Complex Systems Biology approaches are here considered from the viewpoint of Robert Rosen’s (M,R)-systems, Relational Biology and Quantum theory, as well as from the standpoint of computer modeling. Realizability and Entailment of (M,R)-systems are two key aspects that relate the abstract, mathematical world of organizational structure introduced by Rosen to the various physicochemical structures of complex biological systems. Their importance for understanding biological function and life itself, as well as for designing (...) new strategies for treating diseases such as cancers, is pointed out. The roles played by multiple metastable states in the “continuous uphill flow of Life” supported through internal bioenergetic processes that are coupled to essential inflows are also discussed in relation to dynamic realizations of (M,R)-systems. Furthermore, the roles played by the underlying, many-valued, quantum logics and symbolic computations for ultra-complex biological systems are also briefly discussed. (shrink)

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. (shrink)

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. (shrink)

According to the traditional nomological-deductive methodology of physics and chemistry [Hempel and Oppenheim, 1948], explaining a phenomenon means subsuming it under a law. Logic becomes then the glue of explanation and laws the primary explainers. Thus, the scientific study of a system would consist in the development of a logically sound model of it, once the relevant observables (state variables) are identified and the general laws governing their change (expressed as differential equations, state transition rules, maximization/minimization principles,. . . ) (...) are well determined, together with the initial or boundary conditions for each particular case. Often this also involves making a set of assumptions about the elementary components of the system (e.g., their structural and dynamic properties) and modes of local interaction. In this framework, predictability becomes the main goal and that is why research is carried out through the construction of accurate mathematical models. Thus, physics and chemistry have made most progress so far by focusing on systems that, either due to their intrinsic properties or to the conditions in which they are investigated, allow for very strong simplifying assumptions, under which, nevertheless, those highly idealized models of reality are deemed to be in good correspondence with reality itself. Despite the enormous success that this methodology has had, the study of living and cognitive phenomena had to follow a very different road, because these phenomena are produced by systems whose underlying material structure and organization do not permit such crude approximations. Seen from the perspective of physics or chemistry, biological and cognitive systems are made of an enormous number of parts or elements interacting in non-linear and selective ways, which makes very difficult their tractability through mathematical models. In addition, many of those interacting elements are hierarchically organized, in a way that the “macroscopic” (observable) parts behave according to rules that cannot be, in practice, derived from simple principles at the level of their “microscopic” dynamics.. (shrink)

All the typical global quantum mechanical observables are complex relative phases obtained by interference phenomena. They are described by means of some global geometric phase factor, which is thought of as the “memory” of a quantum system undergoing a “cyclic evolution” after coming back to its original physical state. The origin of a geometric phase factor can be traced to the local phase invariance of the transition probability assignment in quantum mechanics. Beyond this invariance, transition probabilities (...) also remain invariant under the operation of complex conjugation. Most important, geometric phase factors distinguish between unitary and antiunitary transformations in terms of complex conjugation. These two types of invariance functions as an anchor point to investigate the role of loops and based loops in the state space of a quantum system as well as their links and interrelations. We show that arbitrary transition probabilities can be calculated using projective invariants of loops in the space of rays. The case of the double slit experiment serves as a model for this purpose. We also represent the action of one-parameter unitary groups in terms of oppositely oriented-based loops at a fixed ray. In this context, we explain the relation among observables, local Boolean frames of projectors, and one-parameter unitary groups. Next, we exploit the non-commutative group structure of oriented-based loops in 3-d space and demonstrate that it carries the topological semantics of a Borromean link. Finally, we prove that there exists a representation of this group structure in terms of one-parameter unitary groups that realizes the topological linking properties of the Borromean link. (shrink)

Traditional approaches to modeling cognitive systems are computational, based on utilizing the standard tools and concepts of the theory of computation. More recently, a number of philosophers have argued that cognition is too subtle or complex for these tools to handle. These philosophers propose an alternative based on dynamical systems theory. Proponents of this view characterize dynamical systems as (i) utilizing continuous rather than discrete mathematics, and, as a result, (ii) being computationally more powerful than traditional (...) computational automata. Indeed, the logical possibility of such super-powerful systems has been demonstrated in the form of analog artificial neural networks. In this paper I consider three arguments against the nomological possibility of these automata. While the first two arguments fail, the third succeeds. In particular, the presence of noise reduces the computational power of analog networks to that of traditional computational automata, and noise is a pervasive feature of information processing in biological systems. Consequently, as an empirical thesis, the proposed dynamical alternative is under-motivated: What is required is an account of how continuously valued systems could be realized in physical systems despite the ubiquity of noise. (shrink)

The paper discusses how systems biology is working toward complex accounts that integrate explanation in terms of mechanisms and explanation by mathematical models—which some philosophers have viewed as rival models of explanation. Systems biology is an integrative approach, and it strongly relies on mathematical modeling. Philosophical accounts of mechanisms capture integrative in the sense of multilevel and multifield explanations, yet accounts of mechanistic explanation have failed to address how a mathematical model could contribute to such (...) explanations. I discuss how mathematical equations can be explanatorily relevant. Several cases from systems biology are discussed to illustrate the interplay between mechanistic research and mathematical modeling, and I point to questions about qualitative phenomena, where quantitative models are still indispensable to the explanation. Systems biology shows that a broader philosophical conception of mechanisms is needed, which takes into account functional-dynamical aspects, interaction in complex networks with feedback loops, system-wide functional properties such as distributed functionality and robustness, and a mechanism’s ability to respond to perturbations. I offer general conclusions for philosophical accounts of explanation. (shrink)

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures (...) that emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)

