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The study of complexity has emerged out of a number of broadly holistic trends in the physical sciences in the last century, principally in the fields of computing and computer modelling, cybernetics, dynamical system theory (a branch of classical mechanics which studies the properties and interactions of many-bodied systems), and thermodynamics. Contemporary complexity science can be seen as the heir to a number of earlier approaches to the problems associated with articulating a scientific approach to the study of phenomena related to these fields. Philosophical problems associated with complexity include clarifying the meanings of various concepts associated with complexity, such as emergence, non-linearity, feedback, adaptation, and self-organization, and the extent to which these terms can be given scientific meaning, that is, the extent to which these terms can be meaningfully used in the physical sciences themselves. The study of complexity also naturally intersects with more traditional problem areas in the philosophy of the sciences, such as the study of reductionism, modelling, supervenience, functionalism, and causality; however the focus of contemporary philosophy of complexity has largely tended towards the examination of (or in many cases, an attempt at the legitimization of) a scientific grounding of a particular set of approaches to these problem areas. Much of this focus is surely due to the fact that the study of complexity in the twentieth century has largely been driven by scientific practitioners themselves, and not by philosophers or philosophers of science. As such, contemporary complexity theory also makes assumptions about the relationship between scientific and philosophical theories, leading to one of its central problems: its essential ambiguity. Is complexity science a specific branch of physical science (for example, the study of 'complex adaptive systems'); a study of a widespread trans-disciplinary scientific phenomenon (leading to the study of, for example, various broad 'measures of complexity', not to speak of complexity in other divisions of science, including biological and social complexity); or even a general (and allegedly paradigmatic) approach to science itself (the source of many popularizations, and in some cases works bordering on pseudo-science)? This ambiguity (which is reflected in the bibliography) opens up further avenues for exploration, and has implications for the manner in which philosophers should attempt to approach the subject.

Key works Weaver 1948, Simon 1962, and Ashby 1962 are classic early works, generalizing concepts from cybernetics. Buckley 1968 is an early application to sociology and is likely the origin of the concept of a 'Complex Adaptive System', later explored in Holland 1992. Prigogine 1984 explores a model of complexity based on ideas from thermodynamics; Various proposed measures of complexity are explored in Bennett 1988, Lloyd & Pagels 1988 and Gell-Mann 1995. Kauffman 1969 and Bak 1996 are the origins of the influential models of Random Boolean Networks and Self-Organized Criticality, respectively.
Introductions A comprehensive introduction to many of the technical and philosophical issues of complexity can be found in Ladyman et al 2013. Book-length introductions to the diverse areas of research in complexity are Mitchell 2009 and Hooker 2011. Historical context is provided in Abraham 2011 and Francois 1999. There is a paucity of discussion of the subject in a manner that would be familiar to academic philosophers; in addition to Ladyman et al 2013, readers can consult Poser 2007Phelan 2001, and, on a more skeptical note, Taborsky 2014
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  1. H. D. I. Abarbanel (1992). Local Lyapunov Exponents Computed From Observed Data. Journal of Nonlinear Science 2 (3):343-365.
    We develop methods for determining local Lyapunov exponents from observations of a scalar data set. Using average mutual information and the method of false neighbors, we reconstruct a multivariate time series, and then use local polynomial neighborhood-to-neighborhood maps to determine the phase space partial derivatives required to compute Lyapunov exponents. In several examples we demonstrate that the methods allow one to accurately reproduce results determined when the dynamics is known beforehand. We present a new recursive QR decomposition method for finding (...)
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  2. Ralph H. Abraham (2011). The Genesis of Complexity. World Futures 67 (4-5):380 - 394.
    The theories of complexity comprise a system of great breadth. But what is included under this umbrella? Here we attempt a portrait of complexity theory, seen through the lens of complexity theory itself. That is, we portray the subject as an evolving complex dynamical system, or social network, with bifurcations, emergent properties, and so on. This is a capsule history covering the twentieth century. Extensive background data may be seen at www.visual-chaos.org/complexity.
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  3. Michel Alhadeff-Jones (2008). Three Generations of Complexity Theories: Nuances and Ambiguities. Educational Philosophy and Theory 40 (1):66–82.
    The contemporary use of the term ‘complexity’ frequently indicates that it is considered a unified concept. This may lead to a neglect of the range of different theories that deal with the implications related to the notion of complexity. This paper, integrating both the English and the Latin traditions of research associated with this notion, suggests a more nuanced use of the term, thereby avoiding simplification of the concept to some of its dominant expressions only. The paper further explores the (...)
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  4. P. W. Anderson (1994). More is Different. In H. Gutfreund & G. Toulouse (eds.), Biology and Computation: A Physicist's Choice. World Scientific 3--21.
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  5. Philip W. Anderson (forthcoming). The Eightfold Way to the Theory of Complexity: A Prologue. Complexity.
