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  1. Andreas Wagner (1999). Causality in Complex Systems. Biology and Philosophy 14 (1):83-101.
    Systems involving many interacting variables are at the heart of the natural and social sciences. Causal language is pervasive in the analysis of such systems, especially when insight into their behavior is translated into policy decisions. This is exemplified by economics, but to an increasing extent also by biology, due to the advent of sophisticated tools to identify the genetic basis of many diseases. It is argued here that a regularity notion of causality can only be meaningfully defined for systems (...)
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  2. William C. Wimsatt (1994). The Ontology of Complex Systems: Levels of Organization, Perspectives, and Causal Thickets. Canadian Journal of Philosophy 24 (sup1):207-274.
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  3. Kazuko Yamasaki, Kaushik Matia, Fabio Pammolli, Sergey Buldyrev, Massimo Riccaboni, H. Eugene Stanley & Dongfeng Fu, Preferential Attachment and Growth Dynamics in Complex Systems.
    Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the steady influx of new classes. According to the model, the distribution changes from a pure exponential form for zero influx of new classes to a power law with an exponential cut-off form when the influx of new classes is (...)
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  4. P. Ylikoski (2009). Book Review: Sawyer, R. Keith. (2005). Social Emergence: Societies as Complex Systems. Cambridge, UK: Cambridge University Press. [REVIEW] Philosophy of the Social Sciences 39 (3):527-530.
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  5. Elias Zafiris (2005). Complex Systems From the Perspective of Category Theory: I. Functioning of the Adjunction Concept. [REVIEW] Axiomathes 15 (1):147-158.
    We develop a category theoretical scheme for the comprehension of the information structure associated with a complex system, in terms of families of partial or local information carriers. The scheme is based on the existence of a categorical adjunction, that provides a theoretical platform for the descriptive analysis of the complex system as a process of functorial information communication.
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  6. Elias Zafiris (2005). Complex Systems From the Perspective of Category Theory: II. Covering Systems and Sheaves. [REVIEW] Axiomathes 15 (2):181-190.
    Using the concept of adjunction, for the comprehension of the structure of a complex system, developed in Part I, we introduce the notion of covering systems consisting of partially or locally defined adequately understood objects. This notion incorporates the necessary and sufficient conditions for a sheaf theoretical representation of the informational content included in the structure of a complex system in terms of localization systems. Furthermore, it accommodates a formulation of an invariance property of information communication concerning the analysis of (...)
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  7. Elias Zafiris (2005). Complex Systems From the Perspective of Category Theory: I. Functioning of the Adjunction Concept. [REVIEW] Axiomathes 15 (1):147-158.
    We develop a category theoretical framework for the comprehension of the information structure associated with a complex system, in terms of families of partial or local information carriers. The framework is based on the existence of a categorical adjunction, that provides a theoretical platform for the descriptive analysis of the complex system as a process of functorial information communication.
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  8. Elias Zafiris (2005). Complex Systems From the Perspective of Category Theory: II. Covering Systems and Sheaves. [REVIEW] Axiomathes 15 (2):181-190.
    Using the concept of adjunctive correspondence, for the comprehension of the structure of a complex system, developed in Part I, we introduce the notion of covering systems consisting of partially or locally defined adequately understood objects. This notion incorporates the necessary and sufficient conditions for a sheaf theoretical representation of the informational content included in the structure of a complex system in terms of localization systems. Furthermore, it accommodates a formulation of an invariance property of information communication concerning the analysis (...)
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Chaos
  1. Philip Anderson & Jack Cohen (1999). Reviews: Coping with Uncertainty, Insights From the New Sciences of Chaos, Self-Organization, and Complexity, Uri Merry. [REVIEW] Emergence 1 (2):106-108.
    (1999). Reviews: Coping with Uncertainty, Insights from the New Sciences of Chaos, Self-Organization, and Complexity, Uri Merry. Emergence: Vol. 1, No. 2, pp. 106-108.
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  2. S. M. Anlage (2000). Book Review: Quantum Chaos-An Introduction. [REVIEW] Foundations of Physics 30 (7):1135-1138.
  3. I. Antoniou & Z. Suchanecki (1997). The Fuzzy Logic of Chaos and Probabilistic Inference. Foundations of Physics 27 (3):333-362.