A decade ago, Isham and Butterfield proposed a topos-theoretic approach to quantum mechanics, which meanwhile has been extended by Döring and Isham so as to provide a new mathematical foundation for all of physics. Last year, three of the present authors redeveloped and refined these ideas by combining the C*-algebraic approach to quantum theory with the so-called internal language of topos theory (Heunen et al. in arXiv:0709.4364). The goal of the present paper is to illustrate our abstract setup (...) through the concrete example of the C*-algebra M n (ℂ) of complex n×n matrices. This leads to an explicit expression for the pointfree quantum phase space Σ n and the associated logical structure and Gelfand transform of an n-level system. We also determine the pertinent non-probabilisitic state-proposition pairing (or valuation) and give a very natural topos-theoretic reformulation of the Kochen–Specker Theorem.In our approach, the nondistributive lattice ℘(M n (ℂ)) of projections in M n (ℂ) (which forms the basis of the traditional quantum logic of Birkhoff and von Neumann) is replaced by a specific distributive lattice $\mathcal{O}(\Sigma_{n})$ of functions from the poset $\mathcal{C}(M_{n}(\mathbb{C}))$ of all unital commutative C*-subalgebras C of M n (ℂ) to ℘(M n (ℂ)). The lattice $\mathcal{O}(\Sigma_{n})$ is essentially the (pointfree) topology of the quantum phase space Σ n , and as such defines a Heyting algebra. Each element of $\mathcal{O}(\Sigma_{n})$ corresponds to a “Bohrified” proposition, in the sense that to each classical context $C\in\mathcal{C}(M_{n}(\mathbb{C}))$ it associates a yes-no question (i.e. an element of the Boolean lattice ℘(C) of projections in C), rather than being a single projection as in standard quantum logic. Distributivity is recovered at the expense of the law of the excluded middle (Tertium Non Datur), whose demise is in our opinion to be welcomed, not just in intuitionistic logic in the spirit of Brouwer, but also in quantum logic in the spirit of von Neumann. (shrink)

The philosophical logic of Stéphane Lupasco, based on the principles of dynamic opposition and a law of the included middle, offers a needed alternative to the still quasi-exclusive application of classical, binary logic to post-classical natural and social sciences, art theory and political and social action. The system of Lupasco, extended by Basarab Nicolescu by the principle of levels of reality, is grounded in the major discoveries in quantum physics, biology, mathematics and systems science of the twentieth (...) century. It leads to a conception of the unity of knowledge and to a rigorous description of the dynamics of the highest human faculties of consciousness, art and social justice. As one of the ‘pillars’ of transdisciplinarity, this logic provides an interpretation of the fundamental modes of functioning of the physical and mental universes and the emergence of the new reality of ‘cyber-space-time’. The argument is made that an understanding of the underlying logic is essential to the transdisciplinary perspective, practice and attitude. The concepts of Lupasco and Nicolescu are thus relevant to issues discussed in Technoetic Arts. (shrink)

An analysis of two heuristic strategies for the development of mechanistic models, illustrated with historical examples from the life sciences. In Discovering Complexity, William Bechtel and Robert Richardson examine two heuristics that guided the development of mechanistic models in the life sciences: decomposition and localization. Drawing on historical cases from disciplines including cell biology, cognitive neuroscience, and genetics, they identify a number of "choice points" that life scientists confront in developing mechanistic explanations and show how different choices result in (...) divergent explanatory models. Describing decomposition as the attempt to differentiate functional and structural components of a system and localization as the assignment of responsibility for specific functions to specific structures, Bechtel and Richardson examine the usefulness of these heuristics as well as their fallibility—the sometimes false assumption underlying them that nature is significantly decomposable and hierarchically organized. When Discovering Complexity was originally published in 1993, few philosophers of science perceived the centrality of seeking mechanisms to explain phenomena in biology, relying instead on the model of nomological explanation advanced by the logical positivists (a model Bechtel and Richardson found to be utterly inapplicable to the examples from the life sciences in their study). Since then, mechanism and mechanistic explanation have become widely discussed. In a substantive new introduction to this MIT Press edition of their book, Bechtel and Richardson examine both philosophical and scientific developments in research on mechanistic models since 1993. (shrink)

Woodger first gives a rough account of the "Boole-Frege" movement in modern logic and persuasively argues as to the importance of formalized language-systems for the methodology of science. Some of these arguments are as follows: A natural language such as English, he notes, "is not only used for purposes of communication in the scientific sense. It is also used for the writing of poetry, for religious devotion, for political controversy, and for persuading people to buy some of the products (...) of industrial activity which they would not otherwise want. But these pursuits make demands upon language which are very different from those made by science. The requirements of science prove on investigation to be quite surprisingly meagre and the excessive riches of a natural language like English are a source of embarrassment. They tempt us to employ linguistic devices borrowed from extra-scientific usages which can have unfortunate consequences. Metaphors, for example, with which some branches of biology abound, are often suggestive and may be harmless enough if they are recognized for what they are. But at best they are makeshifts and substitutes for genuine biological statements, and the fact that recourse is had to them is surely a sign of immaturity. Science demands great linguistic austerity and discipline, and the canons of good style in scientific writing are different from those of good writing in other kinds of literature." Another argument is that "sooner or later the linguistic habits of everyday life will cease to do justice to... the... increasing complexity and novelty of observation and hypothesis." A third argument is that scientific language is used not only for the purpose of communication, for recording observations, or for formulating general laws or hypotheses. It is also used for calculation and the unearthing of the consequences of our assumptions. The logic underlying a formalized language is explicitly designed to enable us to calculate easily and efficiently. The important, and now thoroughly established, methodological distinction between object-language and meta-language is blurred for natural language and is best maintained in terms of formalized language-systems. And, finally, in natural language the important distinction between syntax and semantics also tends to be blurred. "From both the syntactical and the semantical points of view natural languages are incredibly complicated and unruly. The rules of ordinary gram mar are quite insufficient from the standpoint of the requirements of science, and the problems connected with meaning and truth in relation to natural languages are enormously complicated and perhaps insoluble.". (shrink)

We argue that cognitive functions are not reducible to biological functionality. Since only neural animals can develop complex forms of agency, we assume that genuinely cognitive processes are deeply related with the activity of the nervous system. We first analyze the significance of the appearance of the nervous system in certain multicellular organisms, arguing that it has changed the logic of their biological organization. Then, we focus on the appearance of specifically cognitive capacities within the nervous system. Considering a (...) case of a minimal form of perceptual representation, we analyze the specific functional role of this minimal form of activity in relatively earlier nervous systems, arguing that though this role is only understandable within a biological organization, yet it is not reducible to the underlying biological functionality. Finally, we conclude that the appearance of cognition is in turn linked to the emergence of an autonomous neurodynamic domain and a qualitative change in body complexity. (shrink)

