In June 1998 Hans Primas turned 70 y ears old. Although he himself is not fond of jubilees and although he lik es to play the decimal system of numb ers do wn as contingent, this is nev ertheless a suitable o ccasion to re ect on the professional work of one of the rare distinguished contemp orary scientists who attach equal imp ortance to exp erimen tal and theoretical and conceptual lines of researc h. Hans Primas' in terests ha (...) ve covered an enormous range: metho ds and instruments for n uclear magnetic resonance, theoretical c hemistry , C - and W -algebraic formulations of quantum mechanics, the measurement problem and its various implications, holism and realism in quantum theory , theory reduction, the w ork and p ersonality of Wolfgang Pauli, as well as Jungian psychology . In man y of these elds he provided imp ortan t and original fo o d for though t, in some cases going far b eyond the ev eryda y business in the scientic world. As is the case with other scien tists who are conceptually innov ativ e, Hans Primas is read more than he is quoted. His in uence is due to his writings. Even with the current ood of publications, he still p erforms the miracle of ha ving scientists eagerly a waiting his next publication. His external life, by wa y of contrast, is not very sp ectacular. With the exception of a brief p erio d as a guest professor at Washington Univ ersity at St. Louis, he has never b een a wa y from Zuric h for an y length of time. He has nev er b een a warded an y prizes, nev er organized a congress, nev er done any organizational work in a scientic so ciety . He delib erately distanced himself from the hustle and bustle of national and in ternational scien tic business. (shrink)
1 – Institute for Frontier Areas of Psychology and Mental Health, Wilhelmstr. 3a, 79098 Freiburg, Germany 2 – Parmenides Center, Via Mellini 26-28, 57031 Capoliveri, Italy 3 – Department of Ophtalmology, University of Freiburg, Killianstr. 5, 79106 Freiburg, Germany 4 – Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany Abstract The “Necker-Zeno model”, a model for bistable perception inspired by the quantum Zeno eﬀect, was previously used to relate three basic time scales of cognitive relevance to (...) one another in a quantitative manner. In this paper, the model predictions are compared with experimental results obtained under discontinuous presentation of an ambiguous stimulus. In addition to earlier results for long inter-stimulus intervals, we show that the reversal dynamics according to the Necker-Zeno model is also in agreement with new results for short inter-stimulus intervals. Moreover, we reﬁne the model in such a way that it accounts for the distribution of “dwell times” (inverse reversal rates). Finally, we indicate applications concerning the modiﬁcation of cognitive time scales under conditions of psychopathological impairments and meditationinduced modes of awareness. ∗Address correspondence to this author at the Theory Division of the Institute for Frontier Areas of Psychology, Wilhelmstr. 3a, D–79098 Freiburg, Germany; E-mail: firstname.lastname@example.org.. (shrink)
Two-dimensional coupled map lattices have global stability properties that depend on the coupling between individual maps and their neighborhood. The action of the neighborhood on individual maps can be implemented in terms of ‘‘causal’’ coupling (to spatially distant past states) or ‘‘non-causal’’ coupling (to spatially distant simultaneous states). In this contribution we show that globally stable behavior of coupled map lattices is facilitated by causal coupling, thus indicating a surprising relationship between stability and causality. The inﬂuence of causal versus non-causal (...) coupling for synchronous and asynchronous updating as a function of coupling strength and for different neighborhoods is analyzed in detail. r 2004 Elsevier B.V. All rights reserved. (shrink)
Numerical simulations of coupled map lattices (CMLs) and other complex model systems show an enormous phenomenological variety that is diﬃcult to classify and understand. It is therefore desirable to establish analytical tools for exploring fundamental features of CMLs, such as their stability properties. Since CMLs can be considered as graphs, we apply methods of spectral graph theory to analyze their stability at locally unstable ﬁxed points for diﬀerent updating rules, diﬀerent coupling scenarios, and diﬀerent types of neighborhoods. Numerical studies are (...) found to be in excellent agreement with our theoretical results. (shrink)
