Results for 'Topos'

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  1. Topos Theoretic Quantum Realism.Benjamin Eva - 2017 - British Journal for the Philosophy of Science 68 (4):1149-1181.
    ABSTRACT Topos quantum theory is standardly portrayed as a kind of ‘neo-realist’ reformulation of quantum mechanics.1 1 In this article, I study the extent to which TQT can really be characterized as a realist formulation of the theory, and examine the question of whether the kind of realism that is provided by TQT satisfies the philosophical motivations that are usually associated with the search for a realist reformulation of quantum theory. Specifically, I show that the notion of the quantum (...)
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  2. Topos of existential graphs over Riemann Surfaces.Angie Hugueth - 2025 - Cognitio 26 ( 2316-5278): 1-12.
    Peirce’s Existential Graphs provide a geometrical understanding of a variety of logics (classical, intuitionistic, modal, fi rst-order). The geometrical interpretation is given by topological transformations of closed (Jordan) curves on the plane, but it can be extended to other surfaces (sphere, cylinder, torus, etc.) The result provides the appearance of new logics related to the shapes of the surfaces. Going beyond, one can draw existential graphs over general Riemann Surfaces, and, introducing tools from algebraic geometry (Sheaves, Grothendieck Toposes, Elementary Toposes), (...)
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  3.  33
    The Topos of Music: Geometric Logic of Concepts, Theory and Performance.G. Mazzola - 2002 - Birkhauser Verlag. Edited by Stefan Göller & Stefan Müller.
    The Topos of Music is the upgraded and vastly deepened English extension of the seminal German Geometrie der Töne. It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der Töne in 1990. The conceptual basis has been vastly generalized to topos-theoretic foundations, including a corresponding thoroughly geometric musical logic. The theoretical models and results now include topologies for rhythm, melody, and harmony, as well as a classification theory (...)
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  4. Topos Perspective on the Kochen-Specker Theorem: I. Quantum States as Generalized Valuations.Chris Isham & Jeremy Butterfield - 1998 - International Journal of Theoretical Physics 37 (11).
    Any attempt to construct a realist interpretation of quantum theory founders on the Kochen-Specker theorem, which asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on all operators, and which respects an appropriate version of the functional composition principle. The truth-values assigned to propositions are (i) contextual; and (ii) multi-valued, where the space of contexts and the multi-valued logic for each context (...)
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  5.  46
    Topos de grafos existenciais sobre superfícies de Riemann.Angie Hugueth - 2025 - Cognitio 26 (1):e70114.
    Os Grafos Existenciais de Peirce oferecem uma compreensão geométrica de uma variedade de lógicas (clássica, intuicionista, modal, de primeira ordem). A sua interpretação geométrica é dada por transformações topológicas de curvas fechadas (Jordan) no plano, mas pode ser estendida a outras superfícies (esfera, cilindro, toro etc.). Além disso, é possível desenhar grafos existenciais sobre superfícies de Riemann gerais e, introduzindo ferramentas da geometria algébrica (Feixes, Toposes de Grothendieck, Toposes Elementares), é possível tentar capturar as lógicas nas formas geométricas por meio (...)
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  6.  77
    Rethinking topos in the discourse historical approach: Endoxon seeking and argumentation in Greek media discourses on ‘Islamist terrorism’.Salomi Boukala - 2016 - Discourse Studies 18 (3):249-268.
    The concept of topos has received considerable attention from both argumentation and discourse studies, although its usage and meaning remain obscure. In this article, I argue that the rediscovery of Aristotelian thought might provide a comprehensible explication of topos. Despite the discourse historical approach’s emphasis on topos, its context is found to be limited and this exposes the argumentation strategies of the DHA to criticism. To overcome any shortcomings and provide a better understanding of topos, a (...)
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  7. A topos perspective on the kochen-Specker theorem: III. Von Neumann algebras as the base category.John Hamilton, Chris Isham & Jeremy Butterfield - unknown
    We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory, and of related issues such as the Kochen-Specker theorem. This extension has two main parts: the use of von Neumann algebras as a base category (Section 2); and the relation of our generalized valuations to (i) the assignment to quantities of intervals of real numbers, and (ii) the idea of a subobject of the coarse-graining presheaf (Section 3).