The entry of time and history into biological systems of classification is perhaps the single most significant development in the history of biological systematics in the modern era. Darwin's claiming that descent is ‘… the hidden bond of connexion which naturalists have been seeking under the term of the natural system’, rather than seeing the answer in the multitude of previous attempts to resolve the problem in terms of morphological affinities, analogies, and complex relations of resemblance, marked the (...) turning point in a long search into the meaning of biological taxonomy, and allowed the development of Darwin's insights by Haeckel, Plate and others into modern phylogenetic systematics. (shrink)

" The best way to predict the future is to invent it. —Alan Kay _1_ It is obvious that there are patterns of cultural change—evolution in the neutral sense—and any theory of cultural change worth more than a moment's consideration will have to be Darwinian in the minimal sense of being consistent with the theory of evolution by natural selection of Homo sapiens. —Daniel Dennett _2_ The future is here. It's just not widely distributed yet. —William Gibson _3_ It is (...) the magician's wand, by means of which he may summon into life whatever form and mould he pleases. —Charles Darwin commenting on the power of artificial selection _4_ " This article introduces an applied Theory of Evolution of Artificial Systems, called Directed Evolution. The theory is grounded in fifty years of research on Inventive Engineering known as TRIZ, which started in the former Soviet Union by G. Altshuller and continues today. The theory has generated a set of Patterns and Lines of Evolution that represent a compilation of trends that document strong, historically recurring tendencies in the development of manmade systems in general and technological systems in particular. Directed Evolution is the systematic applied-oriented process for “predicting” future generations of a system by inventing them along these evolutionary patterns. The current article introduces the theory, reflects on its basic underlying logic, and provides a broad historical context and intellectual justification for such an effort. It shows that the quest of DE theory and practice falls well within the boundaries of past pursuits to identify evolutionary patterns of complex systems and to use these patterns to control and manipulate possible futures of artificial systems. (shrink)

Living systems employ several mechanisms and behaviors to achieve robustness and maintain themselves under changing internal and external conditions. Regulation stands out from them as a specific form of higher-order control, exerted over the basic regime responsible for the production and maintenance of the organism, and provides the system with the capacity to act on its own constitutive dynamics. It consists in the capability to selectively shift between different available regimes of self-production and self-maintenance in response to specific signals (...) and perturbations, due to the action of a dedicated subsystem which is operationally distinct from the regulated ones. The role of regulation, however, is not exhausted by its contribution to maintain a living system’s viability. While enhancing robustness, regulatory mechanisms play a fundamental role in the realization of an autonomous biological organization. Specifically, they are at the basis of the remarkable integration of biological systems, insofar as they coordinate and modulate the activity of distinct functional subsystems. Moreover, by implementing complex and hierarchically organized control architectures, they allow for an increase in structural and organizational complexity while minimizing fragility. Finally, they endow living systems, from their most basic unicellular instances, with the capability to control their own internal dynamics to adaptively respond to specific features of their interaction with the environment, thus providing the basis for the emergence of minimal forms of cognition. (shrink)

We argue that living systems process information such that functionality emerges in them on a continuous basis. We then provide a framework that can explain and model the normativity of biological functionality. In addition we offer an explanation of the anticipatory nature of functionality within our overall approach. We adopt a Peircean approach to Biosemiotics, and a dynamical approach to Digital-Analog relations and to the interplay between different levels of functionality in autonomous systems, taking an integrative approach. We (...) then apply the underlying biosemiotic logic to a particular biological system, giving a model of the B-Cell Receptor signaling system, in order to demonstrate how biosemiotic concepts can be used to build an account of biological information and functionality. Next we show how this framework can be used to explain and model more complex aspects of biological normativity, for example, how cross-talk between different signaling pathways can be avoided. Overall, we describe an integrated theoretical framework for the emergence of normative functions and, consequently, for the way information is transduced across several interconnected organizational levels in an autonomous system, and we demonstrate how this can be applied in real biological phenomena. Our aim is to open the way towards realistic tools for the modeling of information and normativity in autonomous biological agents. (shrink)

Willard van Orman Quine once said that he had a preference for a desert ontology. This was in an earlier day when concerns with logical structure and ontological simplicity reigned supreme. Ontological genocide was practiced upon whole classes of upper-level or ‘derivative’ entities in the name of elegance, and we were secure in the belief that one strayed irremediably into the realm of conceptual confusion and possible error the further one got from ontic fundamentalism. In those days, one paid more (...) attention to generic worries about possible errors than to actual errors derived from distancing oneself too far from the nitty-gritty details of actual theory, actual inferences from actual data, the actual conditions under which we posited and detected entities, calibrated and ‘burned in’ instruments, identified and rejected artifacts, debugged programs and procedures, explained the mechanisms behind regularities, judged correlations to be spurious, and in general, to the real complexities and richness of actual scientific practice. (shrink)

Due to the variation, contingency and complexity of living systems, biology is often taken to be a science without fundamental theories, laws or general principles. I revisit this question in light of the quest for design principles in systems biology and show that different views can be reconciled if we distinguish between different types of generality. The philosophical literature has primarily focused on generality of specific models or explanations, or on the heuristic role of abstraction. This (...) paper takes a different approach in emphasizing a theory-constituting role of general principles. Design principles signify general dependency-relations between structures and functions, given a set of formally defined constraints. I contend that design principles increase our understanding of living systems by relating specific models to general types. The categorization of types is based on a delineation of the scope of biological possibilities, which serves to identify and define the generic features of classes of systems. To characterize the basis for general principles through generic abstraction and reasoning about possibility spaces, I coin the term constraint-based generality. I show that constraint-based generality is distinct from other types of generality in biology, and argue that general principles play a unifying role that does not entail theory reduction. (shrink)

