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  1. added 2018-12-17
    Fiat Objects.Barry Smith - 1994 - In Nicola Guarino, Laure Vieu & Simone Pribbenow (eds.), Parts and Wholes: Conceptual Part-Whole Relations and Formal Mereology, 11th European Conference on Artificial Intelligence, Amsterdam, 8 August 1994, Amsterdam:. Amsterdam: European Coordinating Committee for Artificial Intelligence. pp. 14-22.
    Human cognitive acts are directed towards entities of a wide range of different types. What follows is a new proposal for bringing order into this typological clutter. A categorial scheme for the objects of human cognition should be (1) critical and realistic. Cognitive subjects are liable to error, even to systematic error of the sort that is manifested by believers in the Pantheon of Olympian gods. Thus not all putative object-directed acts should be recognized as having objects of their own. (...)
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  2. added 2018-11-26
    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. Basel, Switzerland:
    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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  3. added 2018-11-10
    A Semantic Hierarchy for Intuitionistic Logic.Guram Bezhanishvili & Wesley H. Holliday - forthcoming - Indagationes Mathematicae.
    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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  4. added 2018-11-03
    Topological Foundations of Cognitive Science.Carola Eschenbach, Christopher Habel & Barry Smith (eds.) - 1994 - Hamburg: Graduiertenkolleg Kognitionswissenschaft.
    A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: -/- ** Topological Foundations of Cognitive Science, Barry Smith -/- ** The Bounds of Axiomatisation, Graham White -/- ** Rethinking Boundaries, Wojciech Zelaniec -/- ** Sheaf Mereology and Space Cognition, Jean Petitot -/- ** A Mereotopological Definition of 'Point', Carola Eschenbach -/- ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel -/- ** Mass Reference and (...)
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  5. added 2018-06-06
    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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  6. added 2018-05-30
    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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  7. added 2017-12-19
    Quantum Gravity and Taoist Cosmology: Exploring the Ancient Origins of Phenomenological String Theory.Steven M. Rosen - 2017 - Progress in Biophysics and Molecular Biology 131:34-60.
    In the author’s previous contribution to this journal (Rosen 2015), a phenomenological string theory was proposed based on qualitative topology and hypercomplex numbers. The current paper takes this further by delving into the ancient Chinese origin of phenomenological string theory. First, we discover a connection between the Klein bottle, which is crucial to the theory, and the Ho-t’u, a Chinese number archetype central to Taoist cosmology. The two structures are seen to mirror each other in expressing the psychophysical (phenomenological) action (...)
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  8. added 2017-12-14
    Linear Structures, Causal Sets and Topology.Hudetz Laurenz - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52 (Part B):294-308.
    Causal set theory and the theory of linear structures share some of their main motivations. In view of that, I raise and answer the question how these two theories are related to each other and to standard topology. I show that causal set theory can be embedded into Maudlin’s more general framework and I characterise what Maudlin’s topological concepts boil down to when applied to discrete linear structures that correspond to causal sets. Moreover, I show that all topological aspects of (...)
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  9. added 2017-12-13
    The Formulation and Justification of Mathematical Definitions Illustrated By Deterministic Chaos.Charlotte Werndl - 2009 - In Mauricio Suárez, Mauro Dorato & Miklós Rédei (eds.), Philosophical Issues in the Sciences: Launch of the European Philosophy of Science Association. Springer. pp. 279-288.
    The general theme of this article is the actual practice of how definitions are justified and formulated in mathematics. The theoretical insights of this article are based on a case study of topological definitions of chaos. After introducing this case study, I identify the three kinds of justification which are important for topological definitions of chaos: natural-world-justification, condition-justification and redundancy-justification. To my knowledge, the latter two have not been identified before. I argue that these three kinds of justification are widespread (...)
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  10. added 2017-11-24
    Putting the World Back Into Semantics.Barry Smith - 1993 - Grazer Philosophische Studien 44:91-109.
