# Theoretical Reflections on Reductionism and Systemic Research Issues: Dark Systems and Systemic Domains

## Abstract

**:**

## 1. Introduction

## 2. Reductionism

## 3. Theoretical Aspects of Systemic Reductionism

#### 3.1. Reducing Sufficient Conditions into Necessary Conditions

#### 3.2. Reducing Emergence to Functioning

#### 3.3. General Linearization of Non-Linear Systems

- Additivity: f(x + y) = f(x) + f(y).
- Homogeneity: f(αx) = αf(x) for any parameter α.

#### 3.4. The Macroscopic from the Microscopic

#### 3.5. Reductionistic Interactions

_{1}represents the exchange of kinetic energy between x

_{1}and x

_{2}:

_{1}and f

_{2}occur simultaneously, then we have:

_{n}

_{/}dt at time t

_{n}is input to the system at time t

_{n}

_{+1}. The reductionist view assumes the validity of G. This dynamic is assumed to be then zippable (or, more elementarily, summable) into G.

- -
- Moore neighborhood, which includes, besides the cell under consideration, the eight neighboring cells that share at least one vertex with it;
- -
- Von Neumann neighborhood, where the cell under consideration shares at least one edge with its four neighbors.

^{q}, where q = k

^{r}.

#### 3.6. Social Systemic Reductionism

“For a long time, in sociology the representatives of an individualistic reductionism claimed to have achieved special access to the elementary, empirically graspable foundations of social life” [41] (p. 256).

“Every version of individualistic reductionism has encountered the objection that, as reductionism, it cannot be fair to the ‘emergent’ properties of social systems. We would object further that the issue is not even reductionism, but relating (in an extremely abbreviated way) to psychic rather than social systems.” [41] (p. 257).

“He wanted to avoid above all else the idea that one could capture ‘the truth’ or essence of modern society in one theoretical account. No theory, not even closed systems theory or autopoiesis, can have the last word or give an exclusive or true account of what society, in its totality, is and how it operates. One could even suggest that the first principle of Luhmann’s sociology is that the possibility not only of seeing things differently but of society actually being different is always present. …What he wished to offer, therefore, was a social theory of social theories—a social theory which considered multiple ways of perceiving and understanding society.” [43] (p. 1).

“He fully realized that one could never completely escape reductionism, since any attempt to address and understand events socially necessarily involves selection, rejection and interpretation.” [43] (p. 1).

#### 3.7. Reverse Reductionism

## 4. Opaque Dark Systems

## 5. Theoretical Incompleteness and Logical Openness

#### 5.1. A Note on Theoretical Incompleteness

#### 5.2. A Note on Logical Openness

- Formal and complete descriptions of relationships between a system’s state variables are available.
- Complete and analytically describable representations of interactions between a system and its environment are available.

#### 5.3. Logical Openness of Theoretical Incompleteness

- -
- fluctuations, the breaking of equivalences and symmetries, weak forces, external influences, and randomness in physical systems;
- -
- adaptation and learning in autonomous systems: in short, sequences of processes of emergence and self-organization are not summable and cannot be procedularized or zipped into the resulting one.

## 6. The Establishment of Predominant Systemic Domains

## 7. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Logical Openness | Theoretical Incompleteness |
---|---|

Modeling uses n levels of representations characterized by the following:- -
- Non-equivalence,
- -
- Approaches for moving between levels (thereby allowing the simultaneous use of more than one level),
- -
- The need to find comprehensive indexes, including measures of coherence, long-range correlations, network properties (e.g., the occurrence of small worlds), and properties of attractors in chaotic phenomena.
| Characterized by: Dynamics of multiple equivalences, A single model is not sufficient to represent the complexity of a system, The system variables (degrees of freedom) vary in number and are continuously acquired, Non-equivalent properties are continuously acquired, Systems can assume many equivalent states (as determined by fluctuations). |

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**MDPI and ACS Style**

Minati, G.
Theoretical Reflections on Reductionism and Systemic Research Issues: Dark Systems and Systemic Domains. *Systems* **2024**, *12*, 2.
https://doi.org/10.3390/systems12010002

**AMA Style**

Minati G.
Theoretical Reflections on Reductionism and Systemic Research Issues: Dark Systems and Systemic Domains. *Systems*. 2024; 12(1):2.
https://doi.org/10.3390/systems12010002

**Chicago/Turabian Style**

Minati, Gianfranco.
2024. "Theoretical Reflections on Reductionism and Systemic Research Issues: Dark Systems and Systemic Domains" *Systems* 12, no. 1: 2.
https://doi.org/10.3390/systems12010002