We show that in 4-spacetime modified at very short distances due to the weakening of classical logic, the higher dimensions emerge. We analyse the case of some smooth topoi, and the case of some class of pointless topoi. The pointless topoi raise the dimensionality due to the forcing adding “string” objects and thus replacing classical points in spacetime. Turning to strings would be something fundamental and connected with set theoretical forcing. The field theory/strings dualities originate at the set theoretical level (...) of the theories. It is argued that this fundamental level can help solving some difficulties of the physical dualities. (shrink)

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)

A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a (...) Łukasiewicz–Moisil Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology. (shrink)

A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a (...) Łukasiewicz–Moisil Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology. (shrink)

: In his philosophy of nothingness, Kitar Nishida illuminates the matrix of transformation of the world ‘‘from the Created to the Creating’’ (tsukuru mono kara tsukurareta mono e) through shintai, or the body. In this matrix, shintai enters into the stage of an action-sensation continuum and emerges as the immaculate iconic tool of nothingness to create new figures as extended self. This idea of shintai has resonance with the development of postwar art in Japan. The ‘‘Space of Transparency’’ put forth (...) by Ufan Lee, the leader of Monoha, is the principal example. This essay investigates Nishida’s notion of shintai and its influence on Lee’s theory of art. (shrink)

In his philosophy of nothingness, Kitar Nishida illuminates the matrix of transformation of the world ''from the Created to the Creating'' through shintai, or the body. In this matrix, shintai enters into the stage of an action-sensation continuum and emerges as the immaculate iconic tool of nothingness to create new figures as extended self. This idea of shintai has resonance with the development of postwar art in Japan. The ''Space of Transparency'' put forth by Ufan Lee, the leader of Monoha, (...) is the principal example. This essay investigates Nishida's notion of shintai and its influence on Lee's theory of art. (shrink)

In his philosophy of nothingness, Kitarō Nishida illuminates the matrix of transformation of the world "from the Created to the Creating" (tsukuru mono kara tsukurareta mono e) through shintai, or the body. In this matrix, shintai enters into the stage of an action-sensation continuum and emerges as the immaculate iconic tool of nothingness to create new figures as extended self. This idea of shintai has resonance with the development of postwar art in Japan. The "Space of Transparency" put forth by (...) Ufan Lee, the leader of Monoha, is the principal example. This essay investigates Nishida's notion of shintai and its influence on Lee's theory of art. (shrink)

This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. (...) Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method. (shrink)

Conceptualizing the nature of reality and the way the world functions, Ekaterina Yahyaoui Krivenko analyzes the foundations of human rights law in the strict subject/object dichotomy. Seeking to dismantle this dichotomy using topo-logic, a concept developed by Japanese philosopher Nishida Kitaro, this topical book formulates ways to operationalize alternative visions of human rights practice. Subject/object dichotomy, Yahyaoui Krivenko demonstrates, emerges from and reflects a particular Western worldview through a quest for rationality and formal logic. Taking a metaphysical and epistemological perspective, (...) this book explores the alternative views of reality and logic, developed by Kitaro, to demonstrate how topo-logic can enable both a theoretical and a practical renewal of human rights and overcome the subject/object dichotomy. Examining the recent growth of social movements, decolonization and diversification of discourses about human rights, and substantive equality, the book identifies these developments in contemporary human rights as indications of a movement towards a topo-logical view beyond the subject/object dichotomy. Students and scholars of critical legal studies, legal theory and philosophy, and international human rights law will find this book to be an invigorating read. Laying ground for the possible renewal and enhancement of human rights law, it will also be a useful resource for practitioners of human rights law. (shrink)

