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This article, based on network science, aims to contribute to overcoming its geometric and technological phases. The novelty consists in considering links of networks as linked by superimposed networks, termed here multiple superimposed soft networks (MSSN), which is introduced as a research issue. Such links of links (termed here as passive links) concern, for instance, correspondences, incompatibilities, and temporal synchronizations between the occurrences of pairs of active links of effective networks, such as those based on electrical and telecommunication. A possible constitutive mechanism of such passive linkage consists of linkage representations for practices and histories of use expressed by their validating statistical reoccurrences. We consider the possible emergent nature of the passive linkage. The reason for introducing the design and usage of MSSN properties as a research issue involves making new approaches to profile and manage networks available. Correspondence between active linkage and MSSN properties should be a matter for an experiential, machine-learning approach. Research issues relate their possible usage on the active linkage such as for classification, comparations, detection of criticalities, diagnosis, performance evaluation, and regulatory as weak forces. Furthermore, the possible identification of standard corresponding configurations of passive and active linkage is finalized to avoid their establishment or, conversely, in facilitating their establishment and keeping their replication in different contexts (or partially and in combinations) and identifying related standardized approaches (also for classes of configurations having significant levels of equivalence). This research project has methodological generalizing aspects of trans-disciplinarity. We conclude by mentioning related research issues.

In this article, we explore some theoretical issues related to reductionism and systems. Fundamentally, reductionism neglects that a system can acquire properties. Among various possible reductionist approaches, we consider the reduction of sufficient conditions to necessary conditions in systems, the reduction of emergence to functioning, and the general linearizability of non-linear systems. Furthermore, we consider the reductionistic deductibility of the macroscopic from the microscopic (as a matter of scalarity without intermediary emergence). We examine “reductionistic interacting” as it relates to multiple sequenced interactions being zippable into a single interaction. We consider the theoretical dynamic mixed usage of reductionism and non-reductionism. We then elaborate on theoretical systemic issues around opaque dark systems (as non-evident systems requiring both change in scale and change sequences). We investigate how a phenomenon can be improperly modeled as a system. This is often undertaken for the convenience of an observer (who takes advantage of the readily available approaches and models). We elaborate on the interdependence and possible equivalence of these phenomena’s theoretical incompleteness and the logical openness of their modeling. We also consider the theoretical issue of systemic domains as space. Here, an entering entity only has access to certain actions and degrees of freedom due to the predominance of a previous systemic phenomenon. We conclude by considering the centrality of theoretical research in systems science.

We consider possible cybernetic and systemic approaches to an interdisciplinary general theory of change as a philosophical and scientific project. The approaches considered are intended as necessary; however, they are not necessarily the only ones, probably, at least in some cases, non-sufficient. The aim of such a theory should be that of identifying levels of descriptions suitable to classify, describe, and forecast the consequences of changes, as well as of finding the conditions which allow to control them as introduced by Cybernetics. Historically the scientific contents relate to the theory of phase transitions, its variations, and quantum approaches. However, we consider processes whose dynamics of change may be represented by other approaches such as meta-structural properties, that is, of necessarily dynamic structures between variable clusters rather than between entities considered structurally invariable. Furthermore, we consider the dynamics of processes of emergence, the general process of changing, as dynamics of validity regimes, an approach inspired by considering fields rather than entities in physics. On the philosophical side of the interdisciplinary general theory, we consider how such a hypothetical general theory of change should consider the theoretical incompleteness of changing, based on equivalences and multiplicities, and the quasi-ness of phenomena when properties are continuously lost and recovered. When systems are not always systems, systems are not only systems, and a system is not always the same system. The quasi-ness of the interaction machinery supporting the interaction activity of emergence is given by the variable duration, different start and end instants, inhomogeneity, and the various composability of interactions themselves which, furthermore, interfere with each other. It relates to the keeping of the same identity by continuously changing systems such as emergent systems. A swarm is always a swarm, even if continuously different. Theoretical incompleteness and quasi-ness are philosophical aspects of the meta-structural, mesoscopic approach, suitable to give new philosophical meaning to Cybernetics and General System Theory in the field of complexity. Where 'to regulate' means the ability to induce and to orient complex phenomena (where the replacement substitutes the regulation) with the fundamental role of weak forces as constraints to dynamics, to be processed by systems and not only be formally respected.