A major driving force behind the attention that cognitive neuroscience has received in recent decades is the deep mystery of how consciousness is related to brain activity. Many scientists have been fascinated by the wealth of empirical data for individual neurons, neural assemblies, brain areas, and related psychological and behavioral features, and by progressively powerful computational tools to simulate corresponding cortical networks. At the same time, the interested public has been attracted by fancy illustrations of brain activity (e.g., from imaging (...) techniques) and by pretentious claims of neural solutions to basic philosophical problems (e.g., free will versus determinism) in popular magazines and newspapers. However, heaps of data, extensive simulations, pretty pictures and bold statements cannot replace the insight that is inevitable to relate the available facts to one another in an intelligible manner. I am talking about the old-fashioned stance that understanding is the ultimate goal of scientiﬁc eﬀort. In this respect, the need for new conceptual and theoretical ideas in cognitive neuroscience begins to be recognized by prominent representatives of the ﬁeld. Theory in this sense must not be confused with models ﬁtting data, e.g. by regression algorithms, cluster analyses, etc. It is uncontroversial that experimental and numerical work is and will remain mandatory for scientiﬁc progress. But it can only unfold its full value if it is embedded within a profound theoretical framework. To formulate a serious, clear-cut and transparent formal framework for cognitive neuroscience is a challenge comparable to the early stage of physics four centuries ago. Only very few approaches worth mentioning are visible in contemporary literature. I think that Wallace’s book presents an appreciable step in the right direction. However, it is not the ultimate breakthrough yet. Much is left for future work before a full-ﬂedged theory of consciousness will be established. In two central conceptual respects, Wallace builds on earlier work: Dretske’s (1981) usage of informational terms in consciousness research and Baars’ (1988) global neuronal workspace model.. (shrink)
The emergence of mental states from neural states by partitioning the neural phase space is analyzed in terms of symbolic dynamics. Well-deﬁned mental states provide contexts inducing a criterion of structural stability for the neurodynamics that can be implemented by particular partitions. This leads to distinguished subshifts of ﬁnite type that are either cyclic or irreducible. Cyclic shifts correspond to asymptotically stable ﬁxed points or limit tori whereas irreducible shifts are obtained from generating partitions of mixing hyperbolic systems. These stability (...) criteria are applied to the discussion of neural correlates of consiousness, to the deﬁnition of macroscopic neural states, and to aspects of the symbol grounding problem. In particular, it is shown that compatible mental descriptions, topologically equivalent to the neurodynamical description, emerge if the partition of the neural phase space is generating. If this is not the case, mental descriptions are incompatible or complementary. Consequences of this result for an integration or uniﬁcation of cognitive science or psychology, respectively, will be indicated. (shrink)
Many philosophical and scientiﬁc discussions of topics of mind-matter research make implicit assumptions, in various guises, about the distinction between mind and matter. Currently predominant positions are based on either reduction or emergence, providing either monistic or dualistic scenarios. A more-involved framework of thinking, which can be traced back to Spinoza and Leibniz, combines the two scenarios, dualistic (with mind and matter separated) and monistic (with mind and matter unseparated), in one single picture. Based on such a picture, the transition (...) from a domain with mind and matter unseparated to separate mental and material domains can be viewed as a result of a general kind of symmetry breaking, which can be described formally in terms of inequivalent representations. The possibility of whether this symmetry breaking might be connected to the emergence of temporal directions from temporally non-directed or even non-temporal levels of reality will be discussed. Correlations between mental and material aspects of reality could then be imagined as remnants of such primordial levels. Diﬀerent conceivable types of inequivalent representations would lead to correlations with diﬀerent characteristics. (shrink)
The concept of contextual emergence is proposed as a non-reductive, yet welldeﬁned relation between different levels of description of physical and other systems. It is illustrated for the transition from statistical mechanics to thermodynamical properties such as temperature. Stability conditions are crucial for a rigorous implementation of contingent contexts that are required to understand temperature as an emergent property. It is proposed that such stability conditions are meaningful for contextual emergence beyond physics as well.
