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- Aerts, D. (2005). Ceci n'est pas Heinz von Foerster.
Constuctivist Foundations,1, pp. 13-16.- Aerts, D. (2005). Towards a new democracy: Consensus through quantum parliament. In D. Aerts, B. D'Hooghe and N. Note (Eds.),
Worldviews, Science and Us, Redemarcating Knowledge and its Social and Ethical Implications. Singapore: World Scientific. Archive reference and link: http://uk.arxiv.org/abs/physics/0503078.

Abstract:We compare different actual forms of democracy and analyse in which way they are variations of a 'natural consensus decision process'. We analyse how 'consensus decision followed by majority voting' is open to 'false play' by the majority, and investigate how other types of false play appear in alternative types of democratic decision procedures.We introduce the combined notion of 'quantum parliament' and 'quantum decision procedure', and prove it to be the only one, when applied after consensus decision, that is immune to false play.- Aerts, D. and Deses, D. (2005). State property systems and orthogonality.
International Journal of Theoretical Physics,44, pp. 919-929. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0211095.

Abstract:The structure of a state property system was introduced to formalize in a complete way the operational content of the Geneva-Brussels approach to the foundations of quantum mechanics, and the category of state property systems was proven to be equivalence to the category of closure spaces. The first axioms of standard quantum axiomatics (state determination and atomisticity) have been shown to be equivalent to the T0 and T1 axioms of closure spaces, and classical properties to correspond to clopen sets, leading to a decomposition theorem into classical and purely nonclassical components for a general state property system. The concept of orthogonality, very important for quantum axiomatics, had however not yet been introduced within the formal scheme of the state property system. In this paper we introduce orthogonality in a operational way, and define ortho state property systems. Birkhoff's well known biorthogonal construction gives rise to an orthoclosure and we study the relation between this orthoclosure and the operational orthogonality that we introduced.- Aerts, D., D'Hondt, E. and D'Hooghe, B. (2005). A geometrical representation of entanglement as internal constraint.
International Journal of Theoretical Physics,44, pp. 897-907. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0211094.

Abstract:We study a system of two entangled spin 1/2, were the spin's are represented by a sphere model developed within the hidden measurement approach which is a generalization of the Bloch sphere representation, such that also the measurements are represented. We show how an arbitrary tensor product state can be described in a complete way by a specific internal constraint between the ray or density states of the two spin 1/2. We derive a geometrical view of entanglement as a 'rotation' and 'stretching' of the sphere representing the states of the second particle as measurements are performed on the first particle. In the case of the singlet state entanglement can be represented by a real physical constraint, namely by means of a rigid rod.- Aerts, D. and D'Hooghe, B. (2005). The nature of time as a consequence of how we construct the world. In R. Buccheri, A. C. Elitzur and M. Saniga (Eds.),
Endophysics, Time, Quantum and the Subjective(pp. 113 - 130). Singapore: World Scientific.

Abstract:In classical physics there was a clear understanding of what physical space and time are: physical space is the theatre of the collection of all events that are actual at a certain moment of time, and physical time is the parametrization of the flow of time. 3-dimensional space and 1-dimensional time have been substituted by 4-dimensional time-space in relativity theory. But if reality is the 4-dimensional time-space manifold of relativity theory, what is then the meaning of 'change in time'? We investigate this problem of relativity theory by following an operational approach originally elaborated for quantum mechanics. We show that the contradiction between a geometric view and process view of reality is due to a misconception in the interpretation of relativity theory. We argue that it is not time which is space-like, with the inevitable paradoxical situation of a block universe as result, but on the contrary, it is space which is time-like. This 'dynamic', 'time-like' conception of space answers the question of the meaning of 'change in time' within the 4-dimensional reality of relativity theory, and puts forward a new view on other aspects of the theory.- Aerts, D., D'Hooghe, B. and Note, N. (Eds.), (2005).
Worldviews, Science and Us: Redemarcating Knowledge and its Social and Ethical Implications. Singapore: World Scientific.- Aerts, D., D'Hooghe, B. and Note, N. (2005). Worldviews, sciences and us: Global perspectives. In D. Aerts, B. D'Hooghe and N. Note (Eds.),
Worldviews, Science and Us: Redemarcating Knowledge and Its Social and Ethical Implications. Singapore: World Scientific.- Aerts, D. and Gabora, L. (2005). A theory of concepts and their combinations I: The structure of the sets of contexts and properties.
Kybernetes,34, pp. 167-191. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0402207.