The unreduced many-body interaction problem solution, absent in usual science framework, reveals a new quality of emerging multiple, equally real but mutually incompatible system configurations, or “realisations”, giving rise to the universal concept of dynamic complexity and chaoticity. Their imitation by a single, “average” realisation or trajectory in usual theory (corresponding to postulated “exact” or perturbative problem solutions) is a rough simplification of reality underlying all stagnating and emerging problems of conventional (unitary) science, often in the form of missing, (...) or “dark”, entities and “hidden variables”. We show how the application of unreduced interaction problem solution and the ensuing concept of dynamic complexity provides the desired causally complete and intrinsically unified solutions to respective unitary science problems in the entire range of complexity levels, from elementary particles and cosmology to emergent consciousness and modern development crisis, implying real, essential and urgently needed progress. (shrink)

This contribution is an essay of formal philosophy—and more specifically of formal ontology and formal epistemology—applied, respectively, to the philosophy of nature and to the philosophy of sciences, interpreted the former as the ontology and the latter as the epistemology of the modern mathematical, natural, and artificial sciences, the theoretical computer science included. I present the formal philosophy in the framework of the category theory (CT) as an axiomatic metalanguage—in many senses “wider” than set theory (ST)—of mathematics and logic, both (...) of the “extensional” logics of the pure and applied mathematical sciences (=mathematical logic), and the “intensional” modal logics of the philosophical disciplines (=philosophical logic). It is particularly significant in this categorical framework the possibility of extending the operator algebra formalism from (quantum and classical) physics to logic, via the so-called “Boolean algebras with operators” (BAOs), with this extension being the core of our formal ontology. In this context, I discuss the relevance of the algebraic Hopf coproduct and colimit operations, and then of the category of coalgebras in the computations over lattices of quantum numbers in the quantum field theory (QFT), interpreted as the fundamental physics. This coalgebraic formalism is particularly relevant for modeling the notion of the “quantum vacuum foliation” in QFT of dissipative systems, as a foundation of the notion of “complexity” in physics, and “memory” in biological and neural systems, using the powerful “colimit” operators. Finally, I suggest that in the CT logic, the relational semantics of BAOs, applied to the modal coalgebraic relational logic of the “possible worlds” in Kripke’s model theory, is the proper logic of the formal ontology and epistemology of the natural realism, as a formalized philosophy of nature and sciences. (shrink)

"The question of complex systems is relatively new for critics today. Analyzing complex systems in Renaissance texts shows that the Christian kabbalistical concept of harmonia mundi led to an aesthetical development, reflecting the worldview of harmonious parallel worlds. Failure to perceive the esoteric text uniting apparently contradicting themes has often led Renaissance scholars to elaborate a theory of the instability of atmospheres characterizing the English Baroque. This article gives an example of a complex system in (...) Shakespeare's Antony and Cleopatra revealing that the Christian kabbalistical Hercules unifies contradicting metaphors and intertexts of the play, and reintegrates this work in a form of semantic stability more in harmony with the aesthetics of its time. In the case of postmodern literature, contradictory intertexts appear as a device to deconstruct all values and logic previously established. With the study of a text structured by the optical questions around the refraction of light, this paper shows that in the case of Nabokov, the unifying system of apparently contradicting semantic systems is the underlying logic of scientific theory. In Nabokov's text, failing to perceive the fundamental intertext of scientific debate leads one to assimilate Nabokov's writing to a form of postmodern deconstruction. Both cases studied tend to show a continuity of a form of aesthetics through different epistemological eras.". (shrink)

In their recent book, Ladyman and Wiesner (What is a complex system?, Yale University Press, 2020) delineate the bounds of the exciting interdisciplinary field of complexity science. In this work, they provide examples of generally accepted complex systems and common features which these possess to varying degrees. In this paper, I plan to extend their list to include the formal study of natural language, i.e. linguistics. In fact, I will argue that language exhibits many of the hallmarks (...) of a complex system, specifically a complex biological system. Thus, my aim is to advocate contra the the ‘Minimalist Program’ (Chomsky, The minimalist program, MIT Press, Cambridge, 1995), which motivates simple underlying mechanisms (i.e. Merge) in their idealisations, that biolinguistics should embrace a ‘Maximalist Program’ in which multiple subfields contribute component explanations to an emerging whole. (shrink)

Many scientific models in biology are how-possibly models. These models depict things as they could be, but do not necessarily capture actual states of affairs in the biological world. In contemporary philosophy of science, it is customary to treat how-possibly models as second-rate theoretical tools. Although possibly important in the early stages of theorizing, they do not constitute the main aim of modelling, namely, to discover the actual mechanism responsible for the phenomenon under study. In the paper it is (...) argued that this prevailing picture does not do justice to the synthetic strategy that is commonly used in biological engineering. In synthetic biology, how-possibly models are not simply speculations or eliminable scaffolds towards a single how-actually model, but indispensable design hypotheses for a field whose ultimate goal is to build novel biological systems. The paper explicates this by providing an example from the study of alternative genetic systems by synthetic biologist Steven Benner and his group. The case will also highlight how the method of synthesis, even when it fails, provides an effective way to limit the space of possible models for biological systems. (shrink)