This book is a state-of-the-art review on the Physics of Emergence. Foreword v Gregory J. Chaitin Preface vii Ignazio Licata Emergence and Computation at the Edge of Classical and Quantum Systems 1 Ignazio Licata Gauge Generalized Principle for Complex Systems 27 Germano Resconi Undoing Quantum Measurement: Novel Twists to the Physical Account of Time 61 Avshalom C. Elitzur and Shahar Dolev Process Physics: Quantum Theories as Models of Complexity 77 Kirsty Kitto A Cross-disciplinary Framework for the Description of (...) Contextually Mediated Change 109 Liane Gabora and Diederik Aerts Quantum-like Probabilistic Models Outside Physics 135 Andrei Khrennikov Phase Transitions in Biological Matter 165 Eliano Pessa Microcosm to Macrocosm via the Notion of a Sheaf (Observers in Terms of t-topos) 229 Goro Kato The Dissipative Quantum Model of Brain and Laboratory Observations 233 Walter J. Freeman and Giuseppe Vitiello Supersymmetric Methods in the Traveling Variable: Inside Neurons and at the Brain Scale 253 H.C. Rosu, O. Cornejo-Perez, and J.E. Perez-Terrazas Turing Systems: A General Model for Complex Patterns in Nature 267 R.A. Barrio Primordial Evolution in the Finitary Process Soup 297 Olof Gornerup and James P. Crutchfield Emergence of Universe from a Quantum Network 313 Paola A. Zizzi Occam's Razor Revisited: Simplicity vs. Complexity in Biology 327 Joseph P. Zbilut Order in the Nothing: Autopoiesis and the Organizational Characterization of the Living 339 Leonardo Bich and Luisa Damiano Anticipation in Biological and Cognitive Systems: The Need for a Physical Theory of Biological Organization 371 Graziano Terenzi How Uncertain is Uncertainty? 389 Tibor Vamos Archetypes, Causal Description and Creativity in Natural World 405 Leonardo Chiatti . (shrink)

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and in (...) theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (2nd Edition), Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects, J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2. (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)

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.

The brain in its plasticity and inherent 'sociality' can be proclaimed and projected as a revolutionary organ. Far from the old reactions which opposed the authenticity of political theory and praxis to the dangerous naturalism of 'cognitive science' (with images of men in white coats, the RAND Corporation or military LSD experiments), recent decades have shown us some of the potentiality of the social brain (Vygotsky, and more recently Negri 1995 and Negri 2000, Virno 2001). Is the brain somehow inherently (...) a utopian topos? If in some earlier papers I sought to defend naturalism against these reactions, here I consider a new challenge: the recently emerged disciplines of neuronormativity, which seek in their own way to overcome the nature-normativity divide. This is the task of a materialist brain theory today. 1. The setup: horns of a dilemma There is a lingering zone of what one might think of as sore cognitive muscle tissue in the area of materialism. It is an area of both contested territory and in some cases, a kind of pathos of distance of the 'Ugh! Keep that thing away from me!' sort. I have in mind the combination of materialism as an emancipatory socio-political project (which need not be construed in strictly Marx-Engels terms, if we think of Lucretius et al.) and as a cold-hearted 'spontaneous philosophy of the men in white coats', e.g. nefarious neurophilosophers. Faced with this rather massive alternative, this choice between two projects, I have stubbornly been saying since some discussions with Negri in the late 90s. (shrink)

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and in (...) theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism, Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects, J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2. (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.

It is often helpful in metaphysics to reflect upon the principles that govern how existence claims are made in logic and mathematics. Consider, for example, the different ways in which mathematicians construct inductive definitions. In order to provide an inductive definition of a class of mathematical entities, one must first define a base class and then stipulate further conditions for inclusion by reference to the properties of members of the base class. These conditions can be deflationary, so that the target (...) class is a subclass of the base class, or inflationary, so that the base class is an important subclass of the target class. For example, in defining the set of well-formed sentences of first order logic, one can begin with the set of all possible strings and, in a deflationary manner, exclude the nonsentences. Or one can begin with the set of atomic formulae, and in an inflationary manner, build more complicated sentences out of the atomic formulae. (shrink)

ArgumentThis paper discusses one aspect of the context in which atomic physics developed in Japan between 1905 and 1931. It argues that during this period, there was a social context in which atomic physics was valued as a study of the electron and was thus relevant to electrical engineering. To demonstrate this, I first show that after the Russo-Japanese War, electrical engineering was deemed a valuable and viable field of research in Japan. Second, I show that physicists wrote textbooks and (...) popular accounts about the electron, covering topics from both atomic physics and electrical engineering and presenting the former as relevant to the latter. Finally, as an example of how atomic physics partially emerged from this context, I discuss the group of Kujirai Tsunetarō, an electrical engineer who worked in the physics department of the Institute for Physical and Chemical Research. From Kujirai's group, Nishina Yoshio started his career and became the most important Japanese atomic and nuclear physicist of the 1930s. (shrink)

Representationalism emerges unscathed from Pessoa et al.'s attack. They fail to undermine a key reason for its influence: it has the theoretical resources to explain many illusory visual experiences such as illusory contours and features. Furthermore, in attempting to undermine representationalism, the authors seem to erect an unduly inflated distinction between neural accounts of perception and personal-level accounts of perception.

