Ontology seeks to bring the central conceptual movements of the Hegelian tradition closer to a contemporary operational understanding. It offers a view of knowledge as a relative and developing form that requires continual recognition and revision.
The Limit of Thought#
We begin by trying to reach the limit of thought, where ready-made objects, categories, and logical constructions can no longer serve as a basis.
Thinking usually concerns what is already determinate: things, properties, relations. But if we want to trace how determinacy itself arises, these forms have yet to be arrived at. So let us try, step by step, to abstract from the content we are accustomed to taking as our starting point.
It is difficult to find a foothold here. Even “nothing” already has a name and differs from something, while “emptiness” presupposes something determinate that could be empty. The attempt to free ourselves of all content itself reveals the activity through which we continue to think: we distinguish.
We can approach this moment through experience.
Exercise#
Try to imagine an abstraction at the limit of thought, the emptiest thing it is possible to think. Finding itself “alone” with this abstraction, thinking first makes a distinction, giving rise to two sides. Let us call them “one” and “the other”. Or, alternatively, “being” and “nothing”, 1 and 0, or any other names. For now, names merely help us keep hold of what is happening.
Now try to hold this situation in focus for a while, setting aside interpretations. How exactly does one differ from the other? Any substantive answer adds a determination from which we were trying to abstract. If we do not add one, the sides exchange places and become indistinguishable, although the fact of the initial distinction does not disappear.
We usually pass over this moment as insignificant. Yet the situation has already changed: the initial distinction remains, but its sides cannot be distinguished by their content. What is now distinguishable is the fact of distinction itself and the indistinguishability of its sides. This relation preserves what came before: indistinguishability arises between what has already been distinguished. A new, still almost empty determination thus arises. In philosophy, the closest name for this movement is becoming.
Before looking for an explanation, we need to notice the transition itself. We began with distinction and found something we could not yet point to in its initial sides.
The Brouwerian Moment#
Brouwer offers another, similar experience of the “beginnings” of thought. Notice any act of thought, then perform the next while retaining the first in memory. The first has already passed and given way to the second, but has not disappeared: it persists through retention. If we abstract from the content of both acts, the form “one, then another” remains: two distinguished moments and the transition between them. Brouwer called the empty form that arises here two-ity and saw in it the basic intuition of mathematics, born of the experience of time.
In both experiences, what has been distinguished is retained in a movement that cannot be reduced to either side of the distinction. In the first experience, temporal succession did not serve as the basis for distinction. In the second, the same movement is easier to notice through a succession of acts of thought.
We thus discover something like the limit of the abstraction available to us. To reach it is to notice what we can no longer abstract from while continuing to think.
Revolt Against Limits#
The world may be wider than what a human being can distinguish. But everything we can understand about it becomes accessible through thinking. Even the supposition of something beyond thought already arises within it. Any knowledge available to us, whatever its nature, therefore presupposes some form of thinking.
Drawing on the initial experience of distinction, we begin to name the structures we have distinguished, thereby introducing categories and determining the order in which they develop from one another. This is how a basic tree of categories takes shape. When perceived as externally given to thought rather than immanent to it, this order is easily interpreted as an imposed limitation and provokes revolt: we are accustomed to considering thought boundless without reflecting on whether the quantifier of boundlessness applies. Revolt against such a “limitation” has, in various forms, helped define intellectual life over the last two centuries.
However, revolt itself—the rejection of order—does not yet amount to a constructive move beyond it. We can give categories new names and rediscover the same relations between them. What seems to take us beyond this order then turns out to be elaborate renaming. At that point, the revolt subsides.
We readily accept gravity as a condition of action, but experience the conditions of thought as an infringement on freedom. Yet the freedom to fly comes from technologies that allow us to overcome gravity while working with it as a condition of flight rather than denying it. Likewise, technologies of thinking allow us to overcome the limitations of established ways of thinking by developing the very capacity to distinguish. Attachment to the claim that thought is boundless in any form, however undeveloped, instead keeps us within the limits of those ways. Freedom is replaced here by self-will.