    The logic of a physical system consists of the elementary observables of the system. We show that for chaotic systems the logic is not any more the classical Boolean lattice but a kind of fuzzy logic which we characterize for a class of chaotic maps. Among other interesting properties the fuzzy logic of chaos does not allow for infinite combinations of propositions. This fact reflects the instability of dynamics and it is shared also by quantum systems with diagonal singularity. We (...)
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  4. Harald Atmanspacher, Characterizing Spontaneous Irregular Behavior in Coupled Map Lattices.
    Two-dimensional coupled map lattices display, in a specific parameter range, a stable phase (quasi-) periodic in both space and time. With small changes to the model parameters, this stable phase develops spontaneous eruptions of nonperiodic behavior. Although this behavior itself appears irregular, it can be characterized in a systematic fashion. In particular, parameter-independent features of the spontaneous eruptions may allow useful empirical characterizations of other phenomena that are intrinsically hard to predict and reproduce. Specific features of the distributions of lifetimes (...)
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  5. Harald Atmanspacher, Ontic and Epistemic Descriptions of Chaotic Systems.
    Traditional philosophical discourse draws a distinction between ontology and epistemology and generally enforces this distinction by keeping the two subject areas separated and unrelated. In addition, the relationship between the two areas is of central importance to physics and philosophy of physics. For instance, all kinds of measurement-related problems force us to consider both our knowledge of the states and observables of a system (epistemic perspective) and its states and observables independent of such knowledge (ontic perspective). This applies to quantum (...)
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  6. R. Badii (1997). Complexity: Hierarchical Structures and Scaling in Physics. Cambridge University Press.
    This is a comprehensive discussion of complexity as it arises in physical, chemical, and biological systems, as well as in mathematical models of nature. Common features of these apparently unrelated fields are emphasised and incorporated into a uniform mathematical description, with the support of a large number of detailed examples and illustrations. The quantitative study of complexity is a rapidly developing subject with special impact in the fields of physics, mathematics, information science, and biology. Because of the variety of the (...)
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  7. Robert W. Batterman (1991). Chaos, Quantization, and the Correspondence Principle. Synthese 89 (2):189 - 227.
  8. Robert W. Batterman & Homer White (1996). Chaos and Algorithmic Complexity. Foundations of Physics 26 (3):307-336.
    Our aim is to discover whether the notion of algorithmic orbit-complexity can serve to define “chaos” in a dynamical system. We begin with a mostly expository discussion of algorithmic complexity and certain results of Brudno, Pesin, and Ruelle (BRP theorems) which relate the degree of exponential instability of a dynamical system to the average algorithmic complexity of its orbits. When one speaks of predicting the behavior of a dynamical system, one usually has in mind one or more variables in the (...)
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  9. Gordon Belot & John Earman (1997). Chaos Out of Order: Quantum Mechanics, the Correspondence Principle and Chaos. Studies in History and Philosophy of Science Part B 28 (2):147-182.
  10. Gordon Belot & Lina Jansson (2010). Alisa Bokulich, Reexamining the Quantum-Classical Relation: Beyond Reductionism and Pluralism , Cambridge University Press, Cambridge (2008) ISBN 978-0-521-85720-8 Pp. X+195. [REVIEW] Studies in History and Philosophy of Science Part B 41 (1):81-83.
  11. K.-F. Berggren & T. Ouchterlony (2001). Chaos in a Quantum Dot with Spin-Orbit Coupling. Foundations of Physics 31 (2):233-242.
    Level statistics and nodal point distribution in a rectangular semiconductor quantum dot are studied for different degrees of spin-orbit coupling. The chaotic features occurring from the spin-orbit coupling have no classical counterpart. Using experimental values for GaSb/InAs/GaSb semiconductor quantum wells we find that level repulsion can lead to the semi-Poisson distribution for nearest level separations. Nodal lines and nodal points are also investigated. Comparison is made with nodal point distributions for fully chaotic states.
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  12. O. Bohigas, P. Lebœuf & M. J. Sánchez (2001). Spectral Spacing Correlations for Chaotic and Disordered Systems. Foundations of Physics 31 (3):489-517.
    New aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point correlation function. Their behavior results from two different contributions. One corresponds to (universal) random matrix eigenvalue fluctuations, the other to diffusive or chaotic characteristics of the corresponding classical motion. A closed formula expressing spacing autocovariances in terms of classical dynamical zeta functions, including the Perron–Frobenius operator, is derived. (...)