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  8.  57
    (1 other version)The Topos of Mu and the Predicative Self.J. Baird Callicott - 2023 - Dialogue and Universalism 33 (2):9-35.
    Terminologically, the “topos of mu” and the “predicative self” originated in the Kyoto School and are traceable to the work of its founder NISHIDA Kitarō. The full phrase was coined by NAKAMURA Yūjirō. Conceptually, the topos of mu or place of nothingness is Nishida’s development of the Buddhist notion of anatta or no self and radiating out from that locus of emptiness is a self constituted by its predicates or the things to which it is connected by an (...)
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  9. A topos perspective on the kochen-Specker theorem: II. Conceptual aspects, and classical analogues.Jeremy Butterfield & Chris Isham - unknown
    In a previous paper, we have proposed assigning as the value of a physical quantity in quantum theory, a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a valuation illuminates the Kochen-Specker theorem; and in part mathematical---the valuation arises naturally in the topos theory of presheaves. This paper discusses the conceptual aspects of this proposal. We also undertake two other tasks. First, we explain how the proposed (...)
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  10.  35
    Kulturowy topos Księgi (przyczynek do interpretacji).Bogdan Banasiak - 2009 - Humanistyka I Przyrodoznawstwo 15:7-24.
    Topos księgi należy do najsilniej zakorzenionych motywów w kulturze. Tradycyjnie wiążący się z księgami świętymi, średniowieczną Księgą Natury oraz nowożytną encyklopedią, występujący w filozofii, literaturze, mitach, legendach, religiach i kulturze masowej, oznaczał źródłową prawdę, pełnię sensu, zamknięcie i wyczerpanie, jednym słowem – wiedzę absolutną. Jego nowoczesna wersja jawi się zaś jako księga-kłącze, czyli niesterowny, acentryczny, niehierarchiczny system otwarty, którego współczesną wersję stanowi Internet.
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  11. A topos perspective on the kochen-Specker theorem: IV. Interval valuations.Jeremy Butterfield & Chris Isham - unknown
    We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory. In those papers, the main idea was to assign a sieve as a partial and contextual truth-value to a proposition that the value of a quantity lies in a certain set D of real numbers. Here we relate such sieve-valued valuations to valuations that assign to quantities subsets, rather than single elements, of their spectrum (we call these interval valuations). There are two (...)
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  12. (1 other version)Topos Semantics for Higher-Order Modal Logic.Steve Awodey, Kohei Kishida & Hans-Cristoph Kotzsch - 2014 - Logique Et Analyse 228:591-636.
    We define the notion of a model of higher-order modal logic in an arbitrary elementary topos E. In contrast to the well-known interpretation of higher-order logic, the type of propositions is not interpreted by the subobject classifier ΩE, but rather by a suitable complete Heyting algebra H. The canonical map relating H and ΩE both serves to interpret equality and provides a modal operator on H in the form of a comonad. Examples of such structures arise from surjective geometric (...)
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  13.  80
    Topos of Noise.Inigo Wilkins - 2023 - Angelaki 28 (3):144-162.
    This paper focuses on the significance of the concept of noise for cognition and computation. The concept of noise was massively transformed in the twentieth century with the advent of information theory, cybernetics, and computer science, all of which provide formal accounts of information and noise centrally concerned with contingency. We show how the concept has changed from these classical formulations, through developments in mathematics (topology and topos theory), computing (interactive computing and univalent foundations), and cognitive science (predictive processing (...)
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  14. Some Possible Roles for Topos Theory in Quantum Theory and Quantum Gravity.C. J. Isham & J. Butterfield - 2000 - Foundations of Physics 30 (10):1707-1735.
    We discuss some ways in which topos theory (a branch of category theory) can be applied to interpretative problems in quantum theory and quantum gravity. In Sec.1, we introduce these problems. In Sec.2, we introduce topos theory, especially the idea of a topos of presheaves. In Sec.3, we discuss several possible applications of topos theory to the problems in Sec.1. In Sec.4, we draw some conclusions.
