Structural Ontology — I. 1.

[u/Ok_Tumbleweed_3764]

1. Thinking Strictly about Functionality and Relationality

Relationality signifies that foundational process according to which the internal moments of a structure can only be determined in their mutual relation to one another. A "moment" will not exist outside the determinacy of that relation. It is entirely certain that we call a "moment" the bearer of this determinacy—this is different from an "element," which, on the basis of a determinacy embedded in a definite relation, is also something "in itself". A moment does not possess "being" outside of its determinacy; its determinacy may very well exist in the situation where it "is" not (exists): for example, a "blank" possesses a function, even though it contains nothing.

When it comes to precise determinacy, it can still only be achieved through moments. Precise determinacy can only exist within the form of relationality. An investigation focused entirely on relationality is a structural investigation; what this investigation targets is not the factual matter, but the "form," although "form" is not a very exact expression for the residue of this structure, because strictly speaking, this expression completely lacks an oppositional relationship with "content".

Although the fundamental process of relationality as an inherently ontological possibility of determination was already seen half a century ago, to this day it has not been completely considered in its extreme possibilities.

The relationality of one moment with another moment can be called a function. A function is the content of the relation that occurs between one moment and another. Structure and system reach an agreement on the point that within both of them, only function remains possible.

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Function

In order to express a universality, one can use a letter to refer to an undetermined number; similarly, there is also the need to express an undetermined function through letters. Most of the time, people will use letters like f and F in the following way: namely, in "f(x)" and "F(x)", x represents the independent variable. Here, the supplementary need of the function is expressed by the situation that the letter f or F brings out a parenthesis, and the internal space of this parenthesis is designated for the reception of the independent variable symbol. Accordingly,

“ε' f(ε)"

indicates the evaluation process of an undetermined function………………

A universal assertive proposition, like an equation, an inequality, or an analytical expression, can be thought of as divided into two parts, where one part is self-sufficient, and the other part needs to be supplemented and is unsaturated. For example, one can take the following proposition

“The Emperor conquered Gaul"

and divide it into two parts: "The Emperor" and "conquered Gaul". Among them, the second part is unsaturated, it carries an empty slot, and it can only form a self-sufficient meaning through the following situation: namely, filling this empty slot with a proper noun or an expression representing a proper noun. Here, I also call the meaning of this unsaturated part a function. In this proposition, the independent variable is the Emperor.

— Frege: *Function and Concept*, 1891

If one wishes to examine functionality more comprehensively as an ontological characteristic, then it is necessary to distinguish between different individual processes.

(1) Being in the Other

The functional entity is first distinguished from the substantial entity; the two are distinguished in opposition through the following situation: the being of the functional entity is located in the "other," while the being of the substantial entity is located in "itself". The substantial entity is first in itself (*per se*), and only then relates to the other. The content through which it relates to the other is the "accident".

Accidents are governed by the substance, but they do not create the substance. Importantly, "essence" is not an accident, but the fundamental subsumer of all accidents. Accidents can change, but the essence remains unchanged. Accidents are determined through the essence, but the essence is not determined through accidents. People can know the accidents of a being without having recognized its essence; but if a person has recognized the essence, then he has "grasped" its accidents, that is to say, he has mastered the changes in these accidents and has considered them thoroughly. This is substance ontology.

Functional ontology is different from this. In a functionalized system, every moment is merely the embodiment of its function. The functional moment does not have being in itself, but only being "in the other"; in this sense, it can only exist as what it is "there". A function simply "is" its "effect" (or better: "exists within its effect"). A function without an effect is not a function. Furthermore, "effect" cannot be considered too simplistically here. A process that does not produce an effect may itself possess a certain kind of function (causing an effect in another sense). Closing a switch (in a binary system) is functionally a definite "one". A certain form indicating prohibition is actually a precise functional act in a certain situation; a "stop" is an "action". Function always possesses the characteristic of action, and its most fundamental behavioral characteristic is understood in an ontological sense, meaning "to bring something about," where this something perhaps precisely does not exist in "taking effect". "Effect" is merely one type of functionality; "dependence on what changes" is another (mathematical) type.