Jason Brown started his career as a neurologist specializing in language disorders, perceptive illusions, and impaired action. But beyond his activity as a physician he is a man of genuinely theoretical appetite. As satisfying as it is to help improve the situation of sick fellow humans, this alone does not characterize him well. Those who know him closer know his insistent urge to find a philosophical framework for his clinical practice and research, together with his desire for a more humane (...) society. Those who do not know him will see this immediately when they read his most recent book Process and the authentic life (Brown 2006). This is, in a nutshell, how and why Brown came to look into process philosophy, as an alternative to philosophical systems focusing on substances such as the Cartesian res cogitans and res extensa, on which science and technology are essentially based. Process philosophy holds some radical deviations from these systems, and may be regarded as complementary to them (Roemer 2006), although any such convergence is hotly contested (e.g., Bickhard 2004). Best known among adherents of a process worldview is Whitehead with his opus magnum Process and Reality. Brown’s approach is clearly in the spirit of Whitehead’s. However, due to his medical and psychological background it differs in motivation, and consequently it differs in the way it is carried out. While Whitehead, originally a mathematician, tried to be as precise and detailed as possible in his definitions, arguments and conclusions, Brown strives for his humanistic goal more directly. His accounts are based on examples rather than formal inferences, everyday experiences rather than abstract constructions. (shrink)
A key topic in the work of Burghard Rieger is the notion of meaning. To explore this notion, he and his collaborators developed a most sophisticated approach combining theoretical ideas and concepts of semiotics with empirical and numerical tools of computational linguistics (see  for a most recent comprehensive account). In the present contribution, relations of Rieger’s achievements to some issues of interest in the physics and philosophy of complex systems will be addressed.
The fundamental problem on which Ilya Prigogine and the Brussels- Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like Uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of (...) time was either an artifact of our observations or due to very special initial conditions. An alternative approach, followed by the Brussels-Austin Group, is to consider the observed direction of time to be a basic physical phenomenon due to the dynamics of physical systems. This essay focuses mainly on recent developments in the Brussels-Austin Group after the mid 1980s. The fundamental concerns are the same as in their earlier approaches (subdynamics, similarity transformations), but the contemporary approach utilizes rigged Hilbert space (whereas the older approaches used Hilbert space). While the emphasis on nonequilibrium statistical mechanics remains the same, their more recent approach addresses the physical features of large Poincar´. (shrink)
We present results from numerical studies of supervised learning operations in recurrent networks considered as graphs, leading from a given set of input conditions to predetermined outputs. Graphs that have optimized their output for particular inputs with respect to predetermined outputs are asymptotically stable and can be characterized by attractors which form a representation space for an associative multiplicative structure of input operations. As the mapping from a series of inputs onto a series of such attractors generally depends on the (...) sequence of inputs, this structure is generally noncommutative. Moreover, the size of the set of attractors, indicating the complexity of learning, is found to behave non-monotonically as learning proceeds. A tentative relation between this complexity and the notion of pragmatic information is indicated. (shrink)
HPS: 1959 was indeed early in my career as a PhD, but more than a dozen years into my concerns with these matters. Already in high school I had become very interested in the wave-particle puzzle, and my driving motive in becoming a physicist was really to solve that mystery. Looking now at my 1959 essay I find it remarkably mature. I had a solid grasp of the technical and philosophical aspects of the situation. I find in it today nothing (...) that I would emend or consider naive or deficient. It is a well-reasoned and sober assessment of the situation, and ends with the conclusion that quantum theory “primarily is a synthesis of the idealistic and materialistic world views. To some extent it also reconciles the monistic and pluralistic attitudes, provides a natural understanding of creation, and permits a reconciliation of the deterministic aspects of nature with the action of free will.” I now say much more about these matters, but nothing contrary to what I said then. (shrink)
The idea of complementarity already appears in William James’ (1890a, p. 206) Principles of Psychology in the chapter on “the relations of minds to other things”. Later, in 1927, Niels Bohr introduced complementarity as a fundamental concept in quantum mechanics. It refers to properties (observables) that a system cannot have simultaneously, and which cannot be simultaneously measured with arbitrarily high accuracy. Yet, in the context of classical physics they would both be needed for an exhaustive description of the system.