This article proposes conceptual approaches for both the design and implementation of network linkages, that dependent on context, should respect interlinking topological and parametric constraints, possess formal properties, be compatible with configurational features and combine with an external meta-network as a service option. The purpose is to allow for alternative design and management of networks by adding flexibility, but to also enable design appropriate for highly specific applications.

Within the conceptual framework of number theory, we consider prime numbers and the classic still unsolved problem to find a complete law of their distribution. We ask ourselves if such persisting difficulties could be understood as due to theoretical incompatibilities. We consider the problem in the conceptual framework of computational theory. This article is a contribution to the philosophy of mathematics proposing different possible understandings of the supposed theoretical unavailability and indemonstrability of the existence of a law of distribution of prime numbers. Tentatively, we conceptually consider demonstrability as computability, in our case the conceptual availability of an algorithm able to compute the general properties of the presumed primes’ distribution law without computing such distribution. The link between the conceptual availability of a distribution law of primes and decidability is given by considering how to decide if a number is prime without computing. The supposed distribution law should allow for any given prime knowing the next prime without factorial computing. Factorial properties of numbers, such as their property of primality, require their factorisation (or equivalent, e.g., the sieves), i.e., effective computing. However, we have factorisation techniques available, but there are no (non-quantum) known algorithms which can effectively factor arbitrary large integers. Then factorisation is undecidable. We consider the theoretical unavailability of a distribution law for factorial properties, as being prime, equivalent to its non-computability, undecidability. The availability and demonstrability of a hypothetical law of distribution of primes is inconsistent with its undecidability. The perspective is to transform this conjecture into a theorem.

We consider the peculiarity of unique events, such as those of a natural, evolutionary, and social nature. In particular, we consider unique social events that have had either the claim or the vocation of being salvific for humanity, such as the introduction over time of the Torah, Hinduism, Buddhism, Christianity, and Islam. We question how the claimed, general salvific vocation contrasts, or is inconsistent with, the non-retroactive temporality and locality of such events, which could not have happened otherwise. This undeclared and philosophically unsolved inconsistency then reappears in subsequent cultural contradictions and inadequacies, political and social allowances such as, for instance, homo-centrism and a pathological relation with Nature. In the case of Christianity, this inconsistency is represented by the painting reproduced in the article, a work in which the excluded humans and other living beings are represented as astonished by the occurrence in this moment, and in such an unnatural context. Furthermore, we consider the original understanding as related to concepts of classical physics, or of such concepts naively adopted within the texts considered sacred. However, in some religions, such as Christianity, the inconsistency is theologically solved. We stress the need to update the ancient original elementary, naïve, pre-classic philosophical and conceptual frameworks used so that these alleged inconsistencies and contradictions may be not only theologically solved, but also conceptually solved in more complex understandings of the world, for example, considering relativistic time, long-range interdependence, quantum entanglement, and theories of the universe. Without this update, the unique saving events can affect only religiously, that is, optionally, on the scientific and philosophical conceptions used. Without this adjustment, homo-centrist illusion and egoism prevail as the natural, linear consequential attitude without raising these questions. It rather assumes that the intervention is for involved human beings, and moreover for those who have had and are lucky enough to receive and practice it, ignoring the enormous inconsistency within the message itself, and its presumed general and available salvific nature. This requires theological, philosophical, and scientific interdisciplinarity. The theme concerns inconsistencies within and superficiality of the narratives and their treatment of the unique, salvific events, without any reference to possible general and retroactive effects of how these events are represented in the painting. We conclude that the subject should be debated by taking into account contemporary understandings, such as relativistic space and time, quantum physics, and of the universe, with new philosophical and anthropological approaches. This should be a matter of responsible philosophical and theological interdisciplinary debate involving science, suitable to establish new understandings.

