Topos theory

This book recalibrates literature’s political role for the 21st century by excavating the deep history of storytelling as a civic agency. From Aristotle to Arendt and from the novella to the video story, short narrative forms hence become tangible as active vectors that enable and radically modulate the ontology of human encounters.

“Civic Storytelling lays bare the complex legacies and persistent powers of short narrative forms. Fuchs guides the reader with assurance and learning through fascinating moments in the history and theory of literature”
—Daniel Heller-Roazen, Princeton University

“Why has the novel stolen so much attention from the equally robust lineage of short forms? In his erudite and wide-ranging alternate literary history, Florian Fuchs rebalances accounts, revealing a long backdrop to our data floods and snippet reading. Short forms do not lead us out of the world, but into full engagement with it; they are the democratic media of the commons.”
—John Durham Peters, Yale University

“Civic Storytelling is a timely intervention in our age of debates about fact and fiction. Drawing on Hannah Arendt’s idea of enacted stories, Florian Fuchs makes a convincing case for the particular cognitive productivity of short narratives.”
—Eva Geulen, Humboldt University Berlin and ZfL Berlin

We report first steps towards elucidating the relationship between contextuality, measurement-based quantum computation (MBQC) and the non-classical logic of a topos associated with the computation. We show that, in a class of MBQC, classical universality requires non-classical logic, which is ‘consumed’ during the course of the computation, thereby pinpointing another potential quantum computational resource.

This  paper  examines  the  general  stylistic  features  of  Requiem  KV 626  by  Wolfgang  Amadeus  Mozart.  The  most  common  tonality  for  the  spiritual  genre  that  is  Requiem,  Mass for the dead, is D minor, which is also one of the conventions for the Topic of death, humility and suffering. In accordance with the theory of semanticist Raymond Monelle, the paper considers the Topic characteristic for the genre of Requiem, as well as rhetorical figures that contribute to the highlighting of pain and suffering , but also to the “weeping Topic” which is closely linked to the suffering of Jesus Christ. As these rhetorical figures, which evoke mentioned Topics, occurred in the works of Mozart’s predecessors, as well as his contemporaries, the Topics of death, suffering,  humility and weeping became conventions, recognizable in a variety of genres.

In this paper I describe how several notions and constructions in topos logic can be dualized, giving rise to complement-toposes with their paraconsistent internal logic, instead of the usual standard toposes with their intuitionistic logic.

This book analyses the development of city images of  Pressburg/Bratislava in travel literature from the 18th century to 1945, identifying five stable elements (topoi) that make up the image despite the strong discontinuous development of the history of today's Slovak capital. In its systematic diachronic presentation, accompanied by detailed case studies, the book represents not only a contribution to urban semiotics but also to the history of the itinerary genre.

[This DRAFT book chapter is virtually complete. A slightly edited version of this chapter has been submitted and approved for publication in the forthcoming volume The Philosophical Legacy of Jorge J.E. Gracia, scheduled to be published in 2021by Rowman & Littlefield.]

Abstract: The question of development and its place in the world is one of the oldest in the history of metaphysics. In the course of the formative years of the discipline that culminated in the metaphysical views of Plato and Aristotle, Heraclitus’ emphasis on development qua concrete unity of process and result eventually gave way to a commitment to identify, in one degree or other of abstraction from becoming, the fundamental locus of reality, intelligibility, and goodness with being per se. Classic examples include Plato’s absolutely separate and timeless forms as well as Aristotle’s absolutely immutable and distinct infimae species (including both immaterial and materiate forms), in terms of which his closely related theory of scientific demonstration is constructed.

Despite its subordination, the theme of development, even in the realm of presumably immaterial and timeless being, was never entirely neglected – important Islamaic and Christian metaphysicians often emphasized the active and dynamic as opposed to static nature of pure being or existence. Eventually, however, the categories of what later Christian metaphysicians would come to call “general metaphysics”, and later Islamaic metaphysicians “general matters”, would become increasingly ossified, static, and conceived in ever greater abstraction from the intelligible realities, which are intrinsic values, that they are supposed to be about. In the West, as famously explained by Étienne Gilson: The resultant science of ontology eo nomine became easy prey to Kant’s critique of the powers of abstract a priori reason. That critique would also diminish confidence in the ontological aspects of earlier metaphysical systems which trace, ultimately, to Parmenides; as well as to any intellectual intuition of some separate or absolute rational fact and the associated infallible and incorrigible axioms upon which scientific demonstration depends. Closely related, confidence in the knowability of intrinsic value also diminished, in tandem with the rise of the value-free and purely quantificational conceptions of science that dominate the present age.

In the spirit of several famous post-Kantian and later Islamaic metaphysicians, in this chapter we cast back, beyond Parmenides, to Heraclitus as the starting point of the metaphysical enterprise as well as of the developmental paradigm of metaphysics. The first section builds upon Jorge F. E. Gracia’s conception of metaphysics in terms of categories per se and their interrelations. A development of Gracia’s conception incorporates insights from R. G. Collingwood’s scale of forms and G. R. G. Mure’s conception of development. In the resultant synthesis, the interrelation of categories is conceived in terms of a developing series of categories. The second section situates Heraclitus as the founder of Western metaphysics in general and of the developmental paradigm in particular. The next section discuses aspects of the tension between the developmental and ontological aspects of Aristotle’s metaphysics and associated theory of scientific demonstration; these contributed to the eventual collapse of Aristotelian science. Finally, some basic ideas of mathematician William Lawvere’s adaptation of Hegel’s objective logic are formulated using the language of contemporary mathematical category and topos theory, a framework that holds out the exciting promise of doing for developmental metaphysics what symbolic logic has done for ontology. The preliminary result is illustrated via a metaphysical theory of Benedetto Croce.

More than five years have passed since former British Prime Minister David Cameron delivered a much acknowledged and controversial speech on 23 January 2013, in respect to the British relationship with the European Union (EU). Europe and the EU are now, of course, facing different challenges than five years ago. The contrasting national and transnational identities which emerge in the so-called “Bloomberg Speech” (BS) imply a nationalistic body-politics which constructs the United Kingdom and England as separate entities contrasted to “the continent”, i.e. Europe. Hence, the BS oscillates between two extremes in its attempt to alternatively observe maximum distance to the EU and some proxim- ity to its economic policies. Moreover, both the topoi of urgency and threat/ danger are appealed to – warning the EU that it would suffer under the loss of the United Kingdom, but also warning British voters that Brexit would damage their future and prosperity. This speech can be perceived as the starting point for the referendum on 23 June 2016, which resulted in a tiny majority wanting to leave the EU (“Brexit”). Of course, there is no clear causal connection between the BS and Brexit, but many arguments of the “Remain and Leave campaigns” can be traced to the BS, as well as the huge ambivalence framing Cameron’s position towards the EU.

Den här uppsatsen analyserar argumentationen i popartisten Zara Larssons blogginlägg “Håll käften din lilla slyna”, publicerat i samband med den internationella kvinnodagen 2015, samt ett urval av inläggets tillhörande kommentarer. Syftet är att undersöka materialet utifrån ett toposperspektiv, där vi besvarar frågeställningarna: “Vilka diskussionspunkter och diskussionsgrunder går att utläsa i det valda materialet?” samt “Hur kan de värden och värderingar som tar sig uttryck i materialet ses ur ett maktkritiskt perspektiv?”. Den metod som vi använder oss av utgår från Maria Wolrath Söderbergs utvecklade toposmodell. Vidare utgör Wolrath Söderbergs resonemang om topos samt John Fiskes resonemang om populärkultur våra teoretiska utgångspunkter. I analysen finner vi flera återkommande diskussionspunkter och diskussionsgrunder, och kommer på så sätt fram till vilka värderingar argumenten kan tolkas grunda sig i. Som slutsats konstaterar vi att både Larsson och de som kommenterar hennes blogginlägg kan ses utgå från liknande diskussionsgrund, nämligen att ett rättvist samhälle är eftersträvansvärt. Däremot finns det delade meningar om hur samhället ser ut idag och hur vi utifrån det ska nå rättvisa. Vi kommer även fram till att delar av det bemötande Larsson får kan ses som en del av det strukturella förtryck hon belyser i sitt blogginlägg.

The article presents the way the Holocaust enters the public and popular debate via Internet and becomes a signifier of other experiences. In this process the Holocaust transforms into a tops-like event, a marker instead of a real experience.
The article investigates blogs, institutional and private webpages as well as internet media events such as the (in)famous "Holocaust dance" published on Youtube.

In this paper I will combine ideas of Meinong's objectology ( my preferred translation of "Gegenstandstheorie") with earlier ideas of ethereal or intelligible gunk. I will try to make that useful for a better understanding of 'emergence'. I also spend some remarks on mathematical theories.

I study here the implications of Suszko-like reductive results for the common wisdom on the internal logic of a topos. My aim here is to question certain slogans about topos logic, and especially on its many-valuedness. The originality of this paper comes not from the observation that the internal logic of a topos is bivalent because it is in the scope of Suszko’s or any other reduction; that is easy. Rather, the originality comes from (1) recognizing the import of applying Suszko’s and similar results in a topos-theoretical setting, (2) the suggestions to give categorial content to the reduction, and (3) the extrapolation of the debate about Suszko’s thesis to the topos-theoretical framework, which gives us some insight about the scope of another theorem, namely that stating the intuitionistic character of the internal logic of a topos.

From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models can be topologized in such a way that the theory can be recovered from its space of models. The situation can be cast as a formal duality relating two categories of syntax and semantics, mediated by homming into a common dualizing object, in this case 2. In the present work, we generalize the entire arrangement from propositional to first-order logic. Boolean algebras are replaced by Boolean categories presented by theories in first-order logic, and spaces of models are replaced by topological groupoids of models and their isomorphisms. A duality between the resulting categories of syntax and semantics, expressed first in the form of a contravariant adjunction, is established by homming into a common dualizing object, now $\Sets$, regarded once as a boolean category, and once as a groupoid equipped with an intrinsic topology. The overall framework of our investigation is provided by topos theory. Direct proofs of the main results are given, but the specialist will recognize toposophical ideas in the background. Indeed, the duality between syntax and semantics is really a manifestation of that between algebra and geometry in the two directions of the geometric morphisms that lurk behind our formal theory. Along the way, we construct the classifying topos of a decidable coherent theory out of its groupoid of models via a simplified covering theorem for coherent toposes.

In this paper I describe how complement-toposes, with their paraconsistent internal logic, lead to a more abstract theory of topos logic. Béziau’s work in Universal Logic –including his ideas on logical structures, axiomatic emptiness and on logical many-valuedness– is central in this shift and therefore it is with great pleasure that I wrote this paper for the present commemorative volume.

The goal of this paper is to summarise the first steps in developing a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. In doing so we provide a new answer to Heidegger's timeless question ``What is a thing?''.
Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics uses the topos of sets. Other theories involve a different topos. For the types of theory discussed in this paper, a key goal is to represent any physical quantity $A$ with an arrow $\breve{A}_\phi:\Si_\phi\map\R_\phi$ where $\Si_\phi$ and $\R_\phi$ are two special objects (the `state-object' and `quantity-value object') in the appropriate topos, $\tau_\phi$. We discuss two different types of language that can be attached to a system,$S$. The first, $\PL{S}$, is a propositional language; the second, $\L{S}$, is a higher-order, typed language. Both languages provide deductive systems with an intuitionistic logic. With the aid of $\PL{S}$ we expand and develop some of the earlier work (By CJI and collaborators.) on topos theory and quantum physics. A key step is a process we term `daseinisation' by which a projection operator is mapped to a sub-object of the spectral presheaf $\Sig$--the topos quantum analogue of a classical state space. The topos concerned is $\SetH{}$: the category of contravariant set-valued functors on the category (partially ordered set) $\V{}$ of commutative sub-algebras of the algebra of bounded operators on the quantum Hilbert space $\Hi$.

Il contributo esamina la figura di Giuliano Perleoni (Rustico Romano) e una sezione delle cinque che compongono la sua unica opera: Compendio di sonetti e altre rime de varie testure intitulato lo Perleone. Tra le possibili chiavi di lettura del canzoniere si è scelto di privilegiare l’analisi di una struttura semantica e ideologica portante: il topos della navigazione. Divenuta raffigurazione di un momento di crisi già da Petrarca, tale metaforizzazione passa attraverso l’uso di Giusto de’ Conti e si stabilisce nella corte napoletana grazie all’esempio di Aloisio. Perleoni, dal canto suo, eredita questo espediente e lo utilizza per narrare di una condizione che da metaforica diviene reale.

Die literaturwissenschaftliche Ausrichtung der althistorischen Quellenkritik in den letzten Jahrzehnten hatte fundamentale Auswirkungen auf die Deutung ethnographischer Texte. Durch diesen Forschungsfokus ist die Analyse möglicher Realitätsbezüge weitgehend in den Hintergrund getreten. Bisweilen wird den Aussagen über fremde Völker sogar jedweder Wahrheitsgehalt abgesprochen. Ein wichtiges Element dieser Forschungsproblematik sind Topoi, die in den antiken Texten praktisch omnipräsent sind. Trotz dieser besonderen Bedeutung liegt bis heute keine umfangreiche Betrachtung zum Toposbegriff aus Perspektive der Alten Geschichte vor.

The paper investigates in details Aristotle’s “Rhetoric”, distinguishing two rhetorical methods: the example and the enthymeme. The first one is the method of rhetorical induction; the second is of rhetorical deduction. This clear scheme becomes more complicated when we examine types of enthymemes and types of examples. The text focuses on the cases of enthymeme-example dynamic, demonstrating the lacks and excesses of each method.

Die Michaelsgrotte in Olevano Sul
Tusciano ist ein Berg- und Höhlenheiligtum, das seit der Antike als numinoser Ort gilt. In den ersten Jahrhunderten des Christentums blieb der Ort als heilbringend im Gedächtnis. Möglicherweise entstanden hier frühchristliche Martyria, später ging die Verehrung auf den Erzengel Michael über. Eine grandiose Anlage, die ihresgleichen sucht.

An introduction is given to the logic of sheaves of structures and to set theoretic forcing constructions based on this logic. Using these tools, it is presented an alternative proof of the independence of the Continuum Hypothesis; which simplifies and unifies the classical boolean and intuitionistic approaches, avoiding the difficulties linked to the categorical machinery of the topoi based approach.

Memory is a filter through which humans analyze and experience the space, affecting their behavior and perception. Memory integrates with the space, leading to the multidimensional spatial experience. Because memory is significant due to the fact that it encloses elements of identity and history, the constant search for ways and means to redefine
its content is an important process for societies. A way to emerge memory is through architecture; memorials and museums can be considered “vaults” of memory. An indicative category of museums and memorial spaces that use the experiential approach to preserve, exhibit and communicate memory to deeply affect the visitors, is the one of the Holocaust.
The Battle of Crete (Greece) and the period of the German Occupation of the island during WWII, is characterized as one of the darkest pages of Crete’s history. The chain of events resulted in a number of unique occurrences that
affected the development of the social and collective memory of the participants and left deep “scars” on the residents
and places of the island; a network of memory and destruction. Through the analysis of indicative architectural examples
(museums / memorials) and testimonies of the period, this dissertation aims to explore ways of representing and evoking
memory as well as the diagrammatic spatial interpretation of testimonies.

We give an overview of mathematical music theory as it has been de-veloped in the past twenty years. The present theory includes a formal language for musical and musicological objects and relations. This lan-guage is built upon topos theory and its logic. Various models of ...

Based on the Sheaf Logic approach to set theoretic forcing, a hierarchy of Quantum Variable Sets is constructed, which generalizes and simplifies the analogous construction developed by Takeuti on boolean valued models of set theory. Over this model, two alternative proofs of Takeuti’s correspondence, between self adjoint operators and the real numbers of the model, are given. This approach results to be more constructive, showing a direct relation with the Gelfand representation theorem, and revealing also the importance of these results with respect to the interpretation of Quantum Mechanics in close connection with the Deutsch-Everett multiversal interpretation of quantum theory. Finally, it is shown how in this context the notion of genericity and the corresponding generic model theorem can help to explain the emergence of classicality in Quantum Mechanics also in close connection with the Deutsch-Everett perspective.

Gründungslegenden der hermetischen, also auf Hermes Trismegistos zurückgehenden Alchemie berichten von der Findung des Urtextes der alchemistischen Weisheit, später als Tabula Smaragdina bekannt, in Händen des im Grabe thronenden Hermes Trismegistos. Drei ottonische Quellen berichten mit den gleichen Erzähltopoi von der Sitzbestattung Karls des Großen in der Aachener Marienkirche. Die Einzelelemente dieser aus so unterschiedlichen Kontexten stammenden Legenden weisen soviel Ähnlichkeit miteinander auf, dass ein Vergleich gerechtfertigt scheint.

According to the Butterfield–Isham proposal, to understand quantum gravity we must revise the way we view the universe of mathematics. However , this paper demonstrates that the current elaborations of this programme neglect quantum interactions. The paper then introduces the Faddeev–Mickelsson anomaly which obstructs the renormalization of Yang–Mills theory, suggesting that to theorise on many-particle systems requires a many-topos view of mathematics itself: higher theory. As our main contribution, the topos the-oretic framework is used to conceptualise the fact that there are principally three different quantisation problems, the differences of which have been ignored not just by topos physicists but by most philosophers of science. We further argue that if higher theory proves out to be necessary for understanding quantum gravity, its implications to philosophy will be foundational: higher theory challenges the propositional concept of truth and thus the very meaning of theorising in science.

The author discusses the process of nationalizing literature, that is, the formation of a national literary canon in Slovene poetry from the Enlightenment to Post-Romanticism. The utopian projection and formation of a ‘Slovenised’ literary system has been intertwined with the successful establishment of a unified Slovene literary language. The use of images of Parnassus and Elysium, these topoi in the European cultural memory, was one of the self-regulatory strategies acquired by Slovene writers to mark the distinction between their own discourse and the norms of the ‘classics’ and a competitive comparison with other modern national literatures in order to achieve integration into the canon of ‘world literature’.

This paper is the second in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. In this paper, we study in depth the topos representation of the propositional language, PL(S), for the case of quantum theory. In doing so, we make a direct link with, and clarify, the earlier work on applying topos theory to quantum physics. The key step is a process we term `daseinisation' by which a projection operator is mapped to a sub-object of the spectral presheaf--the topos quantum analogue of a classical state space. In the second part of the paper we change gear with the introduction of the more sophisticated local language L(S). From this point forward, throughout the rest of the series of papers, our attention will be devoted almost entirely to this language. In the present paper, we use L(S) to study `truth objects' in the topos. These are objects in the topos that play the role of states: a necessary development as the spectral presheaf has no global elements, and hence there are no microstates in the sense of classical physics. Truth objects therefore play a crucial role in our formalism.

This paper deals with the laments of princess Milica as very important rhetorical subgenres present in the orations honouring prince Lazar and the Battle of Kosovo by the unknown monk from the Ravanica monastery, Danilo of Banya and Andonius Raphail. It aims at explaining the rhetorical strategies used by the princess in order to celebrate prince Lazar as the new Christian martyr. These strategies consist of the use of different common places (topoi) and ancient rhetorical arguments, which, via Byzantine literary models, made a strong impact on the medieval Serbian literature.