The study of instabilities in perception has attracted much interest in recent decades. The presented investigations focus on electrophysiological correlates of orientation reversals of both ambiguous visual stimuli and alternating non-ambiguous stimuli, representing the two options of the ambiguous version. Based on a refined experimental setup, significant features in the event-related potentials associated with the perception of orientation reversal were found in both cases. Their occipital location, their early occurence (200–250 ms), and their latency difference (50 ms) offer interesting perspectives (...) for an understanding of unstable brain states in terms of basic concepts of dynamical systems. (shrink)
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 (...) and emergence rates of irregular states display such parameter-independent properties. Ó 2004 Elsevier Ltd. All rights reserved. (shrink)
Two distinct conceptions for the relation between reversible, time-reversal invariant laws of nature and the irreversible behavior of physical systems are outlined. The standard, extrinsic concept of irreversibility is based on the notion of an open system interacting with its environment. An alternative, intrinsic concept of irreversibility does not explicitly refer to any environment at all. Basic aspects of the two concepts are presented and compared with each other. The significance of the terms extrinsic and intrinsic is discussed.
Summary. We discuss a specific way in which the notion of complementarity can be based on the dynamics of the system considered. This approach rests on an epistemic representation of system states, reflecting our knowledge about a system in terms of coarse grainings (partitions) of its phase space. Within such an epistemic quantization of classical systems, compatible, comparable, commensurable, and complementary descriptions can be precisely characterized and distinguished from each other. Some tentative examples are indicated that, we suppose, would have (...) been of interest to Pauli. (shrink)
Weakly interacting lattices of coupled maps can be modeled as ordinary coupled map lattices separated from each other by boundary regions with small coupling parameters. We demonstrate that such weakly interacting lattices can nevertheless have unexpected and striking effects on each other. Under specific conditions, particular stability properties of the lattices are significantly influenced by their weak mutual interaction. This observation is tantamount to an efficacious information flow across the boundary.
The behavior of two-dimensional coupled map lattices is studied with respect to the global stabilization of unstable local fixed points without external control. It is numerically shown under which circumstances such inherent global stabilization can be achieved for both synchronous and asynchronous updating. Two necessary conditions for inherent global stabilization are derived analytically.
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 (...) systems in particular. (shrink)
The behavior of Lyapunov exponents λ and dynamical entropies h, whose positivity characterizes chaotic motion, under Lorentz and Rindler transformations is studied. Under Lorentz transformations, λ and h are changed, but their positivity is preserved..
The machine sculpture “Klamauk” (English: hubbub) by the Swiss artist Jean Tinguely (1925–1991), featured on the cover, looks like a perfect example of a deterministic process, but it also looks as if thrown together “by chance”. This tension between determinism and chance has been of longstanding concern in the sciences and the humanities. And nowhere is this tension stronger than in debates about free will and our place in the world, where determinism seems bound to crowd freedom out of the (...) picture, yet freedom in the absence of some ordered realm of causes seems inconceivable. (shrink)
Systems exhibiting relationships between mental states and material states, briefly mind-matter systems, offer epistemological and methodological problems exceeding those of systems with mental states or material states alone. Some of these problems can be addressed by proceeding from standard firstorder approaches to more sophisticated second-order approaches. These can illuminate questions of reference and validity, and their ramifications for the topic of reproducibility. For various situations in complex systems it is shown that second-order approaches need to be employed. Considering mind-matter systems (...) as generalized complex systems provides some guidelines for analyzing the problem of reproducibility in such systems from a novel perspective. (shrink)
“Man klagt zu Unrecht, dass unsere Zeit keine Philosophen mehr habe”, pflegte der Theologe und Wissenschaftsorganisator von Harnack zu sagen, “sie sitzen nur jetzt in der anderen Fakult¨ at, und ihre Namen sind Planck und Einstein.” Mit beiden sind die Anf¨.