We discuss mathematical and physical arguments contrasting continuous and discrete, limitless discretization as arbitrary granularity. In this regard, we focus on Incomputable (lacking an algorithm that computes in finite time) Real Numbers (IRNs). We consider how, for measurements, the usual approach to dealing with IRNs is to approximate to avoid the need for more detailed, unrealistic surveys. In this regard, we contrast effective computation and emergent computation. Furthermore, we consider the alternative option of taking into account the properties of the decimal part of IRNs, such as the occurrence, distribution, combinations, quasi-periodicities, and other contextual properties, e.g., topological. For instance, in correspondence with chaotic behaviors, quasi-periodic solutions, quasi-systems, uniqueness, and singularities, non-computability represents and corresponds to theoretically incomplete properties of the processes of complexity, such as emergence and quantum-like properties. We elaborate upon cases of equivalences and symmetries, characterizing complexity and infiniteness as corresponding to the usage of multiple non-equivalent models that are constructively and theoretically incomplete due to the non-exhaustive nature of the multiplicity of complexity. Finally, we detail alternative computational approaches, such as hypercomputation, natural computing, quantum computing, and analog and hybrid computing. The reality of IRNs is considered to represent the theoretical incompleteness of complex phenomena taking place through collapse from equivalences and symmetries. A world of precise finite values, even if approximated, is assumed to have dynamics that are zippable in analytical formulae and to be computable and symbolically representable in the way it functions. A world of arbitrary precise infinite values with dynamics that are non-zippable in analytical formulae, non-computable, and, for instance, sub-symbolically representable, is assumed to be almost compatible with the coherence of emergence. The real world is assumed to be a continuous combination of the two—functioning and emergent—where the second dominates and is the norm, and the first is the locus of primarily epistemic extracts. Research on IRNs should focus on properties representing and corresponding to those that are detectable in real, even if extreme, phenomena, such as emergence and quantum phenomena.

The article is based on the dual concepts of theoretical incompleteness in systems science and theoretical incomprehensibility in philosophy previously introduced in the literature. Issues of incompleteness relate to the logical openness of complexity models in their nonequivalence and necessary non-zippable incompletable multiplicity. This concerns the quasi-ness of phenomena and the constructivist nature of models. Theoretically, incomprehensibility is considered in different ways, such as the inexhaustible multiplicity of the constructivist reality corresponding to the logical openness of both the world and of understanding itself and in reference to incomprehensibilities such as questions like the divide between species, cognitive systems, and after-death experience (if any). In conjunction with the need for non-classic, interdisciplinary approaches in science to deal with complexity, unanswerable questions need suitable scientifically updated philosophical reasoning in interdisciplinary humanistic backgrounds to allow for new social representations, understandings, and plausible social imaginary. Such approaches more properly allow for effective philosophical representations of the world. Knowing how to deal with these issues through philosophical reasoning updated to the current scientific levels and humanistic interdisciplinarity allows for higher levels of awareness and new comprehensive philosophical understanding, introducing new powerful social imaginary. Such new philosophical reasoning is expected to allow a conception of the world that is no longer just utilitarian, but theoretically necessarily, and not only concessively respectful of diversity with significant, even self-ethical effects.

The aim of the article is to propose a conceptual framework, constructs, and conjectures to act as a guide for future, related research finalized to design and implement versions of Artificial Intelligence encompassing an artificially simulated unconscious suitable for human-like artificial cognitive processing. This article considers the concept of the unconscious in psychoanalysis. The interdisciplinary understanding of this concept is considered to be the unavoidable property of sufficiently complex, cognitive processing. We elaborate on the possibility of an artificial unconscious, able to both self-acquired properties through usage, and self-profile through a supposed implicit, parasitic usage of explicit cognitive processing. Memory activities are considered to be integrated into cognitive processing, with memory no longer only being storage and reminding no longer only being finding. We elaborate on the artificial unconscious as an implicit, usage-dependent, self-profiling, and emergent process. Conceptual characteristics of the research project are the implementation of weighted networked, fuzzified memorizations; self-generated networks of links of inter-relationships as nodes, self-variation of the intensity of the links according to the use, and activation of internal self-processes such as the introduction of fictitious links intended as variations and combinations of the current ones. Application examples suitable for experimental implementation are also discussed with reference to chatbot technology that has been extended with features of an artificial unconscious. Thus, we introduce the concept of the AU-chatbot. The main purpose is to allow the artificial cognitive processing to acquire suitable human-like attitudes in representing, interfacing, and learning, potentially important in supporting and complementing human-centered activities. Examples of expected features are the ability to combine current and unconscious links to perform cognitive processing such as representing, deciding, memorizing, and solving equivalencies, and also learning meta-profiles, such as in supporting doctor–patient interactions and educational activities. We also discuss possible technologies suitable for implementing experiments for the artificial unconscious.