Change is the fundamental idea of evolution. Explaining the extraordinary biological change we see written in the history of genomes and fossil beds is the primary occupation of the evolutionary biologist. Yet it is a surprising fact that for the majority of evolutionary research, we have rarely studied how evolution typically unfolds in nature, in changing ecological environments, over space and time. While ecology played a major role in the eventual acceptance of the population genetic viewpoint of evolution in the (...) synthetic era (circa 1918-1956), it held a lesser role in the development of evolutionary theory until the 1980s, when we began to systematically study the evolutionary dynamics of natural populations in space and time. As a result, early evolutionary theory was initially constructed in an abstract vacuum that was unrepresentative of evolution in nature. The subtle synthesis between ecology with evolutionary biology (eco-evo synthesis) over the past 40 years has progressed our knowledge of natural selection dynamics as they are found in nature, thus revealing how natural selection varies in strength, direction, form, and, more surprisingly, level of biological organization. Natural selection can no longer be reduced to lower levels of biological organization (i.e., individuals, selfish genes) over shorter timescales but should be expanded to include adaptation at higher levels and over longer timescales. Long-term and/or emergent evolutionary phenomena, such as multilevel selection or evolvability, have thus become tenable concepts within an evolutionary biology that embraces ecology and spatiotemporal change. Evolutionary biology is currently suspended at an intermediate stage of scientific progress that calls for the organization of all the recent knowledge revealed by the eco-evo synthesis into a coherent and unified theoretical framework. This is where philosophers of biology can be of particular use, acting as a bridge between the subdisciplines of biology and inventing new theoretical strategies to organize and accommodate the recent knowledge. Philosophers have recommended transitioning away from outdated philosophies that were originally derived from physics within the philosophical zeitgeist of logical positivism (i.e., monism, reductionism, and monocausation) and toward a distinct philosophy of biology that can capture the natural complexity of multifaceted biological systems within diverse ecosystems—one that embraces the emerging philosophies of pluralism, emergence, and multicausality. Therefore, I see recent advances in ecology, evolutionary biology, and the philosophy of biology as laying the groundwork for another major biological synthesis, what I refer to as the Second Synthesis because, in many respects, it is analogous to the aims and outcomes of the first major biological synthesis (but is notably distinct from the inorganic and contrived progressive movement known as the extended evolutionary synthesis). With the general development of a distinctive philosophy of science, biology has rightfully emerged as an autonomous science. Thus, while the first synthesis legitimized biology, the Second Synthesis autonomized biology and afforded biology its own philosophy, allowing biology to finally realize its full scientific potential. (shrink)

Living systems employ several mechanisms and behaviors to achieve robustness and maintain themselves under changing internal and external conditions. Regulation stands out from them as a specific form of higher-order control, exerted over the basic regime responsible for the production and maintenance of the organism, and provides the system with the capacity to act on its own constitutive dynamics. It consists in the capability to selectively shift between different available regimes of self-production and self-maintenance in response to specific signals (...) and perturbations, due to the action of a dedicated subsystem which is operationally distinct from the regulated ones. The role of regulation, however, is not exhausted by its contribution to maintain a living system’s viability. While enhancing robustness, regulatory mechanisms play a fundamental role in the realization of an autonomous biological organization. Specifically, they are at the basis of the remarkable integration of biological systems, insofar as they coordinate and modulate the activity of distinct functional subsystems. Moreover, by implementing complex and hierarchically organized control architectures, they allow for an increase in structural and organizational complexity while minimizing fragility. Finally, they endow living systems, from their most basic unicellular instances, with the capability to control their own internal dynamics to adaptively respond to specific features of their interaction with the environment, thus providing the basis for the emergence of minimal forms of cognition. (shrink)

At the core of anthropomorphism lies a false-positive cognitive bias to over-attribute the pattern of the human body and/or mind. Anthropomorphism is independently discussed in various disciplines, is presumed to have deep biological roots, but its cognitive bases are rarely explored in an integrative way. I present an inclusive, multifaceted interdisciplinary approach to refine the psychological bases of mental anthropomorphism. I have integrated 13 conceptual dissections of folk finalistic reasoning into four psychological inference systems (physical, design, basic-goal and belief (...) stances); the latter three are truly teleological and thus prone to anthropomorphisms. I then have empirically integrated the cross-disciplinary genetic, neural, cognitive, psychiatric, developmental, comparative and evolutionary/adaptive evidence that converge supporting the nature of the distinct stances. The over-reactive calibration of the three teleological systems is framed as an evolved design feature to avoid harmful ancestral contexts. Nowadays, these stances easily engage with scientific reasoning about bio-evolutionary matters with negative and positive consequences. Design, basic-goal, and belief stances benefit biology by providing cognitive foundations, expressing a high-powered explanatory system, promoting functional generalization, fostering new research questions and discoveries, enabling metaphorical/analogical thinking and explaining didactically with brevity. Hence, it is neither feasible nor advantageous to completely eliminate teleology from biology. Instead, we should engage with the eight classes of problems in bio-philosophy and bio-education that relate to the three stances: types of anthropomorphism, variety of misunderstandings, misleading appeal, legitimacy controversy, gateway to mysticism, total prohibition and its backfire effect. Recognizing the distinction among design, basic-goal, and belief stances helps to elucidate much of the logic underlying these issues, so that it enables a much more detailed taxonomy of anthropomorphisms, and organizes the various misunderstandings about evolution by natural selection. It also offers a solid psychological grounding for anchoring definitions and terminology. This tripartite framework also shed some light on how to better deal with the over-reactive stances in bio-education, by organizing previous pedagogical strategies and by suggesting new possibilities to be tested. Therefore, this framework constitutes a promising approach to advance the debate regarding the psychological underpinnings of anthropomorphisms and to further support regulating and clarifying teleology and anthropomorphism in biology. (shrink)

By quoting extensively from unpublished letters written by John von Neumann to Garret Birkhoff during the preparatory phase (in 1935) of their ground-breaking 1936 paper that established quantum logic, the main steps in the thought process leading to the 1936 Birkhoff–von Neumann paper are reconstructed. The reconstruction makes it clear why Birkhoff and von Neumann rejected the notion of quantum logic as the projection lattice of an infinite dimensional complex Hilbert space and why they postulated in their (...) 1936 paper that the quantum propositional system should be isomorphic to an abstract projective geometry. Looking at the paper now I see, that I forgot to say this, which should be said somewhere in the first §: That while common logics did apply to quantum mechanics, if the notion of simultaneous measurability is introduced as an auxiliary notion, we wished to construct a logical system, which applies directly to quantum mechanics – without any extraneous secondary notions like simultaneous measurability. And in order to have such a consequent, one-piece system of logics, we must change the classical class calculus of logics. (J. von Neumann to G. Birkhoff, November 21, 1935). (shrink)

The logic of genetic discovery has changed little over time, but the focus of biology is shifting from simple genotype–phenotype relationships to complex metabolic, physiological, developmental, and behavioral traits. In light of this, the traditional reductionist view of individual genes as privileged difference‐making causes of phenotypes is re‐examined. The scope and nature of genetic effects in complex regulatory systems, in which dynamics are driven by regulatory feedback and hierarchical interactions across levels of organization are considered. This (...) review argues that it is appropriate to treat genes as specific actual difference‐makers for the molecular regulation of gene expression. However, they are often neither stable, proportional, nor specific as causes of the overall dynamic behavior of regulatory networks. Dynamical models, properly formulated and validated, provide the tools to probe cause‐and‐effect relationships in complex biological systems, allowing to go beyond the limitations of genetic reductionism to gain an integrative understanding of the causal processes underlying complex phenotypes. (shrink)

Systems architecture and its associated parallel biology generate architectural forms that are both green and surreal by nature. The connection between systems architecture and Leo Lionni's fantastic book Parallel Botany are considered as architects are now starting to have the ability to create great works of biological parallelism using technologies that are highly sur real, they are on top of the real.

