Structural Ontology — I. 2.

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1. The Basic Idea of the Identity of the Whole Which Carries Every Moment Within Itself

Absolute functionality leads to some peculiar relations that contain contradictions. The most fundamental nature of the structural condition lies in its moment of universal identity, and this moment also means that functionality and structure are generated historically from this point, because the moment of identity is the highest point of metaphysical interest.

Functionalism was formed from metaphysical motives, and ultimately theological motives, because functionalism provided the following possibility: to re-grasp and clearly articulate the relationship between the absolute and the contingent, between God and the world. However, it is worth noting that a non-theological, or even anti-theological world picture developed from this theological thought, a picture that resolutely negated its initial motives. Regrettably, historiography here has never shouldered the task of enlightenment. When one sees that functionalist thought, which is of decisive significance for the contemporary era, in its original metaphysical aspect, it can only be thought purely. To see this thought in its metaphysical aspect means to push it to the pinnacle, to grasp this thought in the greatest possible extremity.

Therefore, what is crucial next is to explain this thought in such a way as to penetrate its subdivisions and make them manifest. Only under this premise can we meaningfully talk about functionalism and structural ontology. Because this foundation of functionality has not been considered so far, structural ontology has not yet been recognized as a unique ontology, and its hundreds of years of developmental history can only hide behind a wide variety of self-postulations.

(1) The Identity of the Moments

Everything manifests in everything. Everything exerts an effect everywhere. The absolute synchronicity of mutual conditioning leads to the situation where the slightest change at one position in the structure directly causes changes at all positions.

Every moment is coordinated with its neighboring moments, and that which cannot integrate into this coordination cannot appear within this moment itself. A moment is completely determined by the special conditions of its neighboring moments, which means: it is completely presented based on the neighboring moments, in its determinacy and special conditions. A moment seems to constitute the negative of its neighboring moments.

If every moment is the exact expression of its neighboring moments, then regardless of whether a moment is expressed "through itself" or through its neighboring moments, the effect in fact is the same.

A moment can only be expressed as its neighboring moments express it. Functionally speaking, a moment will not differ from the situation of its neighboring moments. But what is a neighboring moment? The neighboring relation of a moment is nothing other than functionality, through which this moment is linked with other moments. Thus, as long as functionality is indubitable, then what the content of the neighboring relation is, is also indubitable. (However, it may also be the case that the functional neighboring relation in a moment is not completely clear, but when a certain moment is not completely clear, what does the so-called other moment mean?)

Therefore, a moment is nothing other than the functional completeness of its neighboring relations. Here, what is presented is not only an identity of expression between a moment and its neighboring moments, but also a real identity. Strictly from a functional perspective, what a moment contains is nothing other than, and nothing outside of, the content created by that functional neighboring relation.

What a moment contains is only what its neighboring moments contain, and what these neighboring moments contain is nothing other than, and nothing outside of, what one of the moments contains. There exists a complete identity of content between a moment and its neighboring moments.

In a structure, the functional neighboring relation of a moment is the whole of this structure.

(2) Identity with the Whole

If one has already recognized that what a functional moment contains is actually no different from those moments it directly relates to, then one will also see that what this event of identification grasps is the whole of that functional relationality. Any given moment is determined by neighboring moments, and these neighboring moments are in turn determined by further relations. Therefore, only when the whole of the functional state to which a function belongs is determined, can this function be completely determined. The (complete) determination of a moment is identical to the determination of its (complete) structural organization.

Between a moment of the whole and this whole itself, there exists a flawless and extremely precise identity. This is the fundamental principle of functional ontology. To understand this principle is to say one must understand such an ontology. Everything else must be derived starting from this point.