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Scientific research takes place in the field of tension between accepted coherent knowledge and not understood, not integrated fragments: between orthodoxy and anomaly. Orthodox knowledge is characterized by laws and norms which can be conceived formally (deterministic or statistical laws), methodologically (criteria for scientific work), or conceptually (frameworks of thinking, regulative principles). I propose to classify anomalies according to their feasibility of being systematically connected with accepted knowledge. In this way, one can distinguish anomalies at the frontier of our knowledge, (...) interior anomalies surrounded by accepted knowledge, and anomalies in no man’s land. I discuss examples which are intended to exemplify essential characteristics of each of these groups. Anomalies are the salt in the soup of science and dissolve where the domain of accepted knowledge extends or deepens – either by being elucidated or by being abolished. (shrink)
Stable neuronal assemblies are generally regarded as neural correlates of mental representations. Their temporal sequence corresponds to the experience of a direction of time, sometimes called the psychological time arrow. We show that the stability of particular, biophysically motivated models of neuronal assemblies, called coupled map lattices, is supported by causal interactions among neurons and obstructed by non-causal or anti-causal interactions among neurons. This surprising relation between causality and stability suggests that those neuronal assemblies that are stable due to causal (...) neuronal interactions, and thus correlated with mental representations, generate a psychological time arrow. Yet this impact of causal interactions among neurons on the directed sequence of mental representations does not rule out the possibility of mentally less efficacious non-causal or anti-causal interactions among neurons. (shrink)
This contribution reflects on Nicholas Rescher's discussion of “process and persons” in his book Process Metaphysics. Its main purposes are to offer conceptual commentary on some of Rescher's terms, and to suggest some options for process thinking more radical than Rescher's, partly motivated by recent developments in science and philosophy. First, a brief analysis of the relation between process and time is presented, emphasizing irreversibility and temporal holism as crucial for a processual worldview. Second, instability and transiency are introduced as (...) key concepts for a better understanding of notions such as creativity and freedom. Third, the importance of the sociocultural domain is pointed out in addition to psychological and biophysical factors for the constitution of personhood. And fourth, it is argued that such an extension can be endowed with ontological significance in the framework of a non-reductive and non-hierarchical ontological relativity. (shrink)
ungster Zeit tritt allerdings im Selbstverst¨ andnis mancher Wissenschaftsbereiche die Rolle theoretischer Arbeit zunehmend zugunsten von anderen, zum Teil sachfremden Erw¨ agungen (wie etwa Aufmerksamkeit seitens von Medien und Wirtschaft) in den Hintergrund. Theoretische Arbeit wird in solchen F¨.
More than thirty years ago, Amari and colleagues proposed a statistical framework for identifying structurally stable macrostates of neural networks from observations of their microstates. We compare their stochastic stability criterion with a deterministic stability criterion based on the ergodic theory of dynamical systems, recently proposed for the scheme of contextual emergence and applied to particular inter-level relations in neuroscience. Stochastic and deterministic..
Summary. It is proposed to translate the mind-matter distinction into terms of mental and physical time. In the spirit of this idea, we hypothesize a relation between the intensity of mental presence and a crucial time scale (some seconds) often referred to as a measure for the duration of nowness. This duration is experimentally accessible and might, thus, offer a suitable way to characterize the intensity of mental presence. Interesting consequences with respect to the idea of a generalized notion of (...) mental presence, with human consciousness as a special case, are outlined. Our approach includes some features consistent with other, related ideas which are indicated. (shrink)
A novel conceptual framework for theoretical psychology is presented and illustrated for the example of bistable perception. A basic formal feature of this framework is the non-commutativity of operations acting on mental states. A corresponding model for the bistable perception of ambiguous stimuli, the Necker–Zeno model, is sketched and some empirical evidence for it so far is described. It is discussed how a temporal non-locality of mental states, predicted by the model, can be understood and tested.