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  15.  81
    Modality and Contextuality in Topos Quantum Theory.Benjamin Eva - 2016 - Studia Logica 104 (6):1099-1118.
    Topos quantum theory represents a whole new approach to the formalization of non-relativistic quantum theory. It is well known that TQT replaces the orthomodular quantum logic of the traditional Hilbert space formalism with a new intuitionistic logic that arises naturally from the topos theoretic structure of the theory. However, it is less well known that TQT also has a dual logical structure that is paraconsistent. In this paper, we investigate the relationship between these two logical structures and study (...)
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  16.  26
    Temporal Topos and Physics.Goro C. Kato - 2025 - In Temporal Topos Methods for the Philosophy of Natural Sciences: The Nexus of Ontology and Epistemology. Singapore: Springer Nature Singapore. pp. 41-57.
    Motivated by the desire to unify the physical realm with the biological realm, we first present the unified physical consequences of microcosmMicrocosmand macrocosmMacrocosm as applications of temporal toposTemporal topos, t-topos. That means that for the quantum realm, we must provide the formulations for the quantum dualityDuality, the quantum entanglementQuantum entanglement, the uncertainties, and the crucially important measurement problem. For the macrocosmMacrocosm, we give the notion of an ur-lightconeUr-lightcone corresponding to the notion of a light-cone in relativity. A formulation (...)
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  17. Topos theory as a framework for partial truth.Jeremy Butterfield - unknown
    This paper develops some ideas from previous work (coauthored, mostly with C.J.Isham). In that work, the main proposal is to assign as the value of a physical quantity in quantum theory (or classical physics), not a real number, but a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a valuation illuminates the Kochen-Specker theorem; in part mathematical---the valuations arise naturally in the theory of presheaves; and in part (...)
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  18.  83
    Negations and Meets in Topos Quantum Theory.Yuichiro Kitajima - 2021 - Foundations of Physics 52 (1):1-27.
    The daseinisation is a mapping from an orthomodular lattice in ordinary quantum theory into a Heyting algebra in topos quantum theory. While distributivity does not always hold in orthomodular lattices, it does in Heyting algebras. We investigate the conditions under which negations and meets are preserved by daseinisation, and the condition that any element in the Heyting algebra transformed through daseinisation corresponds to an element in the original orthomodular lattice. We show that these conditions are equivalent, and that, not (...)
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  19.  53
    Relating Topos Theory and Set Theory Via Categories of Classes.Steve Awodey, Alex Simpson & Thomas Streicher - unknown
    We investigate a certain system of intuitionistic set theory from three points of view: an elementary set theory with bounded separation, a topos with distinguished inclusions, and a category of classes with a system of small maps. The three presentations are shown to be equivalent in a strong sense.
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  20.  25
    Topos of the Origins in Local Epigraphic Commemorations – a Historian’s Reflections.Maciej Janik - 2019 - Philosophical Discourses 1:47-80.
    The present work depicts the content and functions of very specific carriers of collective memory, namely the epigraphic transmissions. The rich tradition of using epigraphic objects, their durability and communicative seriousness, make them consistently attractive forms of transferring memory also in small local communities of towns, villages, parishes, schools and working commu-nities. Those seen as particularly interesting ones are epigraphic objects, whose task is to “commemorate the origins”. The use of the “topos of origins” creates an initiation moment on (...)
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  21.  82
    (2 other versions)Topos based semantic for constructive logic with strong negation.Barbara Klunder - 1992 - Mathematical Logic Quarterly 38 (1):509-519.
    The aim of the paper is to show that topoi are useful in the categorial analysis of the constructive logic with strong negation. In any topos ϵ we can distinguish an object Λ and its truth-arrows such that sets ϵ have a Nelson algebra structure. The object Λ is defined by the categorial counterpart of the algebraic FIDEL-VAKARELOV construction. Then it is possible to define the universal quantifier morphism which permits us to make the first order predicate calculus. The (...)