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  13. Oriol Bohigas, Patricio Leboeuf & M. J. Sanchez (2001). Spectral Spacing Correlations for Chaotic and Disordered Systems. Foundations of Physics 31 (3):489-517.
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  14. D. M. Borchert (ed.) (2006). Encyclopedia of Philosophy, Second Edition.
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  15. Seamus Bradley, Scientific Uncertainty: A User's Guide. Grantham Institute on Climate Change Discussion Paper.
    There are different kinds of uncertainty. I outline some of the various ways that uncertainty enters science, focusing on uncertainty in climate science and weather prediction. I then show how we cope with some of these sources of error through sophisticated modelling techniques. I show how we maintain confidence in the face of error.
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  16. Jean E. Burns (2007). Vacuum Radiation, Entropy, and Molecular Chaos. Foundations of Physics 37 (12):1727-1737.
    Vacuum radiation causes a particle to make a random walk about its dynamical trajectory. In this random walk the root mean square change in spatial coordinate is proportional to t 1/2, and the fractional changes in momentum and energy are proportional to t −1/2, where t is time. Thus the exchange of energy and momentum between a particle and the vacuum tends to zero over time. At the end of a mean free path the fractional change in momentum of a (...)
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  17. C. M. Caves (1994). Quantum Theory: Concepts and Methods. Foundations of Physics 24:1583-1583.
  18. Boris V. Chirikov (1986). Transient Chaos in Quantum and Classical Mechanics. Foundations of Physics 16 (1):39-49.
    Bogolubov's classical example of statistical relaxation in a many-dimensional linear oscillator is discussed. The relation of the discovered relaxation mechanism to quantum dynamics as well as to some new problems in classical mechanics is considered.
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  19. R. Clifton (1995). Quantum Theory: Concepts and Methods. Foundations of Physics 25:205-205.
  20. Peter Coles (2006). From Cosmos to Chaos: The Science of Unpredictability. Oxford University Press.
    Cosmology has undergone a revolution in recent years. The exciting interplay between astronomy and fundamental physics has led to dramatic revelations, including the existence of the dark matter and the dark energy that appear to dominate our cosmos. But these discoveries only reveal themselves through small effects in noisy experimental data. Dealing with such observations requires the careful application of probability and statistics. But it is not only in the arcane world of fundamental physics that probability theory plays such an (...)
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  21. James T. Cushing (2000). Bohmian Insights Into Quantum Chaos. Philosophy of Science 67 (3):445.
    The ubiquity of chaos in classical mechanics (CM), as opposed to the situation in standard quantum mechanics (QM), might be taken as speaking against QM being the fundamental theory of physical phenomena. Bohmian mechanics (BM), as a formulation of quantum theory, may clarify both the existence of chaos in the quantum domain and the nature of the classical limit. Two interesting possibilities are (i) that CM and classical chaos are included in and underwritten by quantum mechanics (BM) or (ii) that (...)
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  22. Roman Frigg, Chaos and Randomness: An Equivalence Proof of a Generalized Version of the Shannon Entropy and the Kolmogorov–Sinai Entropy for Hamiltonian Dynamical Systems.
    Chaos is often explained in terms of random behaviour; and having positive Kolmogorov–Sinai entropy (KSE) is taken to be indicative of randomness. Although seemly plausible, the association of positive KSE with random behaviour needs justification since the definition of the KSE does not make reference to any notion that is connected to randomness. A common way of justifying this use of the KSE is to draw parallels between the KSE and ShannonÕs information theoretic entropy. However, as it stands this no (...)
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  23. Sheldon Goldstein, Absence of Chaos in Bohmian Dynamics.
    In a recent paper [1], O. F. de Alcantara Bonfim, J. Florencio, and F. C. S´ a Barreto claim to have found numerical evidence of chaos in the motion of a Bohmian quantum particle in a double square-well potential, for a wave function that is a superposition of five energy eigenstates. But according to the result proven here, chaos for this motion is impossible. We prove in fact that for a particle on the line in a superposition of n + (...)
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  24. Dennis A. Hejhal & Andreas Strömbergsson (2001). On Quantum Chaos and Maass Waveforms of CM-Type. Foundations of Physics 31 (3):519-533.