    To what in reality do the logically simple sentences with empirical content correspond? Two extreme positions can be distinguished in this regard: 'Great Fact' theories, such as are defended by Davidson; and trope-theories, which see such sentences being made the simply by those events or states to which the relevant main verbs correspond. A position midway between these two extremes is defended, one according to which sentences of the given sort are made tme by what are called 'dependence structures', or (...)
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  11. added 2017-09-26
    A Note on Multi-Dimensional Time.C. T. K. Chari - 1957 - British Journal for the Philosophy of Science 8 (30):155-158.
  12. added 2017-09-25
    Doubling Constant Mean Curvature Tori in S3.Adrian Butscher & Frank Pacard - 2006 - Annali della Scuola Normale Superiore di Pisa 5 (4):611-638.
    The Clifford tori in $S^3$ constitute a one-parameter family of flat, two-dimensional, constant mean curvature submanifolds. This paper demonstrates that new, topologically non-trivial CMC surfaces resembling a pair of neighbouring Clifford tori connected at a sub-lattice consisting of at least two points by small catenoidal bridges can be constructed by perturbative PDE methods. That is, one can create a submanifold that has almost everywhere constant mean curvature by gluing a re-scaled catenoid into the neighbourhood of each point of a sub-lattice (...)
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  13. added 2017-08-24
    Kognitionsforskningens topologiske grundlag.Barry Smith - 2003 - Semikolon 3 (7):91-105.
    The paper introduces the concepts at the heart of point-set-topology and of mereotopology (topology founded in the non-atomistic theory of parts and wholes) in an informal and intuitive fashion. It will then seek to demonstrate how mereotopological ideas can be of particular utility in cognitive science applications. The prehistory of such applications (in the work of Husserl, the Gestaltists, of Kurt Lewin and of J. J. Gibson) will be sketched, together with an indication of the field of possibilities in linguistics, (...)
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  14. added 2017-08-23
    Envisioning Transformations – The Practice of Topology.Silvia De Toffoli & Valeria Giardino - 2016 - In Brendan Larvor (ed.), Mathematical Cultures. Zurich, Switzerland: Birkhäuser. 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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  15. added 2017-08-23
    An Inquiry Into the Practice of Proving in Low-Dimensional Topology.Silvia De Toffoli & Valeria Giardino - 2015 - In Gabriele Lolli, Giorgio Venturi & Marco Panza (eds.), From Logic to Practice. Zurich, Switzerland: Springer International Publishing. pp. 315-116.
    The aim of this article is to investigate specific aspects connected with visualization in the practice of a mathematical subfield: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justifications can be based on sequences of pictures. Three theses will be defended. First, the representations used (...)
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  16. added 2017-01-26
    Some Remarks on Abstract Distance in General Topology.Z. P. Mamuzic - 1979 - Eleutheria 2:433-446.
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  17. added 2017-01-23
    Philosophical Topology.Yi Jiang - 2008 - Proceedings of the Xxii World Congress of Philosophy 15:59-74.
    In this paper I will try to argue for a new version in philosophy entitled as Philosophical Topology. It is inspired by the thought of Peter Strawson as well as ones of some of so-called Continental philosophers like Heidgger. Unlike any of metaphilosophy in general, the philosophical topology focuses rather on analyses of processes of make-up in philosophers’ thinking, especially by revealing the internal logic of philosophical ideas in making and processing in order to explain the intrinsic continuation of philosophical (...)
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  18. added 2017-01-17
    Intuitive Topology.Roberto Casati - unknown
    Understanding of elementary topological equivalencies is impaired by preconceptions about the topological structure of ordinary objects, so that the equivalencies turn out to be counterintuitive. Here I will discuss some of these preconceptions, namely the dominance of gestalt properties of the visual display of the configuration, the neglect of holistic properties, the dominance of transformations the preserve metric properties over those that preserve topological properties only, the assumption that holes are objects of their own. These factors delineate an empirical research (...)
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  19. added 2017-01-16
    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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  20. added 2017-01-16
    The Topology of Homophase Misorientation Spaces.S. Patala & C. A. Schuh - 2011 - Philosophical Magazine 91 (10):1489-1508.