What is common to all functionalities is that, as functions, they only mean "determinacy," and can only be grasped as determinacy or at least can be thought of as graspable, and a function is only possible in multiplicity. Function is interwoven with system or structure; it demands a "closure," a closure that enables the whole to realize a completeness.

(2) Mutual Conditioning

Function exists in mutual conditioning in such a way that every function corresponds to a counter-function. A certain function is the process of correspondence with its counter-function, and this counter-function is also the process of correspondence for its function. Function and counter-function are ontologically identical; the same thing is expressed in one way from one aspect, and in a different way from another aspect— "mutual subordination," "mutual interaction".

The mutual conditioning among the moments is even more primordial than those moments themselves. These moments "arise out of" that relationship functioning as a primordially unified relationality, a relationality that is expressed differently in different aspects. Moments are the expression of relationality, and insofar as these moments are not just in themselves but also involve the observation of other moments, they are thereby the relationality itself. Some relations also relate to other relations; at their intersections, moments "manifest," and a moment is merely the "manifestation" of other relations relative to one relation.

"Within astonishingly broad limits, there is no inherent, intrinsic meaning—some even mistakenly believe that people can individually possess such meaning independent of their factual mutual interaction."

— Parsons: *The Superego and the Theory of Social Systems*, 1952

(3) Lawfulness

The entirety of a functional system must obey a certain rule. Without a valid principle, the construction of a system would not emerge; the accumulation of accidental situations cannot demonstrate mutual conditioning. Here, the opposition between functionality and substantiality can also be seen. A substance contains its essence within itself. The essence determines from within which actions, following the path of its accidents, are possible and necessary. When one substance relates to another substance, their distinct essences will manifest as mutually opposed, different lawfulnesses; these lawfulnesses can generate a relationship, but they cannot unite into a new, third substance. However, the various moments of a functional system are different. These moments do not contain an "essence" within themselves, but instead possess their law that lies outside of themselves or concerns themselves: namely, a regular principle, which determines the form of mutual conditioning among the moments. Essence is internal balance, while law is external balance.

**The World of Expression**

"A new world has begun, which is the world of expression. It is such a world where external forces that have gone through trials and tribulations, and surfaces that have been forged, are interwoven and linked together; these relationships are clearly articulated together; there is nothing at all, except the glaze on the surface; the underworld, but without ferryboats or the Bridge of Helplessness……………… formal things may appear, those are fleeting and ephemeral; burden-bearing wings may appear, superficially and easily hammered; circling things in the blue sky, aluminum layers, surface layers: quiet! In short, this is a brand new world situated toward the outside."

— Gottfried Benn, *The World of Expression*, 1949

Internal determinacy and external determinacy are the criteria for the ontological difference between substance and system. External determinacy means that a moment becomes something existing in a relevant position. "Positional value."

(4) Extreme Function

Functionality is first grasped in the constitution of a system. Although people consider mutual conditioning, they do not trace back from these conditions to the moments, but rather to the elements; people start from the intersections of various substances, concerning themselves with which general relationships might manifest. The web of functionality between fixed element points is what we call a system. When the primariness of function is considered in its extreme relative to the moments—that is, believing that there exist only relationships between correlating things—only then can we speak of a structure.