We consider how processes of dynamical, multiple, overlapping, interfering, correlated interactions establishing collective systems are analytically intractable. The meta-structures project has the purpose of using mesoscopic (rather than macroscopic or statistical) representations to allow interventions which can suitably modify various properties acquired by emergent collective behaviours. We consider mesoscopic variables and mesoscopic properties as suitable for representing such systems of interactions. Properties of collective systems, such as coherence(s), are considered to be suitably represented by mesoscopic dynamics. Finally, mesoscopic interventions are considered as suitable for acting upon collective systems.

This contribution tentatively outlines the presumed conceptual duality between the issues of incompleteness and incomprehensibility—The first being more formal in nature and able to be declined in various ways until specified in the literature as theoretical incompleteness. This is theoretical and not temporary, which is admissible and the completion prosecutable. As considered in the literature, theoretical incompleteness refers to uncertainty principles in physics, incompleteness in mathematics, oracles for the Turing Machine, logical openness as the multiplicity of models focusing on coherence more than the optimum selections, fuzziness, quasiness, e.g., quasi-crystals, quasi-systems, and quasi-periodicity, which are intended as the space of equivalences that allow for coherent processes of emergence. The issue of incomprehensibility cannot be considered without reference to an agent endowed with cognitive abilities. In this article, we consider incomprehensibility as understood here as not generally scientifically explicable, i.e., with the available knowledge, as such incomprehensibility may be temporary, pending theoretical and technological advances, or deemed to be absolute as coincident with eventual definitive, theoretical non-explicability, and incomprehensibility. We considered the theoretically incomprehensibility mostly in three main ways: as the inexhaustibility of the multiplicity of constructivist reality as given by the theoretically incomprehensible endless loop of incomprehensible−comprehensible, and by existential questions. Moreover, theoretical incomprehensibility is intended as evidence of the logical openness of both the world and of understanding itself. The role of theoretical incomprehensibility is intended as a source of theoretical research issues such as paradoxes and paradigm shifts, where it is a matter of having cognitive strategies and approaches to look for, cohabit, combine, and use comprehensibility and (theoretical) incomprehensibility. The usefulness of imaginary numbers comes to mind. Can we support such research for local, temporary, and theoretical incomprehensibility with suitable approaches such as software tools, for instance, that simulate the logical frameworks of incomprehensibility? Is this a step toward a kind of artificial creativity leading to paradigm shifts? The most significant novelty of the article lies in the focus on the concept of theoretical incomprehensibility and distinguishing it from incomprehensibility and considering different forms of understanding. It is a matter of identifying strategies to act and coexist with the theoretically incomprehensible, to represent and use it, for example when dealing with imaginary numbers and quantum contexts where classical comprehensibility is theoretically impossible. Can we think of forms of non-classical understanding? In this article, these topics are developed in conceptual and philosophical ways.

This contribution shortly outlines and reviews a theoretical and computational approach for a theory of change concerning systems where it is not possible to apply the laws of motion ab initio. The concept of meta-structure relates to the emergence of forms of spatiotemporal coherences in collective behaviours intended as coherent sequences of multiple structures. The essential difference compared with traditional methods is the role of the cognitive design by the observer when identifying multiple mesoscopic variables. The goal is both to study the "change without physics" of the dynamics of change and to design non-catastrophic interventions having the purpose to induce, change, keep or restore collective behaviours by influencing -at the mesoscopic level -and not prescribing explicit rules and changes.