We give a formal interpretation of Martin-Löf's Constructive Theory of Types in Elementary Topos Theory which is presented as a formalised theory with intensional equality of objects. Types are interpreted as arrows and variables as sections of their types. This is necessary to model correctly the working of the assumption x ∈ A. Then intensional equality interprets equality of types. The normal form theorem which asserts that the interpretation of a type is intensional equal to the pullback of its (...) “alignment” along some “base” arrow relates this interpretation to categorical semantic of types. (shrink)

The view that toposes originated as generalized set theory is a figment of set theoretically educated common sense. This false history obstructs understanding of category theory and especially of categorical foundations for mathematics. Problems in geometry, topology, and related algebra led to categories and toposes. Elementary toposes arose when Lawvere's interest in the foundations of physics and Tierney's in the foundations of topology led both to study Grothendieck's foundations for algebraic geometry. I end with remarks on a categorical view of (...) the history of set theory, including a false history plausible from that point of view that would make it helpful to introduce toposes as a generalization from set theory. (shrink)

Topos Theory is an important branch of mathematical logic of interest to theoretical computer scientists, logicians and philosophers who study the foundations of mathematics, and to those working in differential geometry and continuum physics. This compendium contains material that was previously available only in specialist journals. This is likely to become the standard reference work for all those interested in the subject.

Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Because of this, an account of topos theory which approaches the subject from one particular direction can only hope to give a partial picture; the aim of this compendium is to present as comprehensive an account as possible of all the main approaches and (...) thereby to demonstrate the overall unity of the subject. The material is organised in such a way that readers interested in following a particular line of approach may do so by starting at an appropriate point in the text. (shrink)

We present a scenario describing how time emerges in the framework of weak quantum theory. In a process similar to the emergence of time in quantum cosmology, time arises after an epistemic split of an undivided unus mundus as a quality of the individual conscious mind. Synchronization with matter and other mental systems is achieved by entanglement correlations. In the course of its operationalization, time loses its original quality and the time of physics as measured by clocks appears. avoided/explicated.

Our aim in this reply is to defend Global Workspace theory (GWT) from the challenge of Block's article. We argue that Block's article relies on an outdated and imprecise concept of access, and perpetuates a common misunderstanding of GWT that conflates the global workspace with working memory. In the light of the relevant clarifications, Block's conclusion turns out to be unwarranted, and the basic tenets of GWT emerge unscathed.

There is consensus among emotion scientists that emotions can be powerful motivators of actions. However, little progress has been made so far in the scientific study of that relation. The main reason for this disappointing state of affairs lies, in my view, in an overly simplistic “boxology” that treats actions as outputs of emotional stimulations. A promising way out of this situation is an interdisciplinary approach that connects emotion sciences with theories in motivation and action sciences—an emerging field that I (...) call “emotional action sciences.”. (shrink)

In order to account for the mode of existence of social rules and norms, the author develops a theory of the emergence of institutional facts. Just as other kinds of institutional fact, rules and norms are meanings. Therefore, insight into the emergence of social rules and norms can be achieved by studying the recognition and the communication of meanings. Following accounts of meaning and factuality, institutional facts are characterized as unquestionable shared typifications. It is argued that, in becoming (...) an institutional fact, a typification goes through two phases. First, it becomes a social habit. Second, this habit turns into an obligation by being objectified. (shrink)

My purpose in this short response to Clinton's interesting article On Bender's orientation to models: Towards a philosophical debate on covering laws, theory, emergence and mechanisms in nursing science, which is published in this issue, is not to provide any counterargument to Clinton's interpretation of my own argument; readers are welcome to interrogate both articles at their leisure and make their own conclusions. What I will do instead is provide a brief critical assessment of my own (il)logic re bringing (...) in the notion of mechanism as conceived by Machamer, Darden and Craver into an argument for models versus theories as a carrier of nursing knowledge. (shrink)