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  21. added 2017-01-16
    Tilings, Tiling Spaces and Topology.L. Sadun - 2006 - Philosophical Magazine 86 (6-8):875-881.
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  22. added 2017-01-15
    Topology Change and the Unity of Space.Craig Callender & Robert Weingard - 2000 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 31 (2):227-246.
    Must space be a unity? This question, which exercised Aristotle, Descartes and Kant, is a specific instance of a more general one; namely, can the topology of physical space change with time? In this paper we show how the discussion of the unity of space has been altered but survives in contemporary research in theoretical physics. With a pedagogical review of the role played by the Euler characteristic in the mathematics of relativistic spacetimes, we explain how classical general relativity (modulo (...)
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  23. added 2017-01-14
    Topology, Holes and Sources.Alexander Afriat - unknown
    The Aharonov-Bohm effect is typically called ``topological.'' But it seems no more topological than magnetostatics, electrostatics or Newton-Poisson gravity. I distinguish between two senses of ``topological.''.
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  24. added 2016-12-18
    The Logic and Topology of Kant's Temporal Continuum.Riccardo Pinosio & Michiel van Lambalgen - manuscript
    In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesimals, which capture Kant’s theory of rest (...)
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  25. added 2016-12-12
    Vagueness, Kant and Topology: A Study of Formal Epistemology.Giovanni Boniolo & Silvio Valentini - 2008 - Journal of Philosophical Logic 37 (2):141-168.
    In this paper we propose an approach to vagueness characterised by two features. The first one is philosophical: we move along a Kantian path emphasizing the knowing subject’s conceptual apparatus. The second one is formal: to face vagueness, and our philosophical view on it, we propose to use topology and formal topology. We show that the Kantian and the topological features joined together allow us an atypical, but promising, way of considering vagueness.
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  26. added 2016-12-08
    Fuzzy Topology and Łukasiewicz Logics From the Viewpoint of Duality Theory.Yoshihiro Maruyama - 2010 - Studia Logica 94 (2):245-269.
    This paper explores relationships between many-valued logic and fuzzy topology from the viewpoint of duality theory. We first show a fuzzy topological duality for the algebras of Łukasiewicz n -valued logic with truth constants, which generalizes Stone duality for Boolean algebras to the n -valued case via fuzzy topology. Then, based on this duality, we show a fuzzy topological duality for the algebras of modal Łukasiewicz n -valued logic with truth constants, which generalizes Jónsson-Tarski duality for modal algebras to the (...)
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  27. added 2016-12-08
    Propositional Logic for Topology-Like Matrices: A Calculus with Restricted Substitution.Thomas M. Leschine - 1978 - Studia Logica 37 (2):161-165.
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  28. added 2016-03-23
    Countable Fusion Not yet Proven Guilty: It May Be the Whiteheadian Account of Space Whatdunnit.G. Oppy - 1997 - Analysis 57 (4):249-253.
    I criticise a paper by Peter Forrest in which he argues that a principle of unrestricted countable fusion has paradoxical consequences. I argue that the paradoxical consequences that he exhibits may be due to his Whiteheadean assumptions about the nature of spacetime rather than to the principle of unrestricted countable fusion.
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  29. added 2015-07-30
    Towards a Point-Free Account of the Continuous.Geoffrey Hellman & Stewart Shapiro - 2012 - Iyyun 61:263.
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  30. added 2015-06-29
    Peirce's Potential Continuity and Pure Geometry.Jean-Louis Hudry - 2004 - Transactions of the Charles S. Peirce Society 40 (2):229 - 243.
  31. added 2015-06-09
    Global and Local.James Franklin - 2014 - Mathematical Intelligencer 36 (4).
    The global/local contrast is ubiquitous in mathematics. This paper explains it with straightforward examples. It is possible to build a circular staircase that is rising at any point (locally) but impossible to build one that rises at all points and comes back to where it started (a global restriction). Differential equations describe the local structure of a process; their solution describes the global structure that results. The interplay between global and local structure is one of the great themes of mathematics, (...)