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  22.  47
    Zum Topos des,lnterkulturellen‘ in interkulturell gekennzeichneten Konflikten im Sport. Eine konflikttheoretische Analyse/ The Topos of ‘Interculturality’ in Interculturally Labelled Conflicts in Sport. A Conflict Theoretical Analysis.Ansgar Thiel & Klaus Seiberth - 2014 - Sport Und Gesellschaft 11 (1):52-75.
    Zusammenfassung Der Begriff,interkultureller Konflikt' wird nicht nur in Medien und Öffentlichkeit, sondern auch in der wissenschaftlichen Diskussion zur Bezeichnung von Auseinandersetzungen verwendet, an denen Menschen mit Migrationshintergrund beteiligt sind. Den Konfliktbeteiligten werden dabei Mentalitätsunterschiede attestiert, die häufig mit Verweis auf kulturelle Differenzen erklärt werden. Der Beitrag liefert Erklärungen dafür, warum solche Auseinandersetzungen im Sport so selbstverständlich als,interkulturelle' Konflikte gekennzeichnet werden. Im Mittelpunkt der konflikt­theoretischen Analyse steht die Frage, wie das,Interkulturelle' zum Topos von Konflikten im Sport wird. Ziel ist es, (...)
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  23.  48
    Introduction to topo-philosophy.Roman Krzanowski - 2023 - Zagadnienia Filozoficzne W Nauce 75:267-276.
    In philosophy, it is always refreshing to introduce unconventional ideas. It requires a certain audacity from the author; he or she may face the wall of silence or be shunned by academia, both treatments being undesirable. However, these are more rewarding than gathering laurels for beating the dead philosophical cats like Humes, Leibnitzs, Wittgensteins, Whiteheads, and others, a practice that for many philosophers is their life's opus. Bartłomiej Skowron’s book _Part and Whole: Towards Topo-Ontology_, published by Oficyna Wydawnicza Politechniki Warszawskiej (...)
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  24. A topos-theoretic approach to reference and modality.Gonzalo E. Reyes - 1991 - Notre Dame Journal of Formal Logic 32 (3):359-391.
  25.  16
    A topos for extended Weihrauch degrees.Samuele Maschio & Davide Trotta - 2026 - Annals of Pure and Applied Logic 177 (9):103781.
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  26. Percepts, Valence, and Neural Computation: A Topos-Theoretic Framework.Robert Cacioppo - manuscript
    Version 3 (April 2026). We develop a mathematical framework for neural computation in which percepts are modeled as probabilistic structures on directed acyclic graphs of subthreshold oscillatory (STO) activity, and affective valence is defined in terms of entropy dynamics on these structures. A central problem in the study of consciousness is how structured subjective experience, including both perceptual organization and affective tone, arises from distributed physical processes in the brain. Directed acyclic graphs (DAGs) representing time-stamped STO activity are assigned two (...)
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  27. Topos perspective on the Kochen–Specker theorem: I. Quantum states as generalized valuations.Jeremy Butterfield & Christopher J. Isham - 1998 - International Journal of Theoretical Physics 37 (11):2669–2733.
     
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  28. Topos und Enthymem in der Aristotelischen Rhetorik.Jürgen Sprute - 1975 - Hermes 103 (1):68-90.
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  29.  28
    Category/Topos Theory.John L. Bell - 2019 - In The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics. Cham: Springer Verlag. pp. 197-207.
    Category theory is a framework for the investigation of mathematical form and structure in their most general manifestations. Central to it is the concept of structure-preserving map, or transformation. While the importance of this notion was long recognized in geometry (witness, for example, Klein’s Erlanger Programm of 1872), its pervasiveness in mathematics did not really begin to be appreciated until the rise of abstract algebra in the 1920s and 30s, where, in the form of homomorphism, the idea had been central (...)
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  30. (1 other version)Percepts, Valence, and Neural Computation: A Topos-Theoretic Framework.Robert Cacioppo - unknown
    Version 6 (May 10, 2026) We develop a mathematical framework for neural computation in which percepts are modeled as probabilistic structures on directed acyclic graphs of subthreshold oscillatory (STO) activity, and affective valence is defined in terms of entropy dynamics on these structures. A central problem in the study of consciousness is how structured subjective experience, including both perceptual organization and affective tone, arises from distributed physical processes in the brain. Directed acyclic graphs (DAGs) representing time-stamped STO activity are assigned (...)