Nursing scholars continuously refine nursing knowledge and the philosophical foundations of nursing practice. They advance nursing knowledge by creating new knowledge and weighing the relevance of developments in cognate sciences. Nurse philosophers go further by providing epistemological and ontological arguments for explanations of nursing phenomena. In this article, I engage with Bender's arguments about why mechanisms should have more primacy as carriers of nursing knowledge. Despite the careful scholarship involved, Bender's arguments need to be more convincing. Accordingly, this article encourages (...) debate about Bender's arguments for reorientating nursing science to mechanisms. I begin by suggesting that the claim that the theory‐practice divide can be overcome by reorientating to mechanisms is acceptable only if we accept Bender's depiction of the challenge. Then I question the ontology Bender relies on to justify reorientating nursing science. After that, I argue that mechanisms in models that parallel analytical sociology undermine the kind of nursing science Bender advocates. I illustrate my arguments with a social mechanism thought experiment. Then I explain why Bender's arguments cannot escape the received view of science or inform emancipatory nursing action without theory. Finally, I mention some caveats and implications for nursing science. (shrink)

In order to account for the mode of existence of social rules and norms, the author develops a theory of the emergence of institutional facts. Just as other kinds of institutional fact, rules and norms are meanings. Therefore, insight into the emergence of social rules and norms can be achieved by studying the recognition and the communication of meanings. Following accounts of meaning and factuality, institutional facts are characterized as unquestionable shared typifications. It is argued that, in becoming (...) an institutional fact, a typification goes through two phases. First, it becomes a social habit. Second, this habit turns into an obligation by being objectified. (shrink)

This essay considers the extent to which a concept of emergence can be associated with Effective Field Theories (EFTs). I suggest that such a concept can be characterized by microphysicalism and novelty underwritten by the elimination of degrees of freedom from a high-energy theory, and argue that this makes emergence in EFTs distinct from other concepts of emergence in physics that have appeared in the recent philosophical literature.

Quantum field theories are notoriously difficult to understand, physically as well as philosophically. The aim of this paper is to contribute to a better conceptual understanding of gauge quantum field theories, such as quantum chromodynamics, by discussing a famous physical limit, the ’t Hooft limit, in which the theory concerned often simplifies. The idea of the limit is that the number N of colours goes to infinity. The simplifications that can happen in this limit, and that we will consider, are: (...) the theory’s Feynman diagrams can be drawn on a plane without lines intersecting ; and the theory, or a sector of it, becomes integrable, and indeed corresponds to a well-studied system, viz. a spin chain. Planarity is important because it shows how a quantum field theory can exhibit extended, in particular string-like, structures; in some cases, this gives a connection with string theory, and so with its representation of gravity. Previous philosophical literature about how one theory might be emergent from, and-or reduced to, another one has tended to emphasize cases, such as occur in statistical mechanics, where the system before the limit has finitely many degrees of freedom. But here, our quantum field theories, including those on the way to the ’t Hooft limit, will have infinitely many degrees of freedom. Nevertheless, we will show how a recent schema by Butterfield and taxonomy by Norton apply to the quantum field theories we consider; and we will classify three physical properties of our theories in these terms. These properties are planarity and integrability, as in and above; and the behaviour of the beta-function reflecting, for example, asymptotic freedom. Our discussion of these properties, especially the beta-function, will also relate to recent philosophical debate about the propriety of assessing quantum field theories, whose rigorous existence is not yet proven. (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)

This book introduces a set of methods and techniques for studying mathematical theories and relating them to each other through the use of Grothendieck toposes.

Relationships between current theories, and relationships between current theories and the sought theory of quantum gravity (QG), play an essential role in motivating the need for QG, aiding the search for QG, and defining what would count as QG. Correspondence is the broad class of inter-theory relationships intended to demonstrate the necessary compatibility of two theories whose domains of validity overlap, in the overlap regions. The variety of roles that correspondence plays in the search for QG are illustrated, using examples (...) from specific QG approaches. Reduction is argued to be a special case of correspondence, and to form part of the definition of QG. Finally, the appropriate account of emergence in the context of QG is presented, and compared to conceptions of emergence in the broader philosophy literature. It is argued that, while emergence is likely to hold between QG and general relativity, emergence is not part of the definition of QG, and nor can it serve usefully in the development and justification of the new theory. (shrink)

In this essay Elizabeth de Freitas follows Tim Ingold's groundbreaking anthropological work on lines and their cultural and material significance to argue that the line is the engine of theory, be it the drawn line of inscription or mathematical measure, the exclusionary line of delineation, or the undulating generative line of flight. De Freitas focuses on contemporary theories of perception that deploy the line — and mobilize the force of theory — so as to encode and reconfigure the student's body. (...) She draws on the work of Gilles Deleuze to develop a topological approach to the line, and argues that such an approach aligns with current philosophical approaches to social interaction that might be termed “topo-philosophy.”. (shrink)