Online research in philosophy

Qualitative Complexity offers a critique of the humanist paradigm in contemporary social theory. Drawing from sources in sociology, philosophy, complexity theory, 'fuzzy logic', systems theory, cognitive science and evolutionary biology, the authors present a new series of interdisciplinary perspectives on the sociology of complex, self-organizing structures.

Science, and with it our understanding of evolutionary processes, is itself undergoing evolution. The evolutionary framework still most frequently used by the general public to describe and guide processes of societal development is erroneously grounded in Darwinian perspectives or, at the very least, draws facile analogies from biological evolution. The present inquiry incorporates fresh insights on the general systemic nature of developmental dynamics from the most recent advances in the transdisciplinary realm of the sciences of complexity (e.g., general evolution theory, cybernetics, information and communication theory, chaos theory, dynamical systems theory, and nonequilibrium thermodynamics). The description of the evolutionary trajectory of complex dynamical systems as irreversible, periodically chaotic, and strongly nonlinear agrees with certain features of the historical processes of societal development. But there are additional features of the evolutionary dynamic of natural systems that are seldom portrayed as part of human developmental deportment. These features include elements such as the convergence of existing systems at progressively higher levels of organization, the increasingly efficient utilization of environmental energy, and the complexification of system structures in states that are progressively further removed from chemical and thermodynamic equilibria. The sciences of complexity offer insight into the laws and dynamics that govern the evolution of complex systems across a variety of disciplinary areas of investigation. Through a study of the isomorphisms across disciplinary constructs in the theoretical analyses of the principles governing the evolution of human societies, it is possible to enrich the account of developmental dynamics at the socio-civilizational level. Such an account would further our understanding of the phenomenon of societal development and provide the means for the purposeful guidance of this phenomenon in accordance with general evolutionary principles. This article sets forth the type of considerations, and outlines a general research agenda, for inquiry toward an operational model of the evolutionary development of social systems.

This paper examines the rising competition between computational and dynamic conceptualizations of complexity in economics. While computable economics views the complexity as something rigorously defined based on concepts from probability, information, and computability criteria, dynamic complexity is based on whether a system endogenously and deterministically generates erratically dynamic behavior of certain kinds. On such behavior is the phenomenon of emergence, the appearance of new forms or structures at higher levels of a system from processes occurring at lower levels. While the two concepts can overlap, they represent substantially different perspectives. A competition of sorts between them may become more important as new, computerized market systems emerge and evolve to higher levels of complexity of both kinds.

Fundamental properties of N-valued logics are compared and eleven theorems are presented for their Logic Algebras, including Łukasiewicz–Moisil Logic Algebras represented in terms of categories and functors. For example, the Fundamental Logic Adjunction Theorem allows one to transfer certain universal, or global, properties of the Category of Boolean Algebras.

Introduction to complexity and complex systems -- Introduction to large linear systems -- Introduction to biochemical oscillators and nonlinear biochemical systems -- Modularity, redundancy, degeneracy, pleiotropy and robustness in complex biological systems -- The evolution of biological complexity; invertebrate immune systems -- Irreducible and specified complexity in living systems -- The complex adaptive and innate human immune systems -- Complexity in quasispecies : microRNAs -- Introduction to complexity in economic systems -- Complexity in quasispecies : micrornas -- Dealing with complexity.

Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically (atom-molecule-organism). This is the first intuition of the theory of levels. Even if the further development of the theory will require imposing a number of qualifications to this initial intuition, the idea of a series of entities organized on different levels of complexity will prove correct. Living systems as well as social systems and the human mind present features remarkably different from those characterizing non-living, simple physical and chemical systems. We propose that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation.

A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a Łukasiewicz–Moisil Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology.