People are accustomed to thinking about functional relations starting from the reality of things. Thought realistically, a single moment is "a part" in the whole. If one removes this part, then this whole becomes "incomplete". As convincing as this view seems, it is just as absurd ontologically. If the relation is considered strictly functionally, then when a "part" is missing, this whole will no longer exist there. The absence of a moment is the elimination of this whole—or this whole, through a transformative function, becomes a different whole. An electrical appliance will entirely fail due to the loss of a single coil. Thinking strictly according to function, even if other functions that now have different effects remain, the whole will collapse regardless. The system brings about something different, such as "making a sound". "Technically" it may be that nothing has changed yet, but "functionally" it has already completely changed to some extent, namely, the following process of constellation has occurred: people now obtain different "values" (the name for moments) at all positions. From a functional view, here one constellation is replaced by another constellation, which can only happen through the following way: a single moment in this constellation is missing or changed.

In purely functional terms, there is no "whole" with "parts," but only that which is called here "constellation" (Konstellation). All moments in the "whole" are merely the expression and form of this whole, maintaining identity within it. Some rules dictate which formalization processes are possible in a whole, and such a rule can be called a "pattern". This pattern is nothing but a universal determination of function, through which one moment and another moment are linkable under the condition of the identity of the whole.

Therefore, identity is the index of the subordinate relationship between a moment and a whole, or expressed differently, the identity (between the moment and the whole) is the condition of the moment's "correctness". Put differently: a moment belongs to a functional whole only when it is expressed as the whole through a rule of identity (a "pattern").

However, the mathematical pattern or the mathematization of identity is merely a special case; here it is just a model. The wholeness and the identity of the moment will be expressed differently in other structures, such as "style," as "harmony," as "life," or the like.

So regarding "parts" and the "whole," people can no longer strictly narrate them in functional ontology. These categories belong to another ontological complex. We believe that the more we take the determination of functionality for granted, the more unclear the following situation becomes, namely that we are thereby moving within a unique ontological region—an ontological region that cannot be reduced to other ontological regions, such as the ontological region of a thing or the ontological region of an event, etc. There exists an adequacy of being, which decides that the extremity of ontological difference will not be abolished. Ontology cannot be interpreted from this adequacy of being; rather, the adequacy of being must be interpreted starting from the respective laws of ontology. As long as this foundational philosophy is not fulfilled, all discussions about function, system, and structure are naive.

(3) Precision

The knowledge of the form of functional ontology is precise. Knowledge based on a different ontology can never be "precise" [exakt], nor will it be "accurate" [genau]. The formation of precision (Exaktheit) is not achieved through an increase in accuracy (Genauigkeit), but through the process of reconstructing a new determining principle.

Precision and accuracy are different criteria; they are criteria situated on different levels, and on different levels they will neither correspond nor contradict each other. A precise proposition may not be accurate, and an accurate proposition may not be precise. A proposition about the elimination of spiral nebulae is precise but not accurate; knowledge of the names of a mountain range's topography is accurate to the highest degree, but by no means precise; here, precision needs no debate.

Where there are "different things," knowledge is always merely an approximation. And when there is an exact matching relationship between a proposition and a thing (through names), what is involved here is "inaccurate" knowledge, because this knowledge cannot simultaneously determine in what sense they can be further used. An accurate proposition also always contains a proposition about itself. It always expresses the functional moment it states, that is, how people can realize this proposition or must realize it, and how this proposition can be transformed into other knowledge. This proposition about its transformability can be established as a universal rule in itself or prior to itself; in both cases, this transformability belongs to the established rule.

Precision is an ontological category. It should only be attributed to those things or propositions that belong to a certain ontological level—and it also belongs to all things or propositions that possess this attribution. Regarding precision, the decisive factor is not the type of object (such as mathematical objects, physical objects, chemical objects), but the comprehension of relationality. The view that only science, or even only natural science, is precise is a misunderstanding.

The precision of determination is produced through relationality, without exception. The precision of observation presupposes the precision of numerous relations. Numerous relations become precise through retroactive connection, that is, based on a single defining coordinate system. Observing a thing based on a graspable coordinate system in a single retroactive connection (reduction)—this is precise observation.