In this article I argue that there is a sense in which logic is empirical, and hence open to influence from science. One of the roles of logic is the modelling and extending of natural language reasoning. It does so by providing a formal system which succeeds in modelling the structure of a paradigmatic set of our natural language inferences and which then permits us to extend this structure to novel cases with relative ease. In choosing the best system of (...) those that succeed in this, we seek certain virtues of such structures such as simplicity and naturalness (which will be explained). Science can influence logic by bringing us, as in the case of quantum mechanics, to make natural language inferences about new kinds of systems and thereby extend the set of paradigmatic cases that our formal logic ought to model as simply and naturally as possible. This can alter which structures ought to be used to provide semantics for such models. I show why such a revolution could have led us to reject one logic for another through explaining why complex claims about quantum mechanical systems failed to lead us to reject classical logic for quantum logic. (shrink)

We address the question of whether and to what extent explanatory and modelling strategies in systems biology are mechanistic. After showing how dynamic mathematical models are actually required for mechanistic explanations of complex systems, we caution readers against expecting all systems biology to be about mechanistic explanations. Instead, the aim may be to generate topological explanations that are not standardly mechanistic, or to arrive at design principles that explain system organization and behaviour in general, (...) but not specific mechanisms. These abstraction strategies serve various aims, including prediction and control, that are central to understanding the epistemic diversity of systems biology. (shrink)

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. (shrink)

Biomedical research is increasingly a matter of the navigation through large computerized information resources deriving from functional genomics or from the biochemistry of disease pathways. To make such navigation possible, controlled vocabularies are needed in terms of which data from different sources can be unified. One of the most influential developments in this regard is the so-called Gene Ontology, which consists of controlled vocabularies of terms used by biologists to describe cellular constituents, biological processes and molecular functions, organized into hierarchies (...) via the relation of class subsumption. Here we seek to provide a rigorous account of the logic of classification that underlies GO and similar biomedical ontologies. Drawing on Aristotle, we develop a system of axioms and definitions for the treatment of biological classes and instances. (shrink)

When a group of processes achieves such closure that a set of states of affairs recurs continually, then the effect of that coherence on the world differs from what would occur in the absence of that closure. Such altered effectiveness is an attribute of the system as a whole, and would have consequences. This indicates that the network of processes, as a unit, has ontological significance. Whenever a network of processes generates continual return to a limited set of states of (...) affairs, the system may function as a “whole”— with respect to appropriate interaction partners. The balance achieved by the processes provides the form of definiteness of a unified agent. The causal powers of such coherent aggregates are indeed just the powers of the “constituents acting in concert”. However, the components act in concert in the specific way they do only because of their inclusion in the closed set of interactions that defines the coherence. This renders the causal powers of the coherence defined by that closure non-redundant, and hence the coherence, as a unit, is ontologically significant. The form of definiteness that provides internal coherence also grounds external efficacy of the societal aggregation. The closure is a structural feature of the coherence — possibly, but not necessarily, apparent in spatial structuring. This approach can provide a unified account that includes quantum microphysics, systems biology, and the philosophy of organism ─ without reducing any of these to another. (shrink)

Until the late 19th century scientists almost always assumed that the world could be described as a rule-based and hence deterministic system or as a set of such systems. The assumption is maintained in many 20th century theories although it has also been doubted because of the breakthrough of statistical theories in thermodynamics (Boltzmann and Gibbs) and other fields, unsolved questions in quantum mechanics as well as several theories forwarded within the social sciences. Until recently it has furthermore (...) been assumed that a rule-based and deterministic system was also predictable if only the rules were known, but this assumption has now been undermined by modern chaos-theory describing rule-based and deterministic, but unpredictable systems, while catastrophe-theory delivers a set of types describing various kinds of instability and conditions for the stability of a given system. Hence the main trait in the theoretical development in the 20th-century science can be described as a basic modification and limitation of some of the fundamental and strong assumptions forwarded in the previous epochs of modern science. Ironically, the very same process has been a process in which the human capacity to intervene in nature has expanded dramatically and mainly with the help of the very same theories, and not least because they allow nature to be described and made manipulable on a lower level and a more fine-grained scale. While the overall theoretical consistency between the various theories has gone, the reach of human intervention in nature has increased based on quite new dimensions whether in the area of physics (e.g.: energy technologies, chemical technologies, nanotechnologies etc.) or biology (ge¬netic manipulation) or in the area of psychology, sociology and culture (artificial simulations of mental processes, new means of communication, implying changes in the social infrastructure and cultural behaviour etc.). While some of these changes and new conditions can be reflected from within the conceptual framework of rule-based systems, albeit more complex than formerly recognized, others seem to give rise to the question of whether there are »systems« and relations between different systems in the world which are not rule-based? For instance, it seems to be obvious that the notion of instability represents a major conceptual break with former theories of rule-based systems, as the stability of the latter is an axiomatically given property implied in the very notion of rule-based systems, while instability can only be the result of external influence which should be explained as the result of another rule-based sy¬stem. While there are no difficulties implied concerning the stability of rule-based systems, the notion of unstable states of a system raises the question of how there can be a system at all if there are no invariant stabilising principles? This is the first question which I will address. And I shall do so by taking two examples of such systems as my point of departure. The first example will be the computer and the second will be ordinary language. In both cases I will argue that the stability of these systems (which are both defined by the existence/presence of human intentions) are provided by the help of - differently organised - redundancy functions which both allow the maintenance of systems in unstable macro-states, suspension of previous rules, underdetermination and overdetermination and generation/emergence/creation of new rules more or less independent of previous rules by the help of optional recursions to the permanently accessible underlying levels as for instance the level of binary representation in computers. Since the notion of redundancy is both controversial as such and often avoided, the concept is discussed (as defined in Claude Shannon's mathematical theory of information and in the semiotic framework of J. J. Greimas) and leading to a more general definition in which the redundancy functions serve to overcome noisy conditions, but at the cost of rule-based stability, determination, and predictability. A second question will be how the notion of rule-generating systems relates to the notion of anticipatory systems and it will be argued that rule-generating systems share some features with an¬ticipatory systems and that the former from a certain viewpoint can be seen as a subclass of the latter, although anticipative features are not necessarily a part of the definition of rule-generating systems. On the other hand, it will be discussed whether anticipatory systems which are not rule-generating systems can exist and it will be argued that the capacity to anticipate is strongly limited if it is not part of a rule-generating system. Therefore, it is concluded that the most powerful anticipatory systems need to be rule-generating systems. (shrink)

