Topology

Edited by Nemi Boris Pelgrom (Ludwig Maximilians Universität, München)
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  1. Why did Fermat believe he had `a truly marvellous demonstration' of FLT?Bhupinder Singh Anand - manuscript
    Conventional wisdom dictates that proofs of mathematical propositions should be treated as necessary, and sufficient, for entailing `significant' mathematical truths only if the proofs are expressed in a---minimally, deemed consistent---formal mathematical theory in terms of: * Axioms/Axiom schemas * Rules of Deduction * Definitions * Lemmas * Theorems * Corollaries. Whilst Andrew Wiles' proof of Fermat's Last Theorem FLT, which appeals essentially to geometrical properties of real and complex numbers, can be treated as meeting this criteria, it nevertheless leaves two (...)
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  2. A Pre-formal Proof of Why No Planar Map Needs More Than Four Colours.Bhupinder Singh Anand - manuscript
    Although the Four Colour Theorem is passe, we give an elementary pre-formal proof that transparently illustrates why four colours suffice to chromatically differentiate any set of contiguous, simply connected and bounded, planar spaces; by showing that there is no minimal 4-coloured planar map M. We note that such a pre-formal proof of the Four Colour Theorem highlights the significance of differentiating between: (a) Plato's knowledge as justified true belief, which seeks a formal proof in a first-order mathematical language in order (...)
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  3. Heidegger's silence: Towards a post-modern topology.Babette Babich - manuscript
    in Charles Scott and Arleen Dallery, eds., Ethics and Danger: Currents in Continental Thought. Albany. State University of New York Press. 1992. Pp. 83-106.
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  4. Topology of Modal Propositions Depicted by Peirce’s Gamma Graphs: Line, Square, Cube, and Four-Dimensional Polyhedron.Jorge Alejandro Flórez - forthcoming - Logic and Logical Philosophy:1-14.
    This paper presents the topological arrangements in four geometrical figures of modal propositions and their derivative relations by means of Peirce's gamma graphs and their rules of transformation. The idea of arraying the gamma graphs in a geometric and symmetrical order comes from Peirce himself who in a manuscript drew two cubes in which he presented the derivative relations of some gamma graphs. Therefore, Peirce's insights of a topological order of gamma graphs are extended here backwards from the cube to (...)
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  5. A Topological Analysis of Space-Time-Consciousness: Self, Self-Self, Self-Other.Hye Young Kim - forthcoming - In When Form Becomes Substance. Power of Gesture, Grammatical Intuition and Phenomenology of Space.
    This paper attempts to explore a possibility to visualize the structure of time-consciousness in a knot shape. By applying Louis Kauffman’s knot-logic, the consistency of subjective consciousness, the plurality of now’s, and the necessary relationship between subjective and intersubjective consciousness will be represented in topological space.
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  6. On the Zariski Topology on Endomorphism Monoids of Omega-Categorical Structures.Michael Pinsker & Clemens Schindler - forthcoming - Journal of Symbolic Logic:1-19.
    The endomorphism monoid of a model-theoretic structure carries two interesting topologies: on the one hand, the topology of pointwise convergence induced externally by the action of the endomorphisms on the domain via evaluation; on the other hand, the Zariski topology induced within the monoid by (non-)solutions to equations. For all concrete endomorphism monoids of $\omega $ -categorical structures on which the Zariski topology has been analysed thus far, the two topologies were shown to coincide, in turn yielding that the pointwise (...)
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  7. On categorical structures arising from implicative algebras: From topology to assemblies.Samuele Maschio & Davide Trotta - 2024 - Annals of Pure and Applied Logic 175 (3):103390.
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  8. Cosmic Topology, Underdetermination, and Spatial Infinity.Patrick James Ryan - 2024 - European Journal for Philosophy of Science 14 (17):1-28.
    It is well-known that the global structure of every space-time model for relativistic cosmology is observationally underdetermined. In order to alleviate the severity of this underdetermination, it has been proposed that we adopt the Cosmological Principle because the Principle restricts our attention to a distinguished class of space-time models (spatially homogeneous and isotropic models). I argue that, even assuming the Cosmological Principle, the topology of space remains observationally underdetermined. Nonetheless, I argue that we can muster reasons to prefer various topological (...)
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  9. Non-Relativistic Regime and Topology: Topological Term in the Einstein Equation.Quentin Vigneron - 2024 - Foundations of Physics 54 (1):1-47.
    We study the non-relativistic (NR) limit of relativistic spacetimes in relation with the topology of the Universe. We first show that the NR limit of the Einstein equation is only possible in Euclidean topologies, i.e., for which the covering space is \(\mathbb {E}^3\). We interpret this result as an inconsistency of general relativity in non-Euclidean topologies and propose a modification of that theory which allows for the limit to be performed in any topology. For this, a second reference non-dynamical connection (...)
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  10. Who's Afraid of Mathematical Diagrams?Silvia De Toffoli - 2023 - Philosophers' Imprint 23 (1).
    Mathematical diagrams are frequently used in contemporary mathematics. They are, however, widely seen as not contributing to the justificatory force of proofs: they are considered to be either mere illustrations or shorthand for non-diagrammatic expressions. Moreover, when they are used inferentially, they are seen as threatening the reliability of proofs. In this paper, I examine certain examples of diagrams that resist this type of dismissive characterization. By presenting two diagrammatic proofs, one from topology and one from algebra, I show that (...)
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  11. Don’t forget the boundary problem! How EM field topology can address the overlooked cousin to the binding problem for consciousness.Andrés Gómez-Emilsson & Chris Percy - 2023 - Frontiers in Human Neuroscience 17:1233119.
    The boundary problem is related to the binding problem, part of a family of puzzles and phenomenal experiences that theories of consciousness (ToC) must either explain or eliminate. By comparison with the phenomenal binding problem, the boundary problem has received very little scholarly attention since first framed in detail by Rosengard in 1998, despite discussion by Chalmers in his widely cited 2016 work on the combination problem. However, any ToC that addresses the binding problem must also address the boundary problem. (...)
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  12. The topology of persons, and surviving to some degree.Zbigniew Król, Tomasz Kąkol & Bartłomiej Skowron - 2023 - Synthese 202 (6):1-37.
    Braddon-Mitchell and Miller put forward the claim that the relation of being-the-same-person is gradable: a person can be the same person tomorrow as today, but only half the same. To justify their thesis, they propose a model of persons that is intended to be metaphysically neutral. This article sets out to show that such a model implicitly contains strong metaphysical assumptions that run contrary to the authors’ own statements. Using Roman Ingarden’s phenomenological ontology, we aim to demonstrate that within the (...)
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  13. Топология субъектности.Andrej Poleev - 2023 - Enzymes 21.
    Техника представления информации о внешнем и внутреннем мире постоянно развивается, и сейчас она достигла уровня отображения реальности в многообразных её проявлениях и измерениях, прежде недоступных человеческому восприятию. Язык, текст, фотография, звукозапись, а теперь ещё и техника искусственного интеллекта для моделирования человеческой субъектности и её описания в доступной для человеческого понимания форме, стали эпохальными событиями в теории информации. Однако несмотря на то, что на данном этапе её развития она позволяет оперировать с непрерывно возрастающими объёмами информации, это не приближает её теоретиков к (...)
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  14. The introduction of topology into analytic philosophy: two movements and a coda.Samuel C. Fletcher & Nathan Lackey - 2022 - Synthese 200 (3):1-34.
    Both early analytic philosophy and the branch of mathematics now known as topology were gestated and born in the early part of the 20th century. It is not well recognized that there was early interaction between the communities practicing and developing these fields. We trace the history of how topological ideas entered into analytic philosophy through two migrations, an earlier one conceiving of topology geometrically and a later one conceiving of topology algebraically. This allows us to reassess the influence and (...)
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  15. Topology optimization of computer communication network based on improved genetic algorithm.Kayhan Zrar Ghafoor, Jilei Zhang, Yuhong Fan & Hua Ai - 2022 - Journal of Intelligent Systems 31 (1):651-659.
    The topology optimization of computer communication network is studied based on improved genetic algorithm, a network optimization design model based on the establishment of network reliability maximization under given cost constraints, and the corresponding improved GA is proposed. In this method, the corresponding computer communication network cost model and computer communication network reliability model are established through a specific project, and the genetic intelligence algorithm is used to solve the cost model and computer communication network reliability model, respectively. It has (...)
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  16. Not so distinctively mathematical explanations: topology and dynamical systems.Aditya Jha, Douglas Campbell, Clemency Montelle & Phillip L. Wilson - 2022 - Synthese 200 (3):1-40.
    So-called ‘distinctively mathematical explanations’ (DMEs) are said to explain physical phenomena, not in terms of contingent causal laws, but rather in terms of mathematical necessities that constrain the physical system in question. Lange argues that the existence of four or more equilibrium positions of any double pendulum has a DME. Here we refute both Lange’s claim itself and a strengthened and extended version of the claim that would pertain to any n-tuple pendulum system on the ground that such explanations are (...)
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  17. Topological Explanations: An Opinionated Appraisal.Daniel Kostić - 2022 - In I. Lawler, E. Shech & K. Khalifa (eds.), Scientific Understanding and Representation: Modeling in the Physical Sciences. Routledge. pp. 96-115.
    This chapter provides a systematic overview of topological explanations in the philosophy of science literature. It does so by presenting an account of topological explanation that I (Kostić and Khalifa 2021; Kostić 2020a; 2020b; 2018) have developed in other publications and then comparing this account to other accounts of topological explanation. Finally, this appraisal is opinionated because it highlights some problems in alternative accounts of topological explanations, and also it outlines responses to some of the main criticisms raised by the (...)
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  18. Topological Models of Columnar Vagueness.Thomas Mormann - 2022 - Erkenntnis 87 (2):693 - 716.
    This paper intends to further the understanding of the formal properties of (higher-order) vagueness by connecting theories of (higher-order) vagueness with more recent work in topology. First, we provide a “translation” of Bobzien's account of columnar higher-order vagueness into the logic of topological spaces. Since columnar vagueness is an essential ingredient of her solution to the Sorites paradox, a central problem of any theory of vagueness comes into contact with the modern mathematical theory of topology. Second, Rumfitt’s recent topological reconstruction (...)
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  19. Fuzzy topology induced by binary fuzzy relation. Priti & Alka Tripathi - 2022 - In Bhagwati Prasad Chamola, Pato Kumari & Lakhveer Kaur (eds.), Emerging advancements in mathematical sciences. Nova Science Publishers.
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  20. Justified belief, knowledge, and the topology of evidence.Sonja Smets, Aybüke Özgün, Nick Bezhanishvili & Alexandru Baltag - 2022 - Synthese 200 (6):1-51.
    We propose a new topological semantics for evidence, evidence-based justifications, belief, and knowledge. Resting on the assumption that an agent’s rational belief is based on the available evidence, we try to unveil the concrete relationship between an agent’s evidence, belief, and knowledge via a rich formal framework afforded by topologically interpreted modal logics. We prove soundness, completeness, decidability, and the finite model property for the associated logics, and apply this setting to analyze key epistemological issues such as “no false lemma” (...)
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  21. A journey through computability, topology and analysis.Manlio Valenti - 2022 - Bulletin of Symbolic Logic 28 (2):266-267.
    This thesis is devoted to the exploration of the complexity of some mathematical problems using the framework of computable analysis and descriptive set theory. We will especially focus on Weihrauch reducibility as a means to compare the uniform computational strength of problems. After a short introduction of the relevant background notions, we investigate the uniform computational content of problems arising from theorems that lie at the higher levels of the reverse mathematics hierarchy.We first analyze the strength of the open and (...)
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  22. Extension and Self-Connection.Ben Blumson & Manikaran Singh - 2021 - Logic and Logical Philosophy 30 (3):435-59.
    If two self-connected individuals are connected, it follows in classical extensional mereotopology that the sum of those individuals is self-connected too. Since mainland Europe and mainland Asia, for example, are both self-connected and connected to each other, mainland Eurasia is also self-connected. In contrast, in non-extensional mereotopologies, two individuals may have more than one sum, in which case it does not follow from their being self-connected and connected that the sum of those individuals is self-connected too. Nevertheless, one would still (...)
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  23. Two applications of topology to model theory.Christopher J. Eagle, Clovis Hamel & Franklin D. Tall - 2021 - Annals of Pure and Applied Logic 172 (5):102907.
    By utilizing the topological concept of pseudocompactness, we simplify and improve a proof of Caicedo, Dueñez, and Iovino concerning Terence Tao's metastability. We also pinpoint the exact relationship between the Omitting Types Theorem and the Baire Category Theorem by developing a machine that turns topological spaces into abstract logics.
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  24. Topology at Play.Giulio Goria - 2021 - In Silvia Benso & Antonio Calcagno (eds.), Open borders: encounters between Italian philosophy and continental thought. State University of New York Press. pp. 325-339.
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  25. Punctual definability on structures.Iskander Kalimullin, Alexander Melnikov & Antonio Montalban - 2021 - Annals of Pure and Applied Logic 172 (8):102987.
    We study punctual categoricity on a cone and intrinsically punctual functions and obtain complete structural characterizations in terms of model-theoretic notions. As a corollary, we answer a question of Bazhenov, Downey, Kalimullin, and Melnikov by showing that relational structures are not punctually universal. We will also apply this characterisation to derive an algebraic characterisation of relatively punctually categorical mono-unary structures.
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  26. Topology of Balasaguni's Kutadgu Bilig. Thinking the Between.Onur Karamercan - 2021 - In Takeshi Morisato & Roman Pașca (eds.), Vanishing Subjectivity: Flower, Shame, and Direct Cultivation in Asian PhilosophiesAsian Philosophical Texts, no. 3. pp. 69-97.
    In “Topology of Balasaguni’s Kutadgu Bilig: Thinking the Between,” Onur Karamercan focuses on the philosophical dimension of Kutadgu Bilig, a poetic work of Yūsuf Balasaguni, an 11th century Central Asian thinker, poet, and statesman. Karamercan pays special attention to the meaning of betweenness and, in the first step of his argument, discusses the hermeneutic and topological implications of the between, distingushing the dynamic sense of betweenness from a static sense of in-betweenness. He then moves on to analyze Balasaguni’s notion of (...)
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  27. The profinite topology of free groups and weakly generic tuples of automorphisms.Gábor Sági - 2021 - Mathematical Logic Quarterly 67 (4):432-444.
    Let be a countable first order structure and endow the universe of with the discrete topology. Then the automorphism group of becomes a topological group. A tuple of automorphisms is defined to be weakly generic iff its diagonal conjugacy class (in the algebraic sense) is dense (in the topological sense) and the ‐orbit of each is finite. Existence of tuples of weakly generic automorphisms are interesting from the point of view of model theory as well as from the point of (...)
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  28. Część i Całość: W Stronę Topoontologii (Part and Whole: Towards Topoontology).Bartłomiej Skowron - 2021 - Warsaw: Oficyna Wydawnicza Politechniki Warszawskiej, 2021..
    part, whole, ideal quality, foundation, unity, space, topoontology, topophilosophy, formal ontology, topology, mathematical philosophy, topology, topology of the person, topology of mind, mathematics in philosophy, mereology, mereotopology, phenomenology, Benedict Bornstein, Edmund Husserl, Roman Ingarden, Kurt Lewin, René Thom.
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  29. Relational Representation Theorems for Extended Contact Algebras.Philippe Balbiani & Tatyana Ivanova - 2020 - Studia Logica 109 (4):701-723.
    In topological spaces, the relation of extended contact is a ternary relation that holds between regular closed subsets A, B and D if the intersection of A and B is included in D. The algebraic counterpart of this mereotopological relation is the notion of extended contact algebra which is a Boolean algebra extended with a ternary relation. In this paper, we are interested in the relational representation theory for extended contact algebras. In this respect, we study the correspondences between point-free (...)
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  30. Choice-free stone duality.Nick Bezhanishvili & Wesley H. Holliday - 2020 - Journal of Symbolic Logic 85 (1):109-148.
    The standard topological representation of a Boolean algebra via the clopen sets of a Stone space requires a nonconstructive choice principle, equivalent to the Boolean Prime Ideal Theorem. In this article, we describe a choice-free topological representation of Boolean algebras. This representation uses a subclass of the spectral spaces that Stone used in his representation of distributive lattices via compact open sets. It also takes advantage of Tarski’s observation that the regular open sets of any topological space form a Boolean (...)
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  31. Continua.Lu Chen - 2020 - Dissertation, University of Massachusetts Amherst
    The subject of my dissertation is the structure of continua and, in particular, of physical space and time. Consider the region of space you occupy: is it composed of indivisible parts? Are the indivisible parts, if any, extended? Are there infinitesimal parts? The standard view that space is composed of unextended points faces both \textit{a priori} and empirical difficulties. In my dissertation, I develop and evaluate several novel approaches to these questions based on metaphysical, mathematical and physical considerations. In particular, (...)
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  32. Reconciling Rigor and Intuition.Silvia De Toffoli - 2020 - Erkenntnis 86 (6):1783-1802.
    Criteria of acceptability for mathematical proofs are field-dependent. In topology, though not in most other domains, it is sometimes acceptable to appeal to visual intuition to support inferential steps. In previous work :829–842, 2014; Lolli, Panza, Venturi From logic to practice, Springer, Berlin, 2015; Larvor Mathematical cultures, Springer, Berlin, 2016) my co-author and I aimed at spelling out how topological proofs work on their own terms, without appealing to formal proofs which might be associated with them. In this article, I (...)
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  33. From the four-color theorem to a generalizing “four-letter theorem”: A sketch for “human proof” and the philosophical interpretation.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 12 (21):1-10.
    The “four-color” theorem seems to be generalizable as follows. The four-letter alphabet is sufficient to encode unambiguously any set of well-orderings including a geographical map or the “map” of any logic and thus that of all logics or the DNA plan of any alive being. Then the corresponding maximally generalizing conjecture would state: anything in the universe or mind can be encoded unambiguously by four letters. That admits to be formulated as a “four-letter theorem”, and thus one can search for (...)
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  34. Reverse Mathematics of Topology: Dimension, Paracompactness, and Splittings.Sam Sanders - 2020 - Notre Dame Journal of Formal Logic 61 (4):537-559.
    Reverse mathematics is a program in the foundations of mathematics founded by Friedman and developed extensively by Simpson and others. The aim of RM is to find the minimal axioms needed to prove a theorem of ordinary, that is, non-set-theoretic, mathematics. As suggested by the title, this paper deals with the study of the topological notions of dimension and paracompactness, inside Kohlenbach’s higher-order RM. As to splittings, there are some examples in RM of theorems A, B, C such that A (...)
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  35. Peirce's Topical Continuum: A “Thicker” Theory.Jon Alan Schmidt - 2020 - Transactions of the Charles S. Peirce Society 56 (1):62-80.
    Although Peirce frequently insisted that continuity was a core component of his philosophical thought, his conception of it evolved considerably during his lifetime, culminating in a theory grounded primarily in topical geometry. Two manuscripts, one of which has never before been published, reveal that his formulation of this approach was both earlier and more thorough than most scholars seem to have realized. Combining these and other relevant texts with the better-known passages highlights a key ontological distinction: a collection is bottom-up, (...)
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  36. A Semantic Hierarchy for Intuitionistic Logic.Guram Bezhanishvili & Wesley H. Holliday - 2019 - Indagationes Mathematicae 30 (3):403-469.
    Brouwer's views on the foundations of mathematics have inspired the study of intuitionistic logic, including the study of the intuitionistic propositional calculus and its extensions. The theory of these systems has become an independent branch of logic with connections to lattice theory, topology, modal logic and other areas. This paper aims to present a modern account of semantics for intuitionistic propositional systems. The guiding idea is that of a hierarchy of semantics, organized by increasing generality: from the least general Kripke (...)
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  37. Algebraic and topological semantics for inquisitive logic via choice-free duality.Nick Bezhanishvili, Gianluca Grilletti & Wesley H. Holliday - 2019 - In Rosalie Iemhoff, Michael Moortgat & Ruy de Queiroz (eds.), Logic, Language, Information, and Computation. WoLLIC 2019. Lecture Notes in Computer Science, Vol. 11541. Springer. pp. 35-52.
    We introduce new algebraic and topological semantics for inquisitive logic. The algebraic semantics is based on special Heyting algebras, which we call inquisitive algebras, with propositional valuations ranging over only the ¬¬-fixpoints of the algebra. We show how inquisitive algebras arise from Boolean algebras: for a given Boolean algebra B, we define its inquisitive extension H(B) and prove that H(B) is the unique inquisitive algebra having B as its algebra of ¬¬-fixpoints. We also show that inquisitive algebras determine Medvedev’s logic (...)
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  38. Boundaries and Things. A Metaphysical Study of the Brentano-Chisholm Theory.Gonzalo Nuñez Erices - 2019 - Kriterion: Journal of Philosophy 33 (2):15-48.
    The fact that boundaries are ontologically dependent entities is agreed by Franz Brentano and Roderick Chisholm. This article studies both authors as a single metaphysical account about boundaries. The Brentano-Chisholm theory understands that boundaries and the objects to which they belong hold a mutual relationship of ontological dependence: the existence of a boundary depends upon a continuum of higher spatial dimensionality, but also is a conditio sine qua non for the existence of a continuum. Although the view that ordinary material (...)
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  39. Drawing Boundaries.Barry Smith - 2019 - In Timothy Tambassi (ed.), The Philosophy of GIS. New York: Springer. pp. 137-158.
    In “On Drawing Lines on a Map” (1995), I suggested that the different ways we have of drawing lines on maps open up a new perspective on ontology, resting on a distinction between two sorts of boundaries: fiat and bona fide. “Fiat” means, roughly: human-demarcation-induced. “Bona fide” means, again roughly: a boundary constituted by some real physical discontinuity. I presented a general typology of boundaries based on this opposition and showed how it generates a corresponding typology of the different sorts (...)
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  40. Syntax meets semantics during brain logical computations.Arturo Tozzi, James F. Peters, Andrew And Alexander Fingelkurts & Leonid Perlovsky - 2018 - Progress in Biophysics and Molecular Biology 140:133-141.
    The discrepancy between syntax and semantics is a painstaking issue that hinders a better comprehension of the underlying neuronal processes in the human brain. In order to tackle the issue, we at first describe a striking correlation between Wittgenstein's Tractatus, that assesses the syntactic relationships between language and world, and Perlovsky's joint language-cognitive computational model, that assesses the semantic relationships between emotions and “knowledge instinct”. Once established a correlation between a purely logical approach to the language and computable psychological activities, (...)
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  41. Concept and Formalization of Constellatory Self-Unfolding: A Novel Perspective on the Relation between Quantum and Relativistic Physics.Albrecht von Müller & Elias Zafiris - 2018 - Cham: Springer. Edited by Elias Zafiris.
    This volume develops a fundamentally different categorical framework for conceptualizing time and reality. The actual taking place of reality is conceived as a “constellatory self-unfolding” characterized by strong self-referentiality and occurring in the primordial form of time, the not yet sequentially structured “time-space of the present.” Concomitantly, both the sequentially ordered aspect of time and the factual aspect of reality appear as emergent phenomena that come into being only after reality has actually taken place. In this new framework, time functions (...)