Abstract:We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context into the mathematical structure used to describe a concept, and thereby model how context influences the typicality of a single exemplar and the applicability of a single property of a concept. We introduce the notion `state of a concept' to account for this contextual influence, and show that the structure of the set of contexts and of the set of properties of a concept is a complete orthocomplemented lattice. The structural study in this article is a preparation for a numerical mathematical theory of concepts in the Hilbert space of quantum mechanics that allows the description of the combination of concepts (see quant-ph/0402205).- Aerts, D. and Gabora, L. (2005). A theory of concepts and their combinations II: A Hilbert space representation.
Kybernetes,34, pp. 192-221. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0402205.

Abstract:The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are done in Hilbert space makes it possible to model how context influences the state of a concept. Moreover, a solution to the combination of concepts is proposed. Using the tensor product, a procedure for describing combined concepts is elaborated, providing a natural solution to the pet fish problem. This procedure allows the modeling of an arbitrary number of combined concepts. By way of example, a model for a simple sentence containing a subject, a predicate and an object, is presented.- Aerts, S., Aerts, D. and Schroeck, F. E. (2005). Necessity of combining mutually incompatible perspectives in the construction of a global view: Quantum probability and signal analysis. In D. Aerts, B. D'Hooghe and N. Note (Eds.),
Worldviews, Science and Us: Redemarcating Knowledge and Its Social and Ethical Implications. Singapore: World Scientific.

Abstract:The scientific fields of quantum mechanics and signal-analysis originated within different settings, aimed at different goals and started from different scientific paradigms. Yet the development of the two subjects has become increasingly intertwined. We argue that these similarities are rooted in the fact that both fields of scientific inquiry had to deal with finding a single description for a phenomenon that yields complete information about itself only when we consider mutually incompatible accounts of that phenomenon.- Gabora, L. and Aerts, D. (2005). Evolution as context-driven actualization of potential.
Interdisciplinary Science Reviews 30, pp. 69-88. Archive reference and link: http://uk.arxiv.org/abs/q-bio/0511007.

Abstract:While natural selection is often viewed as synonymous with evolution, it is widely felt to be inadequate as a theory of biological evolution; moreover, historically the concept of evolution has not been limited to biology. We propose an integrative framework for characterizing how entities evolve, in which evolution is viewed as a process of context-driven actualization of potential (CAP). Processes of change differ according to the degree of nondeterminism, and the degree to which they are sensitive to, internalize, and depend upon a particular environment or context. The approach enables us to embed phenomena across multiple disciplines into a broader conceptual framework. It suggests that the dynamical evolution of a quantum entity as described by the Schršdinger equation is not fundamentally different from change provoked by a measurement often referred to as collapse but a limiting case, with only one way to collapse. The biological transition to coded replication is seen as a means of preserving structure in the face of context, and sexual replication as a means of increasing potentiality thus enhancing diversity through interaction with context. The integrative framework sheds light on biological concepts like selection and fitness, reveals how exceptional Darwinian evolution is as a means of Ôchange of stateÕ, and clarifies in what sense culture (and the creative process underlying it) is and is not Darwinian.- Gabora, L. and Aerts, D. (2005). Distilling the essence of an evolutionary process, and implications for a formal description of culture. In W. Kistler (Ed.),
Proceedings of Center for Human Evolution Workshop #5: Cultural Evolution, May 2000, Foundation for the Future, Seattle WA.- Note, N., Pinxten, H. and Aerts, D. (2005). Towards a re-delineation of the Human Self-understanding within the western worldview: Its social and ethical implications. In D. Aerts, B. D'Hooghe and N. Note (Eds.),
Worldviews, Science and Us: Redemarcating Knowledge and Its Social and Ethical Implications. Singapore: World Scientific.

Abstract:This article focuses on the relation between worldviews, sciences and us. Its point of departure is the significant mutual influence of the Western worldview and sciences. It shows how the intertwined construction of science and worldview has modelled our conceptual self-understanding, our being and our acting. The issue is considered from a philosophical-anthropological stance, with due attention being given to past delineations and future alternatives. It is argued that, within the framework of the Western worldview, self-realisation is considered essential for being a human self. There is a tacit, yet conscious, agreement that the way to attain self-realisation is through the gradual development of two potentials: the rational potential and the potential for self-expression. The authors recognise that both are indispensable in forming the human self, but point out that the nature of the development of these potentials can conceptually be misinterpreted, causing problems on the individual, societal and ecological levels. In order to prevent the development of the rational potential and the potential for self-expression from receiving undue emphasis, two more potentials are introduced on the conceptual level, to wit the ethical potential and the potential to be situated in and oriented towards a larger and meaningful whole. The assumption is that bringing these to the fore will also affect the very definition of self-realisation.

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1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000,