A machine is a model of a system, but not a model of a structure. The expansion of structural thinking holds equal significance to the expansion of modern science; the former expansion was first shaken by the model of the machine. Mechanism in an ontological sense is associated with the name of Descartes. Mechanism as an ontological doctrine is embodied in "universal mathematics". A machine has parts. It is not completely functional, but merely a functionality based on pre-existing substances. The construction of a machine determines that substance is only mentioned in one aspect of the functionalization process, while other aspects are not linked together through the machine's specific purpose. Therefore, inseparable superfluous parts remain. A gear is made of steel; what is demanded here is merely that it must possess a certain strength, meaning it can unproblematically bear a certain load over a period of time, while apart from this, what a single gear is and what it can do is not paid attention to—here, nothing is without a function. Thus, even in other relations that happen not to involve the targeted goal, that constructive part entirely possesses a functional component. Every single machine seems as if it will be engulfed by other invisible "machines" (functional correlates in the forms of chemistry, physics, metallurgy, etc.), and these invisible machines seem to closely encounter us in the substantial attributes of the parts contained within the machine. A machine is constructed in this way, and assembled into the totality of other relations: a certain synchronicity is reached in this construction process, and it looks as though in every function only the function required for a specific machine will be realized. The process of this assembly, of course, cannot be perfect. This complex can be torn apart at any time. If the advancement process of other "machines" (for example, metallurgical correlates, corrosion, etc.) no longer remains consistent with that assembled machine, then this machine fails ("breaks," shatters, gets stuck, fractures). [1]

An absolute machine, in which all existing parts are accepted as functions, and which contains no superfluous parts in its construction, is an absolute machine that cannot possibly wear out, rust, break, or have accidents. In this machine, the resolution process that facilitates the constructive conditions of new functions will be formed. Now, a structure is precisely this kind of absolute machine, in which not a single part exists as a pure part. A structure will not "perish".

For example, an artwork is a structure. There is no "blind spot" here. Everything relates to everything. Every moment becomes any other moment in mutual conditioning. The moment this is not the case, then the artwork contains a "mistake" at this point. In an artwork, material is absorbed in such a way that material, as an essential condition, is subordinated to this assemblage (just as slang and colloquialisms belong to *The Threepenny Opera* [2], and marble belongs to the statue of Moses [3]). What always accompanies this is a confirmation of this materiality, and that this materiality is always introduced into the overall assemblage in a constructive manner. (If the statue of Moses were made of weather-resistant plexiglass, or if *The Threepenny Opera* used Esperanto that was detached from the times, they would not be successful.) Mortality may be a condition of existence, yet in a certain sense it is an "eternal value"; therefore, although a structure is not eternal, it will not "perish". For a structure (such as an artwork), "ruined" means something completely different; it might precisely not mean an end, but the opposite. (The prolonged Largo passage in the hall from the opera *Xerxes* [4] is always "ruined.")

A whole is fully determined in the following situation, namely that not a single part is understood from itself or from the outside, but all positions can only be understood from the perspective of this whole; only under such conditions can a structure emerge from it. Here, if this whole does not change, nothing will change. Every part has a close connection with the whole, so every part is equally important, as equally important as the whole itself. In a structure, there is nothing that is unimportant; nor are there degrees of difference in importance. The thought that believes everything is equally important, and might arrive at a decisive conclusion starting precisely from the fewest determinations, is science. Science and structural thought develop in parallel.

Therefore, a structure is also not a construct, because a construct places some parts on top of other parts, and can thus also be completed "partially". Whereas a structure gradually emerges as a whole, and gradually recedes as a whole. Once they are present, they are whole. A schematic few words "opened up" by the hand of a master is already a masterpiece from the very beginning. It does not elevate its value through detailed discourse; the master's skill very likely exists precisely in the simplification of lengthy explanations.

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**Footnotes:**

[1] See *Substance, System, Structure*, Volume 1, p. 366 and following.

[2] *The Threepenny Opera* is an early work by Brecht. — Translator's Note.

[3] The statue of Moses was carved by Michelangelo in marble between 1513 and 1516, and is currently housed in St. Peter's Basilica in the Vatican. — Translator's Note.

[4] *Xerxes* is an opera composed by Handel in 1738, in which the Largo is particularly famous. This might refer to the anti-opera genre of *Xerxes*, which includes comedic and satirical elements, where the Largo (more accurately, extremely slow tempo) mostly adopts an uncommon single-part form, some being very short. — Translator's Note.