In investigating the limits of thought, we thereby investigate the world as well, since it is given to our understanding only in the forms that thinking permits.
Bare Distinction#
The initial experience brings to the foreground what we might call pure or, rather, “bare” distinction. Its sides have not yet acquired any stable names or any content. Even “one” and “the other” are already later designations for what is initially given only as the fact of having been distinguished. They result from projecting developed thinking onto the extremely impoverished situation of initial distinctions.
Distinction is called bare precisely because there is nothing here besides it. It does not arise in emptiness or out of nothing: both emptiness and nothing would already be determinations requiring their own distinctions. There is not yet a background against which the distinction could be named.
“Bare distinction” should therefore not be understood as a ready-made object without properties. The object itself, its properties, and the domain to which it belongs would already presuppose further distinctions. Even the statement “there are two elements” introduces developed determinations of existence, number, and element into the beginning.
What Is Initially Given#
But bare distinction cannot be a motionless beginning either. In taking place, it is already movement. Choice is given in the very enactment of distinction, without yet presupposing a predefined list of options. In retaining the distinguished moments of a single movement, extension begins to take shape. Distinction, movement, choice, and extension are present together, though developed to different degrees. They have not yet separated into ready-made categories.
Different ontologies may begin with distinction, movement, choice, or extension, and disputes between them often become disputes over which of these beginnings is primary. We consider them as moments of a single initial givenness in which they cannot yet be separated. Distinguishing them belongs to the further development of thought.
Distinction serves as one possible point of entry. Movement, extension, or choice can also be taken as the beginning. In thought at its most abstract, each of these moments is given together with the others, and unfolding any one of them reveals their inseparability.
The Concept in Development#
A familiar concept is perceived as a relatively fixed definition through which we observe a changing reality. We consider a determination as it develops: it enters new relations, reveals its limits, and acquires content that could not previously be singled out.
Development allows moments initially given together to become separately distinguishable, acquire content, and change their relations to one another. A later form retains what came before in a changed relation. What had not yet been separated becomes determinate and acquires names within a more developed form of thinking.
The fact that these moments are given together does not mean that all their future content is already complete and hidden in the beginning. Further distinction itself generates new determinations and changes the way they develop. The unfolding of a concept therefore cannot be reduced to extracting what was put into it in advance.
A concept thus carries the history of its own becoming. To understand it is to trace what it has retained, which distinction changed it, and which further distinctions it made possible. A definition taken at a single point fixes only one form of this movement.
The way development proceeds itself develops. A new determination changes the situation relative to which further distinction takes place. The conditions and possibilities of the next steps therefore change as well.
Generativity#
In the initial exercise, distinction formed its sides, and retaining them led to a new determination: the indistinguishability of what had been distinguished. It cannot be reduced to either side or to the initial distinction between them. What had been distinguished entered a new relation that had not previously been present.
This is the generativity of distinction: its movement gives rise to a determination irreducible to what has already been distinguished. We did not select it from a list of results drawn up in advance. It arose in the movement itself, and further distinction is now possible in relation to it.
We trace the same principle in the development of the concept. What arises preserves what came before, but changes its organization and opens up content that could not previously be distinguished. Radical novelty thus enters the continuing movement.
Generativity does not presuppose a predefined direction or goal. To specify a goal, we would already have to retain some expected situation and relate the present one to it. That would be a more developed form of distinction. For now, it is enough that the arising of the new changes the possibilities of continuation.
It is also worth noting that “generativity” arises in relation to a state of affairs that we regard as non-generative. As a concept, generativity serves rather to emphasize the fundamental nature of the movement of distinction.
The Distinguisher#
The question “who distinguishes?” usually evokes the image of an observer facing the world. Yet such a description already separates the observer, the world, and the operation performed between them. This separation has not yet been made in the initial experience.
Here, distinction and distinguisher remain undistinguished. The very question of whether they are one or not one would presuppose a distinction between them and developed determinations of one and many. Adding a separate agent to perform the distinction would mean introducing the result of further development in advance.
The distinguisher is the whole situation that has taken shape, since we find no external position from which it could act. It can make those distinctions that its present form permits.