An overview of the following three related papers in this issue presents the Emergence of Highly Complex Systems such as living organisms, man, society and the human mind from the viewpoint of the current Ontological Theory of Levels. The ontology of spacetime structures in the Universe is discussed beginning with the quantum level; then, the striking emergence of the higher levels of reality is examined from a categorical—relational and logical viewpoint. The ontological problems and methodology aspects discussed in the first two papers are followed by a rigorous paper based on Category Theory, Algebraic Topology and Logic that provides a conceptual and mathematical basis for a Categorical Ontology Theory of Levels. The essential links and relationships between the following three papers of this issue are pointed out, and further possible developments are being considered.

A non-Abelian, Universal SpaceTime Ontology is introduced in terms of Categories, Functors, Natural Transformations, Higher Dimensional Algebra and the Theory of Levels. A Paradigm shift towards Non-Commutative Spacetime structures with remarkable asymmetries or broken symmetries, such as the CPT-symmetry violation, is proposed. This has the potential for novel applications of Higher Dimensional Algebra to SpaceTime structure determination in terms of universal, topological invariants of ‘hidden’ symmetry. Fundamental concepts of Quantum Algebra and Quantum Algebraic Topology, such as Quantum Groups, von Neumann and Hopf Algebras are first considered with a view to their possible extensions and future applications in Quantum Field theories. New, non-Abelian results may be obtained through Higher Homotopy, General van Kampen Theorems, Lie Groupoids/Algebroids and Groupoid Atlases, possibly with novel applications to Quantum Dynamics and Local-to-Global Problems, Quantum Logics and Logic Algebras. Many-valued Logics, Łukasiewicz–Moisil Logics lead to Generalized LM-Toposes as global representations of SpaceTime Structures in the presence of intense Quantum Gravitational Fields. Such novel representations have the potential to develop a Quantum/General Relativity Theory in the context of Supersymmetry, Supergravity, Supersymmetry Algebras and the Metric Superfield in the Planck limit of spacetime. Quantum Gravity and Physical Cosmology issues are also considered here from the perspective of multiverses, thus leading also to novel types of Generalized, non-Abelian, Topological, Higher Homotopy Quantum Field Theories (HHQFT) and Non-Abelian Quantum Algebraic Topology (NA-QAT) theories.

A categorical ontology of space and time is presented for emergent biosystems, super-complex dynamics, evolution and human consciousness. Relational structures of organisms and the human mind are naturally represented in non-abelian categories and higher dimensional algebra. The ascent of man and other organisms through adaptation, evolution and social co-evolution is viewed in categorical terms as variable biogroupoid representations of evolving species. The unifying theme of local-to-global approaches to organismic development, evolution and human consciousness leads to novel patterns of relations that emerge in super- and ultra- complex systems in terms of colimits of biogroupoids, and more generally, as compositions of local procedures to be defined in terms of locally Lie groupoids. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ may be found with the help of generalized van Kampen theorems in algebraic topology such as the Higher Homotopy van Kampen theorem (HHvKT). Primordial organism structures are predicted from the simplest metabolic-repair systems extended to self-replication through autocatalytic reactions. The intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution is investigated in terms of categories of many-valued, Łukasiewicz–Moisil logic algebras and then compared with those obtained for (non-commutative) quantum logics. The claim is defended in this essay that human consciousness is unique and should be viewed as an ultra-complex, global process of processes. The emergence of consciousness and its existence seem dependent upon an extremely complex structural and functional unit with an asymmetric network topology and connectivities—the human brain—that developed through societal co-evolution, elaborate language/symbolic communication and ‘virtual’, higher dimensional, non-commutative processes involving separate space and time perceptions. Philosophical theories of the mind are approached from the theory of levels and ultra-complexity viewpoints which throw new light on previous representational hypotheses and proposed semantic models in cognitive science. Anticipatory systems and complex causality at the top levels of reality are also discussed in the context of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. The presence of strange attractors in modern society dynamics gives rise to very serious concerns for the future of mankind and the continued persistence of a multi-stable biosphere. A paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics is suggested to unfold now in physics, mathematics, life and cognitive sciences, thus leading to the realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics.