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 (...) state is problematic for those who view TQT as a realist reformulation of quantum theory. 1Introduction 2Topos Quantum Theory 2.1Phase space 2.2Hilbert space 2.3Beyond Hilbert space 2.4Defining realism 2.5The spectral presheaf 2.6The logic of topos quantum theory 3Interpreting States in Topos Quantum Theory 4Interpreting Truth Values and Clopen Subobjects in Topos Quantum Theory 4.1Interpreting the truth values 4.2Interpreting Subcl 5Neo-realism 5.1The covariant approach 6Conclusion. (shrink)

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 (...) of musical objects that comprises the topos-theoretic concept framework. Classification also implies techniques of algebraic moduli theory. The classical models of modulation and counterpoint have been extended to exotic scales and counterpoint interval dichotomies. The probably most exciting new field of research deals with musical performance and its implementation on advanced object-oriented software environments. This subject not only uses extensively the existing mathematical music theory, it also opens the language to differential equations and tools of differential geometry, such as Lie derivatives. Mathematical performance theory is the key to inverse performance theory, an advanced new research field which deals with the calculation of varieties of parameters which give rise to a determined performance. This field uses techniques of algebraic geometry and statistics, approaches which have already produced significant results in the understanding of highest-ranked human performances. The book's formal language and models are currently being used by leading researchers in Europe and Northern America and have become a foundation of music software design. This is also testified by the book's nineteen collaborators and the included CD-ROM containing software and music examples. (shrink)

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 (...) classical approach to the concept is suggested, derived from Aristotle’s rhetoric and dialectic. By focusing on Greek media discourses on ‘Islamist terrorism’, I seek to illustrate the synthesis between the DHA’s argumentation strategies and Aristotelian topos as a fruitful analytical and theoretical tool. (shrink)

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 (...) come naturally from the topos theory of presheaves. The first step in our theory is to demonstrate that the Kochen-Specker theorem is equivalent to the statement that a certain presheaf defined on the category of self-adjoint operators has no global elements. We then show how the use of ideas drawn from the theory of presheaves leads to the definition of a generalised valuation in quantum theory whose values are sieves of operators. In particular, we show how each quantum state leads to such a generalised valuation. A key ingredient throughout is the idea that, in a situation where no normal truth-value can be given to a proposition asserting that the value of a physical quantity A lies in a set D of real numbers , it is nevertheless possible to ascribe a partial truth-value which is determined by the set of all coarse-grained propositions that assert that some function f(A) lies in f(D), and that are true in a normal sense. The set of all such coarse-grainings forms a sieve on the category of self-adjoint operators, and is hence fundamentally related to the theory of presheave. (shrink)

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 (...) existential copula. Deeply ingrained in Western languages, metaphysics, and religion is the subjective self, in both the linguistic and psychological senses of “subjective.” That Buddhism, as reworked by the Kyota School, or Daoism, or any other non-Western tradition of thought, will catch on in the West was a puerile fantasy of some members of the first generation of environmental philosophers. There is a good chance, however, that the Western worldview may evolve toward a similar conception of the self—as ecological, relational, or systems thinking becomes ever more ingrained. We in the West may come to understand that we are constituted by our social and environmental relationships, in which we are deeply embedded and on which we are utterly dependent, such that world care is the essence of self-help. (shrink)

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 (...) morphisms f : F → E, where H = f∗ΩF. The logic differs from non-modal higher-order logic in that the principles of functional and propositional extensionality are not longer valid but may be replaced by modalized versions. The usual Kripke, neighborhood, and sheaf semantics for propositional and first-order modal logic are subsumed by this notion. (shrink)

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 (...) valuations could arise much more generally than just in quantum physics; in particular, they arise as naturally in classical physics. Second, we give another motivation for such valuations (that applies equally to classical and quantum physics). This arises from applying to propositions about the values of physical quantities some general axioms governing partial truth for any kind of proposition. (shrink)

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).

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 (...) main results. First, there is a natural correspondence between these two kinds of valuation, which uses the notion of a state's support for a quantity (Section 3). Second, if one starts with a more general notion of interval valuation, one sees that our interval valuations based on the notion of support (and correspondingly, our sieve-valued valuations) are a simple way to secure certain natural properties of valuations, such as monotonicity (Section 4). (shrink)

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, (...) gängige Annahmen des Diskurses über interkulturelle Konflikte im Sport kritisch zu hinterfragen. Den theoretischen Rahmen hierfür bildet die systemtheoretische Konfliktsoziologie. (shrink)

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 (...) and cognitive morphodynamics). Ultimately it argues for the central importance of noise not only within a topological conception of cognition and computation, but also in the transcendental-empirical torsion of image schemata and the social interactive elaboration of freedom. (shrink)

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 (...) conceptual---the valuations arise from applying to propositions about the values of physical quantities some general axioms governing partial truth for any kind of proposition. In this paper, I give another conceptual motivation for the proposal. I develop (in Sections 2 and 3) the notion of a topos (of which presheaves give just one kind of example); and explain how this notion gives a satisfactory general framework for making sense of the idea of partial truth. Then I review (in Section 4) how our proposal applies this framework to the case of physical theories. (shrink)

Au début du Sophiste, Socrate demande au visiteur éléate ce qu’ont pensé des genres philosophe, sophiste et politique, « ceux » qui sont de ce lieu-là ». L’article a pour but d’éclairer cette dernière expression et en particulier son mot clef « topos ». Il est montré que les significations de ce terme, dans son contexte, sont multiples et que cette diversité, loin d’apporter la confusion, permet au contraire et précisément d’ouvrir les diverses perspectives du dialogue. At the beginning (...) of the Sophist, Socrates asks the Eleatic Visitor how the three kinds Philosopher, Sophist and Statesman, have been understood by “those who are in this place”. The purpose of this paper is to enlighten this periphrasis and specially its key-word “topos”. We have showed that, in its context, this word has four main meanings, and that this diversity, far from causing confusion, opens up the dialogue to various perspectives. (shrink)

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.

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.

ArgumentGlass vessels such as flasks and test tubes play an ambiguous role in the historiography of modern laboratory research. In spite of the strong focus on the role of materiality in the last decades, the scientific glass vessel – while being symbolically omnipresent – has remained curiously neglected in regard to its materiality. The popular image ortoposof the transparent, neutral, and quasi-immaterial glass container obstructs the view of the physico-chemical functionality of this constitutive inner boundary in modern laboratory environments and (...) its material historicity. In order to understand how glass vessels were able to provide a stable epistemic containment of spatially enclosed experimental phenomena in the new laboratory ecologies emerging in the nineteenth and early twentieth century, I will focus on the history of thematerialstandardization of laboratory glassware. I will follow the rise of a new awareness for measurement errors due to the chemical agency of experimental glass vessels, then I will sketch the emergence of a whole techno-scientific infrastructure for the improvement of glass container quality in late nineteenth-century Germany. In the last part of my argument, I will return to the laboratory by looking at the implementation of this glass reform that created a newoikosfor the inner experimental milieus of modern laboratory research. (shrink)

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 (...) the line of collective memory of a given local community. The observations presented in the work relate to the epigraphic resource, created in the last half century within the spatial framework of the borderland of Silesia and Lesser Poland. (shrink)

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 (...) completeness theorem is proved using the Kripke-type semantic defined by THOMASON. (shrink)

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 (...) diverse Erklärungsansprüche verbunden, die im vorliegenden Band einer wissenschaftsphilosophischen Kritik unterzogen werden. (shrink)

Cet article interroge le statut du magique chez le premier Sartre à la fois comme héritage d'un dialogue avec la psychologie et l'anthropologie françaises et comme le lieu de la coupure phénoménologique par laquelle se développe une philosophie de l'existence originale. L'A. retrace l'apparition de la conscience magique, pour laquelle la spontanéité persiste d'une manière spécifique là où elle semblait mise en défaut, notamment dans les pathologies de l'imagination et dans l'émotion. Aussi la catégorie du magique permet-elle de penser l'autonomie (...) de la conscience irréfléchie en dotant ses différentes attitudes d'une signification selon une approche synthétique de la réalité-humaine. En un autre point névralgique chez Sartre, la conscience absolue s'emprisonne dans le monde selon un phénomène de dégradation grâce auquel apparaît le psychique : cette existence mixte entre pour-soi et en-soi est irréductiblement magique. Or, le fait psychique est le lieu des relations concrètes avec autrui et l'A. montre, qu'en dernière instance, le magique reparaît dans l'ontologie phénoménologique à travers le schème de la possession – possession d'autrui et possession des choses – mettant la transcendance au compte d'une sorcellerie originelle. (shrink)

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...

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 (...) and separate. Taking as a starting point two different taxi scenes offered by Foucault and Woolf respectively, the article outlines and discusses those two contemporary love grammars, focusing on the concepts of lack and fantasy. Whereas Woolf’s taxi scene is reminiscent of a notion of love as a fantasy of unification, Foucault’s notion of love not only observes the need to maintain the other’s specificity and separateness, but also considers lack and fantasy to be primary and fundamental parts of love as lived experience. While Foucault insists on pleasure and action he also observes the central and unavoidable power of imagination that is attributed the name and function of recollection. The article finally addresses the question of if and how we might be responsible for our daydreams and fantasies. (shrink)

RESUMO Este artigo pretende traçar as possibilidades de aproximação entre ambos os filósofos por meio do prisma do espaço, do mundo, da terra, do habitar e da casa. Para isso, foram utilizadas, principalmente, leituras que permeiam o segundo Heidegger, nas obras entre 1936 e 1969, e as obras de Bachelard mais ligadas a terra e ao espaço, entre 1933 e 1948. Desse modo, após várias reflexões sobre as semelhanças e dessemelhanças de ambos os filósofos, foi possível encontrar os pontos de (...) divergência e convergência, estes últimos acabam superando os primeiros nos entre-espaços possíveis, sobretudo, nas visões da arte, mas não tanto da linguagem que cada um utilizou. Por isso, são desafiadoras e instigantes as rupturas causadas na possibilidade de continuidade dessas tendências filosóficas. ABSTRACT The article aims at exploring the possibilities of establishing connections between Heidegger and Bachelard from the perspective of space, world, dwelling, and house. We used works written by Heidegger between 1936 and 1939, after the "second" period, and those written by Bachelard between 1933 and 1948, which deal more with earth and space. Reflection on the similarities and differences between the philosophers makes it possible to find points of divergence and convergence. The latter are greater than the former in the possible in-between spaces, mainly regarding the views on art, but not that many with respect to the language used by each one. For this reason, the breaks in the possible continuity of these philosophic views are challenging and encourage further reflection. (shrink)

This dissertation is concerned with one of the central but most perplexing theories in Plotinus's metaphysics, namely the nature and origin of time. In contrast to those interpretations of Neoplatonism that treat time as an imperfect image and passive product of eternity, I argue for a much more subtle and multifaceted concept that makes the human observer central to Plotinus's account of how time is actualized and thus passes. His emphasis on mystical experience and the individual soul's journey toward the (...) One and the realm of eternity strengthens this account. By reading the treatise On Eternity and Time in this light, I demonstrate the importance of embodied human consciousness for the Plotinian theory of time. ;This emphasis invites comparison with the one contemporary Continental thinker who devoted countless pages in both his published work and his manuscripts to the relationship between time and consciousness. In the second part of the dissertation I argue that the Husserlian and Plotinian subjects have analogous characteristics, in accordance with their parallel roles as sources of time, and that the Husserlian notion of omnitemporality offers the best way of understanding the internal connection between Plotinus's notion of eternity and his notion of actualization through human experience. At the same time, Plotinus challenges a phenomenological account by giving the eternal ontological priority over the human realm of temporality. Nevertheless, these intriguing affinities and oppositions suggest that Plotinus's theory of time and eternity can best be understood and even expanded by uncovering its phenomenological underpinnings. (shrink)

Volume 40, Issue 4, November 2019, Page 389-402.

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.

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 (...) the implications of this relationship for the definition of modal operators in TQT. (shrink)

For more than twenty years, Swiss photographer Tobias Madörin has been working on his photo series Topos. Creating staged tableaux in the manner of nineteenth-century painters, Madörin investigates the interaction between the inhabitants and their surrounding environments in countries as diverse as Spain, Uganda, Indonesia, and Japan. His large-scale images examine communal spaces, the outskirts of metropolises, waste disposals sites, and landscapes marked by agriculture and mining. Madörin's work reveals that these locations are the products of human visions and (...) ideals, yet they are also places of environmental exploitation. This tension, as well as Madörin's intelligent and empathetic approach to his subjects, makes his photographs evocative and complex. This book includes lavish, full-page photographs, many of which have never been published, and an introductory essay by Nadine Olonetzky that explains and contextualizes the photographer's oeuvre. (shrink)

Byzantine authors frequently used the well-known topos of modesty in the opening lines of their literary works. This common introduction, usually served two purposes: The authors expressed a genuine, or, perhaps, feigned concern about their ability to deal adequately with their subject both in terms of form and substance, and they preemptively tried to thwart any possible criticism on the part of the audience for any shortcomings in their work by beginning with this sort of captatio benevolentiae. Typical examples (...) of this topos are not only numerous among hagiographers throughout the Byzantine millennium, but even in such writers as Theophanes Confessor, as one can see from the preamble to his Chronography. It is only after the 11th century that “we sometimes encounter the author's frank appraisal of his talent, for example in Psellos and Tzetzes.” As early an author as John of Damascus, however, also displayed his self-appreciation for his talent and this will be the subject of this short article. Here, I shall examine John of Damascus' own personal stance to the topos of modesty/humility and, in one particular case, his rather interesting variation on it. (shrink)