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  6. Philip Anderson & Jack Cohen (1999). Reviews: Coping with Uncertainty, Insights From the New Sciences of Chaos, Self-Organization, and Complexity, Uri Merry. [REVIEW] Emergence: Complexity and Organization 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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  7. W. Ross Ashby (1962). Principles of the Self-Organizing System. In H. Von Foerster & Zopf Jr (eds.), Principles of Self-Organization: Transactions of the University of Illinois Symposium. Pergamon 255–278.
  8. Fatihcan M. Atay & J.�Rgen Jost (2004). On the Emergence of Complex Systems on the Basis of the Coordination of Complex Behaviors of Their Elements: Synchronization and Complexity. Complexity 10 (1):17-22.
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  9. H. Atmanspacher & G. Demmel (2016). Methodological Issues in the Study of Complex Systems. In H. Atmanspacher & S. Maasen (eds.), Reproducibility: Principles, Problems, Practices, and Prospects. Wiley 233–250.
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  10. David Aubin (2008). 'The Memory of Life Itself': Bénard's Cells and the Cinematography of Self-Organization. Studies in History and Philosophy of Science Part A 39 (3):359-369.
    In 1900, the physicist Henri Bénard exhibited the spontaneous formation of cells in a layer of liquid heated from below. Six or seven decades later, drastic reinterpretations of this experiment formed an important component of ‘chaos theory’. This paper therefore is an attempt at writing the history of this experiment, its long neglect and its rediscovery. It examines Bénard’s experiments from three different perspectives. First, his results are viewed in the light of the relation between experimental and mathematical approaches in (...)
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  11. David Aubin (1998). A Cultural History of Catastrophes and Chaos: Around the Institut des Hautes Études Scientifiques. Princeton.
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  12. David Aubin & Amy Dalmedico (2002). Writing the History of Dynamics Systems and Chaos: Longue Durée and Revolution, Disciplines and Cultures. Historia Mathematica 29:1–67.
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  13. Sunny Auyang, Synthetic Analysis: How Science Combats Complexity.
    In the past two or three decades, complexity not only has been a hot research topic but has caught the popular imagination. Terms such as chaos and bifurcation become so common they find their way into Hollywood movies. What is complexity? What is the theory of complexity or the science of complexity? I do not think there is such a thing as the theory of complexity. Not even a rigid definition of complexity exists in the natural sciences. There are many (...)
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  14. Sunny Auyang (ed.) (1999). Foundations of Complex-System Theories In Economics, Evolutionary Biology, and Statistical Physics. Cambridge U.P..
  15. Nils Baas & Claus Emmeche (1997). On Emergence and Explanation. Intellectica 2 (25):67-83.
    Emergence is a universal phenomenon that can be defined mathematically in a very general way. This is useful for the study of scientifically legitimate explanations of complex systems, here defined as hyperstructures. A requirement is that the observation mechanisms are considered within the general framework. Two notions of emergence are defined, and specific examples of these are discussed.
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  16. 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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  17. 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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  18. Per Bak (1996). How Nature Works: The Science of Self-Organized Criticality. Copernicus.
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  19. Alan Baker (2013). Complexity, Networks, and Non-Uniqueness. Foundations of Science 18 (4):687-705.
    The aim of the paper is to introduce some of the history and key concepts of network science to a philosophical audience, and to highlight a crucial—and often problematic—presumption that underlies the network approach to complex systems. Network scientists often talk of “the structure” of a given complex system or phenomenon, which encourages the view that there is a unique and privileged structure inherent to the system, and that the aim of a network model is to delineate this structure. I (...)
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  20. Anouk Barberousse & Cyrille Imbert (2013). New Mathematics for Old Physics: The Case of Lattice Fluids. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (3):231-241.
    We analyze the effects of the introduction of new mathematical tools on an old branch of physics by focusing on lattice fluids, which are cellular automata -based hydrodynamical models. We examine the nature of these discrete models, the type of novelty they bring about within scientific practice and the role they play in the field of fluid dynamics. We critically analyze Rohrlich's, Fox Keller's and Hughes' claims about CA-based models. We distinguish between different senses of the predicates “phenomenological” and “theoretical” (...)
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  21. Robert W. Batterman (1991). Randomness and Probability in Dynamical Theories: On the Proposals of the Prigogine School. Philosophy of Science 58 (2):241-263.
    I discuss recent work in ergodic theory and statistical mechanics, regarding the compatibility and origin of random and chaotic behavior in deterministic dynamical systems. A detailed critique of some quite radical proposals of the Prigogine school is given. I argue that their conclusion regarding the conceptual bankruptcy of the classical conceptions of an exact microstate and unique phase space trajectory is not completely justified. The analogy they want to draw with quantum mechanics is not sufficiently close to support their most (...)
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  22. 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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  23. William Bechtel & Robert C. Richardson (1993). Discovering Complexity Decomposition and Localization as Strategies in Scientific Research. Princeton.
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  24. A. Beckermann, H. Flohr & Jaegwon Kim (eds.) (1992). Emergence or Reduction? Essays on the Prospect of Nonreductive Physicalism. De Gruyter.
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  25. Mark Bedau, Is Echo a Complex Adaptive System?
    We evaluate whether John Holland’s Echo model exemplifies his theory of complex adaptive systems. After reviewing Holland’s theory of complex adaptive systems and describing his Echo model, we describe and explain the characteristic evolutionary behavior observed in a series of Echo model runs. We conclude that Echo lacks the diversity of hierarchically organized aggregates that typify complex adaptive systems, and we explore possible explanations for this failure.
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  26. Michael J. Behe (2000). Self-Organization and Irreducibly Complex Systems: A Reply to Shanks and Joplin. Philosophy of Science 67 (1):155-162.
    Some biochemical systems require multiple, well-matched parts in order to function, and the removal of any of the parts eliminates the function. I have previously labeled such systems "irreducibly complex," and argued that they are stumbling blocks for Darwinian theory. Instead I proposed that they are best explained as the result of deliberate intelligent design. In a recent article Shanks and Joplin analyze and find wanting the use of irreducible complexity as a marker for intelligent design. Their primary counterexample is (...)
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  27. C. H. Bennett (1988). Logical Depth and Physical Complexity. In R. Herken (ed.), The universal Turing machine, a half century survey. Oxford U.P. 227-257.
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  28. Charles H. Bennett (1986). On the Nature and Origin of Complexity in Discrete, Homogeneous, Locally-Interacting Systems. Foundations of Physics 16 (6):585-592.
    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 (...)
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  29. Cristoforo Sergio Bertuglia & Franco Vaio (2005). Nonlinearity, Chaos, and Complexity: The Dynamics of Natural and Social Systems. OUP Oxford.
    Covering a broad range of topics, this text provides a comprehensive survey of the modelling of chaotic dynamics and complexity in the natural and social sciences. Its attention to models in both the physical and social sciences and the detailed philosophical approach make this an unique text in the midst of many current books on chaos and complexity. Including an extensive index and bibliography along with numerous examples and simplified models, this is an ideal course text.
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  30. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez & D. U. Hwang (2006). Complex Networks: Structure and Dynamics. Physics Reports 424:175–308.
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  31. Fabio Boschetti (2012). Causality, Emergence, Computation and Unreasonable Expectations. Synthese 185 (2):187-194.
    I argue that much of current concern with the role of causality and strong emergence in natural processes is based upon an unreasonable expectation placed on our ability to formalize scientific knowledge. In most disciplines our formalization ability is an expectation rather than a scientific result. This calls for an empirical approach to the study of causation and emergence. Finally, I suggest that for advances in complexity research to occur, attention needs to be paid to understanding what role computation plays (...)
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  32. Fabio Boschetti & Randall Gray (2007). Emergence and Computability. Emergence: Complexity and Organization 9.
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  33. Fabio Boschetti, David McDonald & Randall Gray (2008). Complexity of a Modelling Exercise: A Discussion of the Role of Computer Simulation in Complex System Science. Complexity 13 (6):21-28.
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  34. Erez Braun & Shimon Marom (2015). Universality, Complexity and the Praxis of Biology: Two Case Studies. Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 53:68-72.
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  35. D. R. Brooks (1988). Evolution as Entropy: Toward a Unified Theory of Biology. University of Chicago Press.
    "By combining recent advances in the physical sciences with some of the novel ideas, techniques, and data of modern biology, this book attempts to achieve a new and different kind of evolutionary synthesis. I found it to be challenging, fascinating, infuriating, and provocative, but certainly not dull."--James H, Brown, University of New Mexico "This book is unquestionably mandatory reading not only for every living biologist but for generations of biologists to come."--Jack P. Hailman, Animal Behaviour , review of the first (...)
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  36. Gregory G. Brunk (2000). Understanding Self‐Organized Criticality as a Statistical Process. Complexity 5 (3):26-33.
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  37. Walter Buckley (1968). Society as a Complex Adaptive System. In Modern Systems Research for the Behavioral Scientist. Aldine
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  38. Walter Frederick Buckley (1998). Society-- A Complex Adaptive System Essays in Social Theory.
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  39. Ali Bulent Cambel (1993). Applied Chaos Theory a Paradigm for Complexity.
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  40. Richard Campbell (2009). A Process-Based Model for an Interactive Ontology. Synthese 166 (3):453 - 477.