We propose here a formal approach to study collective behaviors intended as coherent sequences of spatial configurations, adopted by agents through various corresponding structures over time. Multiple, simultaneous structures over time and their sequences are called Meta-Structures and establish sequences of spatial configurations considered as emergent on the basis of coherent criteria chosen and detected by an observer. This coherence is represented by patterns of values of the proper mesoscopic variables adopted, i.e., meta-structural properties. We introduce a formal tool, i.e., the family of mesoscopic general vectors, defined by the observer, able to detect coherent behaviors like ergodic or quasi-ergodic ones. Such approach aims to provide a general framework to study intrinsically stochastic processes where the “universal evolution laws” fail. However, at the same, the system is structured enough to show significant clusters of collective behaviors “invisible to” simple statistics.

We consider Big Data as a phenomenon with acquired properties, similar to collective behaviours, that establishes virtual collective beings. We consider the occurrence of ongoing non-equivalent multiple properties in the conceptual framework of structural dynamics given by sequences of structures and not only by different values assumed by the same structure. We consider the difference between modelling and profiling in a constructivist way, as De Finetti intended probability to exist, depending on the configuration taken into consideration. The past has little or no influence, while events and their configurations are not memorised. Any configuration of events is new, and the probabilistic values to be considered are reset. As for collective behaviours, we introduce methodological and conceptual proposals using mesoscopic variables and their property profiles and meta-profile Big Data and non-computable profiles which were inspired by the use of natural computing to deal with cyber-ecosystems. The focus is on ongoing profiles, in which the arising properties trace trajectories, rather than assuming that we can foresee them based on the past.

The aim of this editorial is to briefly introduce some papers of different nature presented by the contributors to the special issue on “Second Generation General System Theory”. These contributions have been focused on the need for building a post-Bertalanffy Systemics, based on new problems, representations, and approaches to complexity. Furthermore, such new Systemics is expected to be able to theoretically generalize new related systemic concepts and approaches introduced by different disciplines. Such a theoretical generalization is going to coincide with a new kind of interdisciplinarity. The latter should substitute the classical one, based on considering problems and solutions within a discipline as equivalent to problems and solutions within another one. This equivalence was used within the framework of general systemic concepts like Anticipation, Completeness, Feedback, Finality, Forecast, Separability, Openness, and Reversibility. The contributions contained in this special issue constitute very interesting examples of new approaches and of their possibilities of theoretical generalization. Therefore, the issue itself can be considered as a window on the new Systemics and its challenges.

Usual reductionism considers systemic, acquired properties as non-systemic, possessed properties. We consider here the non-systemic usages of systems, misunderstood as non-interacting virtual objects or devices, and the misunderstanding between non-complex (first Systemics) and complex systems (second Systemics) as another form of reductionism. This reductionism leads to inappropriate and ineffective approaches, particularly dealing with complex systems such as socioeconomic systems, whose complexity is often misunderstood and neglected. However, this reductionism should be distinguished from mixed usages of systemic approaches suitable to deal with multiple, dynamic, temporary, and partial systemic natures of phenomena related to complex systems. We consider that we should move from the well-defined, often simplistic, world of Systemics to Quasi-Systemics, which is intended as constructionist Systemics, always in progress, non-ideological, multiple, contradiction-tolerant, incomplete, and in its turn emergent. Rather than recommending a pragmatic attitude, we mention two approaches, one methodological approach called Logical Openness and another, the Meta-Structure approach, which is suitable to more formally deal with such multiple aspects and—based on mesoscopic representations—suitable to represent quasiness.

After having outlined the essential differences between non-complex systems and complex systems we briefly recall the conceptual approaches considered by the pre-complexity General Systems Theory introduced by Von Bertalanffy in 1968 and those of the science of complexity and post-Bertalanffy General Systems Theory. In this context, after outlining the concept of completeness, we consider cases of incompleteness in various disciplines to arrive at theoretical incompleteness. The latter is clarified through several cases of different natures and by approaches in the literature, such as logical openness, the Dynamic Usage of Models (DYSAM), and the principle of uncertainty in physics. The treatment and the contrast between completeness and incompleteness are introduced as a conceptual and cultural context, as knowledge to manage the knowledge society in analogy, for example, with the transition from the logic of certainty to that of uncertainty introduced by De Finetti. The conceptual framework of completeness is not appropriate for dealing with complexity. Conversely, the conceptual framework of incompleteness is consistent and appropriate with interdisciplinary complexity.