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  32. added 2015-04-05
    Place and Experience: A Philosophical Topology.J. E. Malpas - 2000 - Philosophical Quarterly 50 (201):564-566.
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  33. added 2015-04-05
    The Mathematical Philosophy of Contact.A. P. Hazen - 1990 - Philosophy 65 (252):205 - 211.
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  34. added 2015-03-24
    Every Inductively Generated Formal Cover is Spatial, Classically.S. Valentini - 2006 - Journal of Symbolic Logic 71 (2):491-500.
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  35. added 2015-03-24
    The Topology of Revolution.Jason Barker - 2003 - Communication and Cognition. Monographies 36 (1-2):61-72.
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  36. added 2015-03-24
    Topology of Thought.H. M. Hubey - 1996 - Communication and Cognition-Artificial Intelligence 13 (2-3):225-292.
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  37. added 2015-03-23
    Cultural Topology: The Seven Bridges of Königsburg, 1736.R. Shields - 2012 - Theory, Culture and Society 29 (4-5):43-57.
    In an example of Enlightenment ‘engaged research' and public intellectual practice, Euler established the basis of topology and graph theory through his solution to the puzzle of whether a stroll around the seven bridges of 18th-century Königsberg was possible without having to cross any given bridge twice. This ‘Manifesto' argues that, born in a form of cultural studies, topology offers 21st-century researchers a model for mapping the dynamics of time as well as space, allowing the rigorous description of events, situations, (...)
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  38. added 2015-03-23
    Between Inclusion and Exclusion: On the Topology of Global Space and Borders.S. Mezzadra & B. Neilson - 2012 - Theory, Culture and Society 29 (4-5):58-75.
    The research hypothesis that we call border as method offers a fertile ground upon which to test the potentiality and the limits of the topological approach. In this article we present our hypothesis and address three questions relevant for topology. First, we ask how the topological approach can be applied within the heterogeneous space of globalization, which we argue does not obey the dialectic of inclusion and exclusion. Second, we address the claim of neutrality that is often linked to the (...)
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  39. added 2015-03-23
    HIV, Globalization and Topology: Of Prepositions and Propositions.M. Michael & M. Rosengarten - 2012 - Theory, Culture and Society 29 (4-5):93-115.
    In this article we explore how two enactments of HIV – the UN’s AIDS Clock and clinical trials for an HIV biomedical prevention technology or pre-exposure prophylaxis – entail particular globalizing and localizing dynamics. Drawing on Latour’s and Whitehead’s concept of proposition, and Serres’ call for a philosophy of prepositions, we use the composite notion of pre/pro-positions to trace the shifting topological status of HIV. For example, we show how PrEP emerges through topological entwinements of globalizing biomedical standardization, localizing protests (...)
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  40. added 2015-03-23
    Topology and Morphogenesis.X. W. Sha - 2012 - Theory, Culture and Society 29 (4-5):220-246.
    One can use mathematics not as an instrument or measure, or a replacement for God, but as a poetic articulation, or perhaps as a stammered experimental approach to cultural dynamics. I choose to start with the simplest symbolic substances that respect the lifeworld’s continuous dynamism, temporality, boundless morphogenesis, superposability, continuity, density and value, and yet are independent of measure, metric, counting, finitude, formal logic, syntax, grammar, digitality and computability – in short, free of the formal structures that would put a (...)
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  41. added 2015-03-23
    The Spatial Logic of Social Struggle: A Bourdieuian Topology.Nikolaus Fogle - 2011 - Lexington Books.
    This is the first work to explicitly target Bourdieu's philosophy of space as a basic organizing force for his social theory. It draws together his work on both social space and physical space, and it applies the logic that binds them together to problems of architecture and urban development.
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  42. added 2015-03-23
    A Topology for Logical Space.Bogus law Wolniewicz - 1984 - Bulletin of the Section of Logic 13 (4):255-258.
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  43. added 2015-03-21
    Metric Complements of Overt Closed Sets.Thierry Coquand, Erik Palmgren & Bas Spitters - 2011 - Mathematical Logic Quarterly 57 (4):373-378.