    The paper proposes a process-based model for an ontology that encompasses the emergence of process systems generated by increasingly complex levels of organization. Starting with a division of processes into those that are persistent and those that are fleeting, the model builds through a series of exclusive and exhaustive disjunctions. The crucial distinction is between those persistent and cohesive systems that are energy wells, and those that are far-from-equilibrium. The latter are necessarily open; they can persist only by interaction with (...)
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  41. Fritjof Capra (2002). Complexity and Life. Emergence: Complexity and Organization 4 (1):15-33.
    During the last two decades, a new understanding of life emerged at the forefront of science.The development of complexity theory, technically known as nonlinear dynamics, has allowed scientists and mathematicians to model the complexities of living systems in new ways that have yielded many important discoveries. In this article, the author reviews the basic concepts, current achievements and status of complexity theory from the perspective of the new understanding of biological life. Models and theories discussed include the theory of dissipative (...)
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  42. Brian Castellani & Frederick William Hafferty (eds.) (2009). Sociology and Complexity Science. Springer.
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  43. Geoffrey K. Chambers (2015). Understanding Complexity: Are We Making Progress? Biology and Philosophy 30 (5):747-756.
    In recent years a new conceptual tool called Complexity Theory has come to the attention of scientists and philosophers. This approach is concerned with the emergent properties of interacting systems. It has found wide applicability from cosmology to Social Structure Analysis. However, practitioners are still struggling to find the best way to define complexity and then to measure it. A new book Complexity and the arrow of time by Lineweaver et al. contains contributions from scholars who provide critical reviews of (...)
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  44. Paul Cilliers (1998). Complexity and Postmodernism: Understanding Complex Systems. Routledge.
    Complexity and Postmodernism explores the notion of complexity in the light of contemporary perspectives from philosophy and science. The book integrates insights from complexity and computational theory with the philosophical position of thinkers including Derrida and Lyotard. Paul Cilliers takes a critical stance towards the use of the analytical method as a tool to cope with complexity, and he rejects Searle's superficial contribution to the debate.
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  45. J. Collier (2011). Explaining Biological Functionality: Is Control Theory Enough? South African Journal of Philosophy 30 (1):53-62.
    It is generally agreed that organisms are Complex Adaptive Systems. Since the rise of Cybernetics in the middle of the last century ideas from information theory and control theory have been applied to the adaptations of biological organisms in order to explain how they work. This does not, however, explain functionality, which is widely but not universally attributed to biological systems. There are two approaches to functionality, one based on etiology (what a trait was selected for), and the other based (...)
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  46. John Collier, Change and Identity in Complex Systems.
    Complex systems are dynamic and may show high levels of variability in both space and time. It is often difficult to decide on what constitutes a given complex system, i.e., where system boundaries should be set, and what amounts to substantial change within the system. We discuss two central themes: the nature of system definitions and their ability to cope with change, and the importance of system definitions for the mental metamodels that we use to describe and order ideas about (...)
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  47. John Collier, Organized Complexity: Properties, Models and the Limits of Understanding.
    Complexly organized systems include biological and cognitive systems, as well as many of the everyday systems that form our environment. They are both common and important, but are not well understood. A complex system is, roughly, one that cannot be fully understood via analytic methods alone. An organized system is one that shows spatio-temporal correlations that are not determined by purely local conditions, though organization can be more or less localizable within a system. Organization and complexity can vary independently to (...)
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  48. John Collier (1986). Entropy in Evolution. Biology and Philosophy 1 (1):5-24.
    Daniel R. Brooks and E. O. Wiley have proposed a theory of evolution in which fitness is merely a rate determining factor. Evolution is driven by non-equilibrium processes which increase the entropy and information content of species together. Evolution can occur without environmental selection, since increased complexity and organization result from the likely capture at the species level of random variations produced at the chemical level. Speciation can occur as the result of variation within the species which decreases the probability (...)
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  49. John Collier, A Dynamical Approach to Identity and Diversity in Complex Systems.
    The subject of this chapter is the identity of individual dynamical objects and properties. Two problems have dominated the literature: transtemporal identity and the relation between composition and identity. Most traditional approaches to identity rely on some version of classification via essential or typical properties, whether nominal or real. Nominal properties have the disadvantage of producing unnatural classifications, and have several other problems. Real properties, however, are often inaccessible or hard to define (strict definition would make them nominal). I suggest (...)
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  50. John Collier & Cliff Hooker (1999). Complexly Organised Dynamical Systems. Open Systems and Information Dynamics 6 (3):241–302.
    Both natural and engineered systems are fundamentally dynamical in nature: their defining properties are causal, and their functional capacities are causally grounded. Among dynamical systems, an interesting and important sub-class are those that are autonomous, anticipative and adaptive (AAA). Living systems, intelligent systems, sophisticated robots and social systems belong to this class, and the use of these terms has recently spread rapidly through the scientific literature. Central to understanding these dynamical systems is their complicated organisation and their consequent capacities for (...)
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