The “I” effect is particularly easy to mistake for the initial distinguisher. Yet it presupposes an already developed reflexive relation between distinctions, in which distinction itself becomes the object of distinction. Mythologizing begins when the “I” arising in this relation is posited as an independent source preceding all distinction.
Each distinction changes the situation and, with it, the possibilities of further distinction. Let us trace how a stable order arises in this movement and how it becomes a condition for new distinctions.
Elemental Regime and Structure#
A new distinction changes the situation, but its difference from the preceding distinction may not become present relative to the situation under consideration. We call such a movement of distinctions repetition. This does not yet assert their identity: the difference between them is simply not present.
The movement thus reaches distinction at rest. Distinguishing continues, but no new difference becomes present. We will call this an elemental regime.
But distinction at rest itself becomes a determination relative to which further distinction is possible. What is now distinguished is the overall order of repetitions. The distinguished order becomes a condition for continuation: new distinctions are made relative to it, and the earlier repetitions enter the relations it establishes. A structure thus arises over an elemental regime.
The previous movement persists within the new organization. The movements of water continue in a wave, although the form of the wave cannot be reduced to a list of the movements of individual particles. Similarly, the elemental regime enters the structure and continues to operate within the relations established by the new organization.
Elemental regimes and structures are relative states of a developing movement. A structure that has become sufficiently stable can itself serve as an elemental regime for further distinction. Its stability becomes an active condition of new movement.
Stability is also relative. When one structure changes much less than another, it can serve as a stable background or object for the other. This determination arises in the relation between their changes.
If further distinction draws on what has already taken place, in what form does what has taken place enter the new situation?
The World as a Trace of Distinction#
We call distinction as it takes place an act. We call a distinction in which the act itself becomes distinguished a trace. A trace is a distinction in the mode of access to an act.
In the perceptible world, we deal with the results of distinctions. An act that has taken place is accessible through the resulting distinction, that is, in the mode of a trace. In this sense, the world is given as an organization of traces of distinctions.
Turning to what has already taken place is itself a new act of distinction. Its result again enters further movement as a trace.
Interchangeability of Access and Information#
A distinction can become accessible in different forms. A name can be replaced, a record recoded, a mode of recognition restructured. We call such forms interchangeable if replacing them preserves the possibility of distinguishing again what is being accessed and reproducing the relations connected with it.
Naming shows how this possibility takes shape. In a reflexive relation, some results of distinction are recognized through others. We call a stable form of such recognition a name. A name folds a richer organization of distinctions into a form that can be retained and recognized again. This allows repeated access to what has been distinguished without reproducing the entire history of how it arose each time.
A name helps retain access to the result of distinction, but does not belong to that result. Replacing it preserves access if the new form allows the same distinction to be recognized.
Folding involves a loss of distinctions. To access what has been folded, we have to make distinctions anew in the present situation. Unfolding therefore includes a new distinction, and its result depends on what access is now possible.
Considered in informational terms, a trace is a distinguishable result of choice that admits different forms of representation. A correspondence with the mathematical theory of communication arises here. The result of a choice from a given set of possibilities can be represented by different codes. When encoding and decoding are coordinated, the signal changes while the distinguishability of outcomes is preserved. This provides a specific formal model of the interchangeability of traces. But in this model the set of possibilities is already given. The generative movement of distinction can also change this set itself.
The possibility of replacement already presupposes a structure for which access is preserved. We can now broaden the inquiry and change the interpreting structure itself.
The Relativity of Interpretation#
An interpreter is itself a structure of distinctions through which what is other is distinguished. So far, we have changed forms of access relative to a structure of this kind. Replacing the interpreter itself changes the relation in which a trace becomes determinate.
The same inscription can have different meanings for different interpreters. The inscription “10” means ten in the decimal system and two in the binary system. To preserve ten when moving to binary, the inscription is changed to “1010”. The distinction is preserved through a coordinated change in the inscription and the way it is read.
Interchangeability thus concerns the entire relation of access. The trace, the interpreting structure, and the way they are related can all change. Certain connections may be preserved through these transformations. Establishing such a correspondence is itself a distinction.