    In this paper, we report on some machine experiments which suggest that waveforms of CM-type are asymptotically Gaussian-distributed.
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  25. Jeffrey Koperski (2001). Has Chaos Been Explained? British Journal for the Philosophy of Science 52 (4):683-700.
    In his recent book, Explaining Chaos, Peter Smith presents a new problem in the foundations of chaos theory. Specifically, he argues that the standard ways of justifying idealizations in mathematical models fail when it comes to the infinite intricacy found in strange attractors. I argue that Smith's analysis undermines much of the explanatory power of chaos theory. A better approach is developed by drawing analogies from the models found in continuum mechanics.
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  26. Frederick M. Kronz (2000). Chaos in a Model of an Open Quantum System. Philosophy of Science 67 (3):453.
    In a previous essay I argued that quantum chaos cannot be exhibited in models of quantum systems within von Neumann's mathematical framework for quantum mechanics, and that it can be exhibited in models within Dirac's formal framework. In this essay, the negative thesis concerning von Neumann's framework is elaborated further by extending it to the case of Hamiltonian operators having a continuous spectrum. The positive thesis concerning Dirac's formal framework is also elaborated further by constructing a chaotic model of an (...)
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  27. Frederick M. Kronz (1998). Nonseparability and Quantum Chaos. Philosophy of Science 65 (1):50-75.
    Conventional wisdom has it that chaotic behavior is either strongly suppressed or absent in quantum models. Indeed, some researchers have concluded that these considerations serve to undermine the correspondence principle, thereby raising serious doubts about the adequacy of quantum mechanics. Thus, the quantum chaos question is a prime subject for philosophical analysis. The most significant reasons given for the absence or suppression of chaotic behavior in quantum models are the linearity of Schrödinger’s equation and the unitarity of the time-evolution described (...)
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  28. Theodor Leiber (1997). On the Actual Impact of Deterministic Chaos. Synthese 113 (3):357-379.
    The notion of (deterministic) chaos is frequently used in an increasing number of scientific (as well as non-scientific) contexts, ranging from mathematics and the physics of dynamical systems to all sorts of complicated time evolutions, e.g., in chemistry, biology, physiology, economy, sociology, and even psychology. Despite (or just because of) these widespread applications, however, there seem to fluctuate around several misunderstandings about the actual impact of deterministic chaos on several problems of philosophical interest, e.g., on matters of prediction and computability, (...)
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  29. J. Levitan, M. Lewkowicz & Y. Ashkenazy (1997). Enhancement of Decoherence by Chaotic-Like Behavior. Foundations of Physics 27 (2):203-214.
    We demonstrate by use of a simple one-dimensional model of a square barrier imbedded in an infinite potential well that decoherence is enhanced by chaotic-like behavior. We, moreover, show that the transition h→0 is singular. Finally it is argued that the time scale on which decoherence occurs depends, on the degree of complexity of the underlying quantum mechanical system, i.e., more complex systems decohere relatively faster than less complex ones.
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  30. Sergei G. Matinyan & Berndt Müller (1997). Quantum Fluctuations and Dynamical Chaos: An Effective Potential Approach. [REVIEW] Foundations of Physics 27 (9):1237-1255.
    We discuss the intimate connection between the chaotic dynamics of a classical field theory and the instability of the one-loop effective action of the associated quantum field theory. Using the example of massless scalar electrodynamics, we show how the radiatively induced spontaneous symmetry breaking stabilizes the vacuum state against chaos, and we speculate that monopole condensation can have the same effect in non-Abelian gauge theories.
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  31. Matthew W. Parker (1998). Did Poincare Really Discover Chaos? [REVIEW] Studies in the History and Philosophy of Modern Physics 29 (4):575-588.
  32. I. Prigogine (1984). Order Out of Chaos: Man's New Dialogue with Nature. Distributed by Random House.
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  33. R. Dwayne Ramey & N. L. Balazs (2001). Hamiltonian Chaos in Homogeneous ADM Cosmologies? Foundations of Physics 31 (2):371-398.
    Chaos in dynamical systems has best been understood in terms of Hamiltonian systems. A primary method of diagnosis of chaos in these systems is the Lyapunov exponent. According to general relativity, space-time is itself a dynamical system. When the evolution of a model universe is expressed in the ADM form it can be described as a Hamiltonian system. Among the various model cosmologies, the Mixmaster or Bianchi IX cosmology has been extensively studied as a candidate to exhibit chaos. However, the (...)