We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore how probabilistic reasoning under coherence is related to model- theoretic probabilistic reasoning and to default reasoning in System . In particular, we show that the notions of g-coherence and of g-coherent entailment can be expressed by combining notions in model-theoretic probabilistic logic with concepts from default reasoning. Moreover, we show that probabilistic reasoning under coherence is a generalization of default reasoning in System (...) . That is, we provide a new probabilistic semantics for System , which neither uses infinitesimal probabilities nor atomic bound (or big-stepped) probabilities. These results also provide new algorithms for probabilistic reasoning under coherence and for default reasoning in System , and they give new insight into default reasoning with conditional objects. (shrink)

In this work we present a dynamical approach to quantum logics. By changing the standard formalism of quantum mechanics to allow non-Hermitian operators as generators of time evolution, we address the question of how can logics evolve in time. In this way, we describe formally how a non-Boolean algebra may become a Boolean one under certain conditions. We present some simple models which illustrate this transition and develop a new quantum logical formalism based in (...) class='Hi'>complex spectral resolutions, a notion that we introduce in order to cope with the temporal aspect of the logical structure of quantum theory. (shrink)

Logical matrices for orthomodular logic are introduced. The underlying algebraic structures are orthomodular lattices, where the conditional connective is the Sasaki arrow. An axiomatic calculusOMC is proposed for the orthomodular-valid formulas.OMC is based on two primitive connectives — the conditional, and the falsity constant. Of the five axiom schemata and two rules, only one pertains to the falsity constant. Soundness is routine. Completeness is demonstrated using standard algebraic techniques. The Lindenbaum-Tarski algebra ofOMC is constructed, and it is shown to (...) be an orthomodular lattice whose unit element is the equivalence class of theses ofOMC. (shrink)

In this paper we explore the possibility of giving a justification of the “semantic information” content and measure, in the framework of the recent coalgebraic approach to quantum systems and quantum computation, extended to QFT systems. In QFT, indeed, any quantum system has to be considered as an “open” system, because it is always interacting with the background fluctuations of the quantum vacuum. Namely, the Hamiltonian in QFT always includes the quantum system and (...) its inseparable thermal bath, formally “entangled” like an algebra with its coalgebra, according to the principle of the “doubling” of the degrees of freedom between them. This is the core of the representation theory of cognitive neuroscience based on QFT. Moreover, in QFT, the probabilities of the quantum states follow a Wigner distribution, based on the notion and measure of quasiprobability, where regions integrated under given expectation values do not represent mutually exclusive states. This means that a computing agent, either natural or artificial, in QFT, against the quantum Turing machine paradigm, is able to change dynamically the representation space of its computations. This depends on the possibility of interpreting QFT system computations within the framework of category theory logic and its principle of duality between opposed categories, such as the algebra and coalgebra categories of QFT. This allows us to justify and not only to suppose, like in the “theory of strong semantic information” of L. Floridi, the definition of modal “local truth” and the notion of semantic information as a measure of it, despite both measures being defined on quasiprobability distributions. (shrink)

This paper discusses the epistemic status of biology from the standpoint of the systemic approach to living systems based on the notion of biological autonomy. This approach aims to provide an understanding of the distinctive character of biological systems and this paper analyses its theoretical and epistemological dimensions. The paper argues that, considered from this perspective, biological systems are examples of emergent phenomena, that the biological domain exhibits special features with respect to other domains, and that (...) biology as a discipline employs some core concepts, such as teleology, function, regulation among others, that are irreducible to those employed in physics and chemistry. It addresses the claim made by Jacques Monod that biology as a science is marginal. It argues that biology is general insofar as it constitutes a paradigmatic example of complexity science, both in terms of how it defines the theoretical object of study and of the epistemology and heuristics employed. As such, biology may provide lessons that can be applied more widely to develop an epistemology of complex systems. (shrink)

In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as computational (...) models of human cognitive capacities. One interesting area of computational complexity theory is descriptive complexity, which connects the expressive strength of systems of logic with the computational complexity classes. In descriptive complexity theory, it is established that only first-order systems are connected to P, or one of its subclasses. Consequently, second-order systems of logic are considered to be computationally intractable, and may therefore seem to be unfit to model human cognitive capacities. This would be problematic when we think of the role of logic as the foundations of mathematics. In order to express many important mathematical concepts and systematically prove theorems involving them, we need to have a system of logic stronger than classical first-order logic. But if such a system is considered to be intractable, it means that the logical foundation of mathematics can be prohibitively complex for human cognition. In this paper I will argue, however, that this problem is the result of an unjustified direct use of computational complexity classes in cognitive modelling. Placing my account in the recent literature on the topic, I argue that the problem can be solved by considering computational complexity for humanly relevant problem solving algorithms and input sizes. (shrink)