Quantum cognition research applies abstract, mathematical principles of quantum theory to inquiries in cognitive science. It differs fundamentally from alternative speculations about quantum brain processes. This topic presents new developments within this research program. In the introduction to this topic, we try to answer three questions: Why apply quantum concepts to human cognition? How is quantum cognitive modeling different from traditional cognitive modeling? What cognitive processes have been modeled using a quantum account? In addition, a brief introduction to quantum probability (...) theory and a concrete example is provided to illustrate how a quantum cognitive model can be developed to explain paradoxical empirical findings in psychological literature. (shrink)
Dual-aspect monism and neutral monism offer interesting alternatives to mainstream positions concerning the mind-matter problem. Both assume a domain underlying the mind-matter distinction, but they also differ in definitive ways. In the twentieth century, variants of both positions have been advanced by a number of protagonists. One of these variants, the dual-aspect monism due toWolfgang Pauli and Carl Gustav Jung, will be described and commented on in detail. As a unique feature in the Pauli-Jung conception, the duality of mental and (...) material aspects is specified in terms of a complementarity. This sounds innocent, but entails a number of peculiarities distinguishing their conjecture from other approaches. (shrink)
Temporally non-local measurements -- single measurements yielding information about the state of a system at different instances-- may provide a way to observe non-classical behaviour in mental systems. The signature for such behaviour is a violation of temporal Bell inequalities. We present such inequalities applicable to scenarios with two alternating mental states, such as in the perception of ambiguous figures. We indicate empirical options for testing temporal Bell inequalities, and speculate about possible explanations in case these inequalities are indeed violated.
This contribution addresses major distinctions between the notions of determinism, causation, and prediction, as they are typically used in the sciences. Formally, this can be elegantly achieved by two ingredients: (i) the distinction of ontic and epistemic states of a system, and (ii) temporal symmetry breakings based on the mathematical concept of the affine time group. Key aspects of the theory of deterministically chaotic systems together with historical quotations from Laplace, Maxwell, and Poincare provide significant illustrations. An important point of (...) various discussions in consciousness studies (notably about 'mental causation' and 'free agency'), the alleged 'causal closure of the physical', will be analysed on the basis of the affine time group and the breakdown of its symmetries. (shrink)
We propose a distinction between precategorial, acategorial and categorial states within a scientiﬁcally oriented understanding of mental processes. This distinction can be speciﬁed by approaches developed in cognitive neuroscience and the analytical philosophy of mind. On the basis of a representational theory of mental processes, acategoriality refers to a form of knowledge that presumes fully developed categorial mental representations, yet refers to nonconceptual experiences in mental states beyond categorial states. It relies on a simultaneous experience of potential individual representations and (...) their actual “representational ground”, an undiﬀerentiated precategorial state. This simultaneity is possible if the mental state does not reside in a representation but in between representations. Acategoriality can be formally modeled as an unstable state of a dynamical mental system that is subject to particular stability criteria. (shrink)
The concept of contextual emergence has been proposed as a non-reductive, yet well- defined relation between different levels of description of physical and other systems. It is illustrated for the transition from statistical mechanics to thermodynamical properties such as temperature. Stability conditions are shown to be crucial for a rigorous implementation of contingent contexts that are required to understand temperature as an emergent property. Are such stability conditions meaningful for contextual emergence beyond physics as well? An affirmative example from cognitive (...) neuroscience addresses the relation between neurobiological and mental levels of description. For a particular class of partitions of the underlying neurobiological phase space, so-called generating partitions, the emergent mental states are stable under the dynamics. In this case, mental descriptions are (i) faithful representations of the neurodynamics and (ii) compatible with one another. (shrink)
Dual-aspect approaches (or double-aspect approaches)consider mental and material domains of reality as aspects, or manifestations, of one underlying, unseparated reality. In such a framework, the distinction between mind and matter can be regarded as a basic tool for achieving epistemic access to, i.e. gather knowledge about, both the separated do- mains and the underlying reality. In this sense, the status of the underlying, psychophysically neutral domain is ontic relative to the mind-matter distinction.
The role of contingent contexts in formulating relations between properties of systems at different descriptive levels is addressed. Based on the distinction between necessary and sufficient conditions for interlevel relations, a comprehensive classification of such relations is proposed, providing a transparent conceptual framework for discussing particular versions of reduction, emergence, and supervenience. One of these versions, contextual emergence, is demonstrated using two physical examples: molecular structure and chirality, and thermal equilibrium and temperature. The concept of stability is emphasized as a (...) basic guiding principle of contextual property emergence. (shrink)