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  31. Topos Theory in Montréal in the 1970s: My Personal Involvement.Gonzalo E. Reyes - 2019 - History and Philosophy of Logic 40 (4):389-402.
    Volume 40, Issue 4, November 2019, Page 389-402.
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  32.  25
    Topos: Die aristotelische Lehre vom Raum. Eine Interpretation.Hans Günter Zekl - 1990 - Meiner, F.
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  33.  51
    From Entropy Dynamics of Neuronal Coherence to Valenced Percepts: A Topos-Theoretic Construction.Robert Cacioppo - manuscript
    We develop a theory of neural organization in which percepts are modeled as probabilistic structures on directed acyclic graphs of time-stamped subthreshold oscillatory states, and affective valence is defined by entropy dynamics on these structures. Each graph is assigned two pattern functors: a bound functor, whose elements are Bayesian networks compatible with the graph's causal organization, and an unbound functor, whose elements are arbitrary distributions on the corresponding vertex-state spaces. These functors are organized in a set-valued presheaf topos over (...)
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  34. Du topos à la contre-topique. Cartographie du magique comme champ opératoire de la phénoménologie sartrienne.Gautier Dassonneville - 2015 - Methodos 15.
    This article questions the status of the magical in early Sartre both as an inheritage of the reading of french psychology and anthropology and as the place of the phenomenological break by which an original philosophy of existence can be developped. The author traces the apparition of magical consciousness, whose spontaneity persists in a specifical way where it seemed to be hindered, peculiarly in the pathologies of imagination and in the emotion. The category of the magical leads Sartre to think (...)
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  35.  61
    Kritikkens topos.Henning Fjørtoft - 2005 - Agora Journal for metafysisk spekulasjon 23 (4):5-28.
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  36.  16
    Der Topos der Grenze.Manuel Reinhard - 2018 - In Andreas Brenneis, Oliver Honer, Sina Keesser, Annette Ripper & Silke Vetter-Schultheiß, Technik – Macht – Raum. Das Topologische Manifest im Kontext interdisziplinärer Studien. Wiesbaden: Springer Fachmedien Wiesbaden. pp. 335-343.
    Das sokratische Diktum „Ich weiß, dass ich nichts weiß“: Wie kann Philosophie wissen, was sie nicht weiß? Eine Philosophie, die weiß, was sie nicht wissen kann, ist eine Paradoxie – und sie macht aus dieser Paradoxie nicht selten ein Stilmittel. Der algerisch-französische Philosoph Jacques Derrida (1930-2004) hat sich in seinem Projekt der aporetischen Schriften wie kaum ein anderer Philosoph des 20. Jahrhunderts den Grenzen – in seinen Worten: Aporien (von altgriech. oν ἄπόρος: ohne Weg) – traditioneller Wissenskonzepte der Geistesgeschichte angenommen. (...)
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  37.  69
    Topos taxi: Michel Foucault and Virginia Woolf on two modern grammars of love.Anna-Klara Bojö - 2016 - Feminist Theory 17 (1):21-34.
    The concept of love has emerged as a central topic for philosophical and theoretical discussion over the past few years. Whereas the dominant ideology of love in contemporary culture insists that love be understood as a discovery of my long lost second half with whom I merge and finally recreate a whole, contemporary philosophers and theorists have stressed the need to reconsider the concept of love within an ethical framework that can sustain the idea of the other as forever different (...)
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  38. Quantum topo-dynamics in higher dimensions.Y. Aharonov & M. Schwartz - 1986 - In Roger Penrose & C. J. Isham, Quantum concepts in space and time. New York ;: Oxford University Press. pp. 255.
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  39.  14
    Der Topos "Nähe": Ernst Blochs Eintrittsstelle in die Sozialwissenschaften: ein Beitrag zur Ontologie der modernen Gesellschaft.Leo Bartonek - 1992 - Stockholm: Statsvetenskapliga institutionen.