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  34. L. E. Reichl & G. Akguc (2001). Scattering From Spatially Localized Chaotic and Disordered Systems. Foundations of Physics 31 (2):243-267.
    A version of scattering theory that was developed many years ago to treat nuclear scattering processes, has provided a powerful tool to study universality in scattering processes involving open quantum systems with underlying classically chaotic dynamics. Recently, it has been used to make random matrix theory predictions concerning the statistical properties of scattering resonances in mesoscopic electron waveguides and electromagnetic waveguides. We provide a simple derivation of this scattering theory and we compare its predictions to those obtained from an exactly (...)
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  35. A. Richter (2001). Test of Trace Formulas for Spectra of Superconducting Microwave Billiards. Foundations of Physics 31 (2):327-354.
    Experimental tests of various trace formulas, which in general relate the density of states for a given quantum mechanical system to the properties of the periodic orbits of its classical counterpart, for spectra of superconducting microwave billiards of varying chaoticity are reviewed by way of examples. For a two-dimensional Bunimovich stadium billiard the application of Gutzwiller's trace formula is shown to yield correctly locations and strengths of the peaks in the Fourier transformed quantum spectrum in terms of the shortest unstable (...)
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  36. W. -H. Steeb, J. A. Louw & A. Kunick (1987). Quantum Chaos of an Exciton-Phonon System. Foundations of Physics 17 (2):173-181.
    A simple model of an exciton-phonon system is studied in connection with quantum chaos.
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  37. Michael Strevens (2006). Chaos. In D. M. Borchert (ed.), Encyclopedia of Philosophy, second edition.
    A physical system has a chaotic dynamics, according to the dictionary, if its behavior depends sensitively on its initial conditions, that is, if systems of the same type starting out with very similar sets of initial conditions can end up in states that are, in some relevant sense, very different. But when science calls a system chaotic, it normally implies two additional claims: that the dynamics of the system is relatively simple, in the sense that it can be expressed in (...)
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  38. Kazuhisa Tomita (1987). Conjugate Pair of Representations in Chaos and Quantum Mechanics. Foundations of Physics 17 (7):699-711.
    Being based on the observation that a conjugate pair of representations, or dual logic, is a necessity under the presence of chaos, a new interpretation of quantum theory is proposed as describingproto-chaos. This chaos has to be a result of basic nonlinearity in the dynamic structure, of which, however, the nonchaotic phase seems to lie ourside the reach of experimental technique, thus the term proto-chaos. Nevertheless, assuming no extra degrees of freedom, the interpretation clarifies a number of riddles posed hitherto (...)
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  39. C. H. Woo (1989). Chaos, Ineffectiveness, and the Contrast Between Classical and Quantal Physics. Foundations of Physics 19 (1):57-76.
    Classical and quantal physics are fundamentally different in the way that each deals with complexity. We examine both the algorithmic and the computational aspects of this difference. Any comprehensive deterministic theory must contain a certain ineffectiveness in producing long-term predictions of the future, whereas a probabilistic theory is not so handicapped. The relevance of these considerations to chaos is discussed.
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Complexity
  1. Philip Anderson & Jack Cohen (1999). Reviews: Coping with Uncertainty, Insights From the New Sciences of Chaos, Self-Organization, and Complexity, Uri Merry. [REVIEW] Emergence 1 (2):106-108.
    (1999). Reviews: Coping with Uncertainty, Insights from the New Sciences of Chaos, Self-Organization, and Complexity, Uri Merry. Emergence: Vol. 1, No. 2, pp. 106-108.
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  2. R. Badii (1997). Complexity: Hierarchical Structures and Scaling in Physics. Cambridge University Press.
    This is a comprehensive discussion of complexity as it arises in physical, chemical, and biological systems, as well as in mathematical models of nature. Common features of these apparently unrelated fields are emphasised and incorporated into a uniform mathematical description, with the support of a large number of detailed examples and illustrations. The quantitative study of complexity is a rapidly developing subject with special impact in the fields of physics, mathematics, information science, and biology. Because of the variety of the (...)
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  3. Ion C. Baianu (2007). Categorical Ontology of Levels and Emergent Complexity: An Introduction. [REVIEW] Axiomathes 17 (3-4):209-222.
    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 (...)
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