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  42. A visual representation of part-whole relationships in BFO-conformant ontologies.Jose M. Parente de Oliveira & Barry Smith - 2017 - In Á Rocha, A. M. Correia, H. Adeli, L. P. Reis & S. Costanzo (eds.), Recent Advances in Information Systems and Technologies (Advances in Intelligent Systems and Computing, 569). New York: Springer. pp. 184-194.
    In the visual representation of ontologies, in particular of part-whole relationships, it is customary to use graph theory as the representational background. We claim here that the standard graph-based approach has a number of limitations, and we propose instead a new representation of part-whole structures for ontologies, and describe the results of experiments designed to show the effectiveness of this new proposal especially as concerns reduction of visual complexity. The proposal is developed to serve visualization of ontologies conformant to the (...)
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  43. A diagrammatic representation for entities and mereotopological relations in ontologies.José M. Parente de Oliveira & Barry Smith - 2017 - In CEUR, vol. 1908.
    In the graphical representation of ontologies, it is customary to use graph theory as the representational background. We claim here that the standard graph-based approach has a number of limitations. We focus here on a problem in the graph-based representation of ontologies in complex domains such as biomedical, engineering and manufacturing: lack of mereotopological representation. Based on such limitation, we proposed a diagrammatic way to represent an entity’s structure and various forms of mereotopological relationships between the entities.
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  44. Writing the Structures of the Subject: Lacan and Topology.Will Greenshields - 2017 - Cham: Imprint: Palgrave Macmillan.
    This book examines and explores Jacques Lacan's controversial topologisation of psychoanalysis, and seeks to persuade the reader that this enterprise was necessary and important. In providing both an introduction to a fundamental component of Lacan's theories, as well as readings of texts that have been largely ignored, it provides a thorough critical interpretation of his work. Will Greenshields argues that Lacan achieved his most pedagogically clear and successful presentations of his most essential and notoriously complex concepts - such as structure, (...)
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  45. The City of Research Institutes: Notes on the Nuclear Topology.G. A. Orlova - 2017 - Sociology of Power 29 (4):68-103.
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  46. Poincaré on the Foundation of Geometry in the Understanding.Jeremy Shipley - 2017 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2016 Annual Meeting in Calgary, Alberta. Springer. pp. 19-37.
    This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study (...)
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  47. Envisioning Transformations – The Practice of Topology.Silvia De Toffoli & Valeria Giardino - 2016 - In Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 2012-2014. Springer International Publishing. pp. 25-50.
    The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the practitioners; (...)
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  48. I. Topology and the Idea of Form.Angus Fletcher - 2016 - In The Topological Imagination: Spheres, Edges, and Islands. Harvard University Press. pp. 11-40.
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  49. The nature of the topological intuition.L. B. Sultanova - 2016 - Liberal Arts in Russia 5 (1):14.
    The article is devoted to the nature of the topological intuition and disclosure of the specifics of topological heuristics in the framework of philosophical theory of knowledge. As we know, intuition is a one of the support categories of the theory of knowledge, the driving force of scientific research. Great importance is mathematical intuition for the solution of non-standard problems, for which there is no algorithm for such a solution. In such cases, the mathematician addresses the so-called heuristics, built on (...)
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  50. Loops, projective invariants, and the realization of the Borromean topological link in quantum mechanics.Elias Zafiris - 2016 - Quantum Studies: Mathematics and Foundations 3 (4):337-359.
    All the typical global quantum mechanical observables are complex relative phases obtained by interference phenomena. They are described by means of some global geometric phase factor, which is thought of as the “memory” of a quantum system undergoing a “cyclic evolution” after coming back to its original physical state. The origin of a geometric phase factor can be traced to the local phase invariance of the transition probability assignment in quantum mechanics. Beyond this invariance, transition probabilities also remain invariant under (...)
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