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  40.  73
    Topos and Entelechy in the Ethos of Reclusion in China.Alan Berkowitz - 1994 - Journal of the American Oriental Society 114 (4):632-638.
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  41. Topos perspectives on the logic of quantum theory: IV. Categories of representations of physical systems.Jeremy Butterfield & Chris J. Isham - 2007 - International Journal of Theoretical Physics 46 (10):2553–2570.
     
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  42.  25
    Topos-Chôra: L'Espai a Grècia I: Perspectives Interdisciplinàries: Homenatge a Jean-Pierre Vernant I Pierre Vidal-Naquet.Jesús Carruesco (ed.) - 2010 - Institut Català d'Arqueologia Clàssica.
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  43.  14
    Topo-Theologie: Religion und Raum.Christian Cebulj, Christian Höger & Margit Wasmeier-Sailer (eds.) - 2024 - Freiburg: Herder.
    Jahrhundertelang wurde das Christentum vorwiegend als Buchreligion verstanden. Das hat der Theologie den Vorwurf der »Raumvergessenheit« eingebracht. Seit dem »spatial turn« wird auch in den theologischen Disziplinen ein reger Diskurs um die Wahrnehmung von Räumen für die Theoriebildung geführt. Der Band lädt ein zu Ortserkundungen und zeigt, dass Religion nicht im luftleeren Raum existiert.
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  44. Le topos de la souveraineté acquise Par l'amour-centre de convergence Des coordonnées affectives dans le chansonnier du troubadour cercamon.Luminiţa Ciuchindel - 2004 - Fenomenologia. Diálogos Possíveis Campinas: Alínea/Goiânia: Editora da Puc Goiás 9:44-49.
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  45.  41
    Der Topos der Information in den Lebenswissenschaften: Eine Studie am Beispiel der Biosemiotik und der Synthetischen Biologie.Daniel Frank - 2019 - Wiesbaden: Springer Fachmedien Wiesbaden.
    In der Mitte des zwanzigsten Jahrhunderts hielt der Informationsbegriff insbesondere durch die Molekularisierung der Genetik und die entstehende Kybernetik Einzug in die Biologie und avancierte zu einem der zentralen Begriffe der Lebenswissenschaften. Dass es sich dabei jedoch nicht um einen theoretischen Term handelt, sondern um einen schillernden Begriff, der innerhalb unterschiedlicher lebenswissenschaftlicher Paradigmen ganz verschiedenes bedeutet, lässt sich besonders deutlich am Beispiel der Biosemiotik und der Synthetischen Biologie aufzeigen. In beiden Paradigmen sind mit dem Informationsbegriff und dessen semantischem Feld auch (...)
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  46. Wesens-Topos der Betroffenheit ; Substantielles und das Akzidentelle der Tradition.Marian Gruber - 2014 - In Marian Christof Gruber & Walter Brandmüller, Diktatur des Relativismus: der Kampf um die absolute Wahrheit für die Zukunft Europas. Heiligenkreuz im Wienerwald: Be&Be.
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  47.  29
    [Topos Bielefeld ] ; Topos : internationale Beiträge zur dialektischen Theorie. 1. Weltgeschichte.Hans Heinz Holz & Domenico Losurdo - 1993
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  48.  35
    Topos i nomos: prostranstva pravopori︠a︡dkov.I. A. Isaev - 2011 - Moskva: Norma.
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  49.  45
    Temporal Topos Methods for the Philosophy of Natural Sciences: The Nexus of Ontology and Epistemology.Goro C. Kato - 2025 - Singapore: Springer Nature Singapore.
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  50. Le topos du phénomène dans l’allégoriede la caverne.Alexandre Lissner - 2015 - Philosophique 18.
    Les innombrables interprétations de l’allégorie de la caverne, aussi réduc­trices ou spéculatives, aussi fidèles à la lettre ou à l'esprit du texte soient-elles, paraissent s'effacer les unes les autres, comme balayées par la souplesse d'un texte qui autorise les lectures les plus élémentaires comme les plus raffinées. Cet "étrange tableau" qu'expose Socrate s'insère immé­dia­tement entre deux pôles d'intelligibilité censés en assurer la compréhension : l'image de la ligne au...
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