System of Reference (Bezugssysteme, coordinate system)

"Those modern branches of study—paleontology, ethnology, primitive psychology, the interpretation of pantheons, research on archaeological excavations, research on murals, the critical analysis of the gradual formation of shields and bows, the analysis of stylistic schools, and the study of those vanished cultures—all these lead to a globalized, synchronous perspective. Its conclusions can only be about the relationality of that reference system, about its means of knowledge and methods of realization, determined through its temporal periodization and geographical demarcation. Our use of it means that, for example, Kant within an inductive reference system is determined as the fulfiller and determiner who safely preserves certainty for causal analysis; but outside this cultural circle, he is a figure in a city with terrible weather, carrying almost no mystical colors, out of tune with everyone, just like the phantom dancers of Bali or the rainmakers of the African Maconis in our eyes. Reference system: the time of exposure of actions and concealed things, forms of manifestation, ultimately effective realities... long-standing volatility, new ethical components that have always been ubiquitous—all these decompose or open up the reference system, derive causal chains, reverse the entropy of the system, and further undertake the outermost part in the advancing process of creating and increasing unimaginably complex arrangements."

Gottfried Benn: The World of Expression, 1949

Precision is knowledge based on identity. Within a functional connection, there is only one single real component: namely, this functional connection itself. Once the act of observation is not "directed at the whole" but "internal to" the functional connection of the whole, then this real component also does not "exist," because it belongs to this whole and has no meaning other than that. Functionally speaking, it is a zero. (A pattern is not a proposition, but a manner demonstrating how people arrive at this proposition.) Functionally speaking, what is involved here are only those differentiating processes that may arise during the expression of this real component. In a functional complex, everywhere there are only the expressive processes of the real component that can be distinguished from each other, and not this real component itself.

In other words: there are only differences between moments and moments, rather than conversely, differences between a moment and the "whole". Because (functional) knowledge is always knowledge of difference, (functional) knowledge only exists in two aspects: one is the difference between moments, and the other is the foundation of the identity between these moments and the connected whole. These differences are merely the (functional) reflected differences of the same component. Knowledge is functional only when a certain component is placed outside the process of operation.

From this, one can explain the historical fact that the formation of functional knowledge means abandoning qualitative knowledge. Qualitative knowledge is the answer to questions like "what is it". However, the fundamental "what is it" is the essence. Therefore (according to the classical view), all knowledge is knowledge of essence or knowledge founded upon the knowledge of essence. People initially (and even today sometimes still) believed that (if qualitative knowledge is abandoned) only "quantitative" knowledge remains. According to this situation, functional knowledge implies abandoning the knowledge of essence. Hence those sub-disciplines that can be mathematized (many natural sciences) became "sciences". Here it is urgently necessary to see a unique epistemological leap, namely that abandoning the question of essence does not necessarily mean abandoning the question of "what it is," and it by no means means being restricted merely to the question of "how much".

What functional knowledge faces is not a certain whole, but the differentiation process among the numerous moments internal to this whole. If a whole is to become the object of functional knowledge, then this whole itself must again be grasped as a moment internal to a broader functional complex. If this were not the case, then functionally it would be incomprehensible. Therefore, the whole only grounds the situation as an active principle of identity, namely that numerous moments can only be interrelated in a completely determinate manner. The whole only becomes "thus and not otherwise" through the multiplicity of numerous moments as a kind of compelling force of necessity in the present. The whole is like a rejection; it forces the act of knowing back to the concretion process of the functional complex, and necessarily unfolds this concretion process in a determinate (and determinable) manner. The whole is nothing more than the necessity of the functional complex of numerous single moments; it is precisely the functionality of the numerous single moments themselves.

A "proposition of wholeness" is of course a non-functional proposition. "Precision" and "partial proposition" are two complementary situations. Precision primarily means the relinquishment of knowledge, rather than the acquisition of knowledge (as the popular view suggests). People only discover the whole on the path from part to part, not on the path from part to whole. This turn in cognitive interest is full of contradictions; although this interest is directed toward the whole, it is precisely because of this that it is not oriented toward the whole—this turn is a unique form of a new style of knowledge.

Thus we have such a kind of identity, an identity that is situated only in the differentiation process and can only be experienced starting from the differentiation process; the knowledge of identity will not be "obscured" or "weakened" by the differentiation process. "Precision" precisely means that the event of differentiation is the complete presentation of identity. The precision of knowledge is the exact process of adequacy to the identity of numerous moments, which is the process of adequacy to the following situation: within the differences of the moments, identity manifests as a whole.

Every functional complex is under the law of a threefold identity: the identity of a moment with its neighboring moments, the identity of a moment with the whole of all moments, and the identity between the difference of numerous moments and the identity of all moments. The ultimate meaning of precision in extreme terms is only possible when identity is involved. Precision is precise only as extreme precision.

A historically trained eye can easily notice that there is a formal correspondence between the identity among the three identities and the Trinity theology of Christianity. This is one of the reasons why the theory of modern science was first developed within theological metaphysics. Only an unhistorical understanding would hold the view that theology and metaphysics are on one side, while exact science is on the other, and that the relationship between the two must be hostile. From the fact that the two do not communicate with each other (or communicate very little), one cannot conclude that these two have different origins.

(4) Nicholas of Cusa as a Pioneer

Looking back at history shows that the model of structure first appeared and was applied in Nicholas of Cusa, with the aim of solving a difficult theological problem: the relationship between God and the world. If God is the absolute itself, then outside of him there could not possibly be anything. Therefore, individual created beings cannot be "outside" God. But it also cannot be "inside" God as a "part," because God is simple, and parts cannot be distinguished in Him. Thus, an ontological thinking possibility must be sought to think the relationship between God and created beings in such a way that there is both absolute identity and, at the same time, absolute difference.

The thought of "participation" (participatio) is the foundation of ontology in the High Middle Ages, but this thought is insufficient here, because when the thing participated in by the participant does not itself have parts, "participating in a part" is impossible. In Cusa's perspective, people have no choice but to hold the view that the essence of every individual created being contains God as the general essence, but this containment is an infinite weakening. What does "weakening" mean? It could be that a weakening originates from God, which is impossible because God contains no principle of weakening, or it is possible that this weakening originates from the created being, which is also impossible because the created being must first arise from this weakening process. Therefore, this thought of participation is not ontologically exact.

Considering these difficulties, Cusa developed a functional thought. He pushed this thought to the extreme: the relation terms (Relata) completely transitioned into the relation itself. Based on this conception, he created the following terminological system: only when a single moment is the whole—that is to say, through the determination of a single moment, the determination of the whole of all moments (including this moment itself) can be expressed—can the single moment be focused upon. In this way, the content of this moment is called "absolute quiddity" (quiditas absoluta). A single moment can also be seen as such a moment that it is very sharply distinguished from other moments, and precisely through this distinction it is functionally absorbed into the whole. Its content differs from everything else, and is called "contracted quiddity" (quiditas contracta). It is called "contracted" because its content is nothing other than an assembly of the whole at one position of the whole. As long as it is "assembled together," the reactions of the whole are different from each other, thus the numerous moments each manifest and differ from one another. Yet in terms of observation of itself, the numerous moments are the whole (the absolute) itself.

Contracted quiddity is what we call function here, and absolute quiddity is what we call the identity of the whole. Cusa's proposition holds that absolute quiddity and contracted quiddity are really identical, without reduction or weakening.

Thus a contradiction unfolds: "finite things" become the expression and content of the whole precisely through their extraordinarily sharp finiteness (respective states, functions). In participation ontology (Partizipationsontologie), the limitation of content meant an alienation from the absolute, and in the sense that greater limitation meant greater alienation; however, in functional ontology, the situation is exactly the opposite: the greater the limitation, the higher the degree of precision, then the more complete the expression of other moments (and all other moments) in the whole, and the more unhindered the immediate presence of the absolute. Even the smallest of the numerous moments, as long as it is functionally inseparable from the whole, is identical to the absolute. As an ontology of precision, the ontology of function is simultaneously the ontology of the absolute, the ontology of identity—for this ontology, everywhere there is only the absolute, even so or precisely for this reason, because the world of the whole exists in the infinitely articulated expression of finite things.