Due to the variation, contingency and complexity of living systems, biology is often taken to be a science without fundamental theories, laws or general principles. I revisit this question in light of the quest for design principles in systems biology and show that different views can be reconciled if we distinguish between different types of generality. The philosophical literature has primarily focused on generality of specific models or explanations, or on the heuristic role of abstraction. This (...) paper takes a different approach in emphasizing a theory-constituting role of general principles. Design principles signify general dependencyrelations between structures and functions, given a set of formally defined constraints. I contend that design principles increase our understanding of living systems by relating specific models to general types. The categorization of types is based on a delineation of the scope of biological possibilities, which serves to identify and define the generic features of classes of systems. To characterize the basis for general principles through generic abstraction and reasoning about possibility spaces, I coin the term constraint-based generality. I show that constraintbased generality is distinct from other types of generality in biology, and argue that general principles play a unifying role that does not entail theory reduction. (shrink)

This work is mainly concerned with the notion of hierarchical modularity and its use in explaining structure and dynamical behavior of complex systems by means of hierarchical modular models, as well as with a concept of my proposal, antimodularity, tied to the possibility of the algorithmic detection of hierarchical modularity. Specifically, I highlight the pragmatic bearing of hierarchical modularity on the possibility of scientific explanation of complex systems, that is, systems which, according to a chosen (...) basic description, can be considered as composed of elementary, discrete, interrelated parts. I stress that hierarchical modularity is also required by the experimentation aimed to discover the structure of such systems. Algorithmic detection of hierarchical modularity turns out to be a task plagued by the demonstrated computational intractability of the search for the best hierarchical modular description, and by the high computational expensiveness of even approximated detection methods. Antimodularity consists in the lack of a modular description fitting the needs of the observer, a lack due either to absence of modularity in the system’s chosen basic description, or to the impossibility, due to the excessive size of the system under assessment in relation to the computational cost of algorithmic methods, to algorithmically produce a valid hierarchical description. I stress that modularity and antimodularity depend on the pragmatic choice of a given basic description of the system, a choice made by the observer based on explanatory goals. I show how antimodularity hinders the possibility of applying at least three well-known types of explanation: mechanistic, deductive-nomological and computational. A fourth type, topological explanation, remains unaffected. I then assess the presence of modularity in biological systems, and evaluate the possible consequences, and the likelihood, of incurring in antimodularity in biology and other sciences, concluding that this eventuality is quite likely, at least in systems biology. I finally indulge in some metaphysical and historical speculations: metaphysically, antimodularity seems to suggest a possible position according to which natural kinds are detected modules, and as such, due to the computational hardness of the detection of the best hierarchical modular description, they are unlikely to be the best possible way to describe the world, because the modularity of natural kinds quite probably does not reflect the best possible modularity of the world. From an historical point of view, the growing use of computational methods for modularity detection or simulation of complex systems, especially in certain areas of scientific research, hints at the envisioning of a multiplicity of emerging scientific disciplines guided by a self- sustained, growing production of possibly human-unintelligible explanations. This, I suggest, would constitute an historical change in science, which, if has not already occurred, could well be on the verge of happening. (shrink)

In classical physics, the world is considered as a matter-based reality, the arrangement of whose parts in time is uniquely determined by certain dynamic laws. By contrast, modern quantum physics reveals that matter is not composed of matter, but reality is merely potentiality. The world has a holistic structure, which is based on fundamental relations and not material objects, admitting more open, indeterministic developments. In this more flexible causal framework, inanimate and animate matter are not to be considered as (...) fundamentally different but as different order structures of the same immaterial entity. In a stable configuration, effectively all the uncertainties are statistically averaged out, thus the unique and deterministic behavior of ordinary inanimate matter is exhibited; whereas in the case of statically unstable but dynamically stable configurations, the “lively” features of the underlying quantum structure have a chance to surface to the mesocopic level and to be connected with what we observe as the phenomenon of life. This supposition can be more explicitly treated and clarified by identifying the electric dipole moment of biomolecules as the ordering parameter of the corresponding macroquantum system. This has important consequences for biology and medicine. In particular, it suggests the existence of a quantum-based “software,” essential perhaps for the logistics of biological processes, which are hidden behind the matter/energy-based “hardware” that alone is considered in the conventional approach. In medicine it opens an opportunity to build bridges between conventional medicine based essentially on the classical paradigm, and the various forms of complementary medicine, which have strong affinities with the new features of the modern holistic worldview. (shrink)

Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. We study the basic algebraic properties of this system by introducing the notion of Shi-Aharonov quantum computational structure. We show that the quotient of this structure is isomorphic to a structure based on a particular set of complex numbers (the closed disc with center \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\frac{1}{2},\frac{1}{2})$\end{document} (...) and radius \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{1}{2}$\end{document} ). (shrink)

The observed complexity of nature is often attributed to an intrinsic propensity of matter to self-organize under certain (e.g., dissipative) conditions. In order better to understand and test this vague thesis, we define complexity as “logical depth,” a notion based on algorithmic information and computational time complexity. Informally, logical depth is the number of steps in the deductive or causal path connecting a thing with its plausible origin. We then assess the effects of dissipation, noise, and spatial and other symmetries (...) of the initial conditions and equations of motion on the asymptotic complexity-generating abilities of statistical-mechanical model systems. We concentrate on discrete, spatially-homogeneous, locally-interacting systems such as kinetic Ising models and cellular automata. (shrink)

Abstract.At the heart of the most radical proposals in Stuart Kauffman's Investigations is his attempt to show that we find in evolutionary biology some configuration spaces—the sets of possible developments for any given system—that (unlike those in traditional physics of Newtonian, relativistic, and quantum stripes) cannot be completely described in advance. We bring Charles Peirce's work on the philosophy of continuity to bear on the problem and discover, first, that Kauffman's arguments do not succeed; second, that Peirce's metaphysics (...) provide new and sounder arguments for the same propositions; third, that Peirce's rigorous but nonstandard treatment of mathematical continuity shows great promise for modeling the unpredictability and growth we find in evolutionary biology; fourth, that it also strengthens a development only hinted at by biologists thus far—the inevitable involvement of the observer's mind in constituting the objects of science. We close with a logical argument for the surprising relevance of metaphysical hypotheses in the natural sciences and with suggestions for future work that will connect these questions to what Kauffman terms the “narrative stance” in biology. (shrink)

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures (...) that emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)