In formal logic, the dependence of meaning on interpretation is specified explicitly: nonlogical symbols receive meanings within a particular structure. In our inquiry, this is a special case of a reflexive relation between structures of distinctions.
A trace’s determinacy depends absolutely, in this sense, on the interpreting structure. Any determination of a trace, including the claim that its content is independent, itself arises within some relation of distinctions. The interpreting structure is part of the present situation, and changes in it contribute to changes in the distinguisher as a whole.
The adequacy of an interpretation is shown by which connections can be reproduced and carried forward through new distinctions. Preserving these connections allows us to move from changing forms of access to an organization retained through those changes.
Knowledge as Unexpressed Structure#
Different paths can lead to descriptions that can be transformed into one another while preserving the structure of their connections. In this sense, the descriptions are isomorphic. Such convergence made it possible to hypothesize the existence of invariants shared by different forms of description and to make them an object of scientific inquiry. We will call their retention and organization knowledge: a structure over an elemental regime of information.
Knowledge is enacted in how what has been distinguished is recognized, related to something else, and becomes a condition for further distinction. Traces are replaced and modes of access change, yet a certain organization of these relations can persist and be reproduced in new forms.
A written rule is given as a trace. In applying it, we make new distinctions: we determine which situation it concerns and what follows from it in that situation. These acts reproduce the connections expressed by the rule.
The organization of these distinctions can also be described. But such a description again becomes a trace. We call knowledge an unexpressed structure in the sense that it is enacted in the relations between expressions and in their transformations. Each description of these relations itself enters their movement and acquires meaning and application through new distinctions. We therefore retain knowledge by reproducing its connections in transitions between expressions.
A formalism sets explicit rules for connecting and transforming traces. It allows connections to be reproduced and new expressions of knowledge to be obtained. But its rules, states, and results are themselves given in the mode of a trace. If a new distinction cannot be expressed within this organization, the rules themselves become the focus of the work. Extending or changing them presupposes distinguishing what should be preserved and how further work should be reorganized.
New distinctions also change the relations of access themselves. Preserving connections in a changed situation may require revising the organization of knowledge itself.
Continual Revision#
A previous mode of access may cease to preserve essential distinctions. A discrepancy arises between what is happening and how we are able to express it and carry it forward. This discrepancy itself becomes a trace: we notice a gap, although we do not yet know which distinction will allow us to overcome it.
If we immediately reduce it to a familiar name or dismiss it as an error, we may lose precisely what calls for knowledge to change. We must therefore first retain the discrepancy. The previous expression is no longer sufficient, and a new one has not yet been found. We can call this a state of non-closure.
In this state of non-closure, the expression of knowledge itself comes to rest: familiar connections continue to be reproduced, but the new distinction is still expressed only as a discrepancy and does not allow the movement to continue in the previous way. The retained trace of discrepancy makes this rest itself distinguishable. Further distinction now concerns the relation between what is happening and the way we are able to access it.
Further work consists in recognizing which known structures we can still draw on and which continuations they permit. If one of them allows the essential distinctions of the situation to be retained, the movement can continue within it. If several irreducible continuations remain, a choice is required. If continuing requires losing or ignoring the retained trace of discrepancy, the organization of the expression of knowledge itself must be revised.
In revision, a new distinction changes the very organization of the expression of knowledge. Earlier connections enter the new structure as its elemental regime: what continues to work is preserved, but the way it is retained and continued changes. A distinction previously accessible only as a discrepancy finds expression. This overcomes the state of rest in which the previous expression no longer allowed the movement to continue.
Retaining knowledge itself involves continual revision. We preserve accessible connections as we encounter new distinctions and determine anew what can still be retained through them. No completed set of traces does this work in place of the distinguisher.
Retaining a discrepancy, recognizing possible continuations, choosing, and reorganizing knowledge become ways of working that can be studied and developed. We thus approach technologies for consciously organizing the revision of knowledge. Many of these methods are already used in technologies for working with information and in science as a whole, although their common basis is not always explicitly reflected upon.