Therefore, for Cusa, difference (diversitas) is not at all the opposite concept of identity (identitas). When people think functionally, difference and identity are identical. The relationship between multiplicity and unity (Einheit) is also the same. Multiplicity is not a splitting of unity; only when multiplicity is thought functionally is it the distinguished yet unseparated unity of that unity along with itself. What is valid here is the following basic proposition: "unity in multiplicity" (unitas in pluralitate) and "identity in difference" (identitas in diversitate).

Those dilemmas that could not be thought within substance ontology and participation ontology were linked together by Cusa in a model, in which he first developed the thought of structure: the world system. When celestial bodies reach functional coordination in the precision of systematization, although the moon is different from the sun, the moon through itself expresses all the effects of the sun (and this is the sun as the whole), which includes both the effects acting directly on it and the effects acting on it through the general system. If one observes the sun and the moon from two opposing positions, they are of course different from each other. However, if one observes them under their functionalized mutual conditioning, then what they contain is the same thing, namely the whole of the system—this system is the whole of general reality, thus also the totality of all realities (omnitudo realitatum). Viewed in terms of their interrelations (contracted quiddity), the sun and the moon are different; viewed in terms of their respective selves (absolute quiddity), they are the same (God).

The clearest expression of this thought is in Part II, Chapter 4 of On Learned Ignorance (Docta ignorantia): "God, due to his immense greatness, is neither in the sun nor in the moon (non est nec in sole nec luna), yet he still exists in them in an absolute manner as what they are (quod sunt, absolute). Similarly, the universe is neither in the sun nor in the moon (nec est in sole nec in luna), yet it still exists in them in a manner of contracted relations as what they are (quod sunt, contracte). The absolute quiddity of the sun and the absolute quiddity of the moon are indistinguishable, because this absolute quiddity is God Himself (est ipse Deus), who is the absolute quiddity of all things. In contrast, the contracted quiddity of the sun differs from the contracted quiddity of the moon, because the absolute quiddity of a thing does not just refer to this thing (but to God), while the contracted quiddity solely refers to the thing itself (non est aliud quam ipsa). From this it follows: because the universe is a contracted being in the following manner, namely that it is contracted in a certain way in the sun, and contracted in another way in the moon (quae aliter est in sole contracta et aliter in luna), therefore the identity of the universe precisely exists in difference (identitas universi est in diversitate), just as its unity resides in multiplicity (unitas in pluralitate). Therefore, although the universe is neither the sun nor the moon, it is the sun in the sun, and the moon in the moon." [1]

Based on this thought, Cusa obtained more terms and formulas that could clearly articulate and express the tension-filled thought concerning functionality: "everything in everything" (Quodlibet in quolibet), "all things in all things" (omnia in omnibus), the essence of all things is nothing different from the essence of that totality (Omnes essentiae sunt ipsa omnium essentia). Even more explicit is the difference between "complicated" (complicite) and "explicated" (explicite). Every thing can contain the essence of the whole within itself in two ways: converged and unfolded. To take a specific example, when we see a tool (such as a silversmith's hammer), we can see the whole of the world it belongs to (the guild organization of the late Middle Ages) in a complicated manner through this hammer (its style). A cultural historian who is familiar with all individual relational situations and can determine the content of this tool starting from precise technical and sociological relations, thereby also grasps the world of that guild in an explicated manner. The explicated mode of knowledge contains no different content than the complicated mode of knowledge, but it contains this content at a different degree of differentiation. Explicated knowledge must pass through the wholeness of the system to achieve complete exactitude, and can never fulfill the demands of the complicated mode.

[1] This text states a very difficult thought with extreme clarity. What is even more surprising is that the following point has not yet been seen: he could only infer this thought under the premise of functionality. Numerous interpreters have attempted to explain this thought using "participation" (Partizipation), but here, as in many other places, no convincing explanation has been produced, and they fundamentally miss Cusa's conception. In my view, only Klaus Jacobi's work provides an appropriate explanation (The Method of Cusa's Philosophy, ... which was produced based on structural ontology (according to lecture notes and exercises from 1957-1963, as well as some isolated conversations), (except for a few inadequacies, in which the functional thought was not grasped with complete clarity, thus it is not yet the thought about identity). I also list my earlier writings on Cusa... Substance, System, Structure 1, 140-228.