    We show that the set of points of an overt closed subspace of a metric completion of a Bishop-locally compact metric space is located. Consequently, if the subspace is, moreover, compact, then its collection of points is Bishop-compact. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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  44. added 2015-03-21
    A Topology Induced by Uniformity on BL-Algebras.Masoud Haveshki, Esfandiar Eslami & Arsham Borumand Saeid - 2007 - Mathematical Logic Quarterly 53 (2):162-169.
    In this paper, we consider a collection of filters of a BL-algebra A. We use the concept of congruence relation with respect to filters to construct a uniformity which induces a topology on A. We study the properties of this topology regarding different filters. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim).
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  45. added 2015-03-21
    On the Formal Points of the Formal Topology of the Binary Tree.Silvio Valentini - 2002 - Archive for Mathematical Logic 41 (7):603-618.
    Formal topology is today an established topic in the development of constructive mathematics and constructive proofs for many classical results of general topology have been obtained by using this approach. Here we analyze one of the main concepts in formal topology, namely, the notion of formal point. We will contrast two classically equivalent definitions of formal points and we will see that from a constructive point of view they are completely different. Indeed, according to the first definition the formal points (...)
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  46. added 2015-03-18
    The Place of Topology: Responding to Crowell, Beistegui, and Young.Jeff Malpas - 2011 - International Journal of Philosophical Studies 19 (2):295 - 315.
    The idea of philosophical topology, or topography as I call it outside of the Heideggerian context, has become increasingly central to my work over the last twenty years. While the idea is not indebted only to Heidegger’s thinking, it is probably Heidegger to whom I owe the most. Moreover, one of my claims, central to _Heidegger’s Topology_, is that Heidegger’s own work cannot adequately be understood except as topological in character, and so as centrally concerned with place – _topos, Ort, (...)
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  47. added 2015-03-17
    Elementary Polyhedral Mereotopology.Ian Pratt-Hartmann & Dominik Schoop - 2002 - Journal of Philosophical Logic 31 (5):469-498.
    A region-based model of physical space is one in which the primitive spatial entities are regions, rather than points, and in which the primitive spatial relations take regions, rather than points, as their relata. Historically, the most intensively investigated region-based models are those whose primitive relations are topological in character; and the study of the topology of physical space from a region-based perspective has come to be called mereotopology. This paper concentrates on a mereotopological formalism originally introduced by Whitehead, which (...)
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  48. added 2015-03-17
    A Complete Axiom System for Polygonal Mereotopology of the Real Plane.Ian Pratt & Dominik Schoop - 1998 - Journal of Philosophical Logic 27 (6):621-658.
    This paper presents a calculus for mereotopological reasoning in which two-dimensional spatial regions are treated as primitive entities. A first order predicate language ℒ with a distinguished unary predicate c(x), function-symbols +, · and - and constants 0 and 1 is defined. An interpretation ℜ for ℒ is provided in which polygonal open subsets of the real plane serve as elements of the domain. Under this interpretation the predicate c(x) is read as 'region x is connected' and the function-symbols and (...)
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  49. added 2015-03-17
    Zeeman-Göbel Topologies.Adrian Heathcote - 1988 - British Journal for the Philosophy of Science 39 (2):247-261.
    Zeeman argued that the Euclidean (i. e. manifold) topology of Minkowski space-time should be replaced by a strictly finer topology that was to have a closer connection with the indefinite metric. This proposal was extended in 1976 by Rudiger Göbel and Hawking, King and McCarthy to the space-times of General Relativity. It is the purpose of this paper to argue that these suggestions for replacement misrepresent the significance of the manifold topology and overstate the necessity for a finer topology. The (...)
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  50. added 2014-12-18
    How Can We Signify Being? Semiotics and Topological Self-Signification.Steven M. Rosen - 2014 - Cosmos and History 10 (2):250-277.
    The premise of this paper is that the goal of signifying Being central to ontological phenomenology has been tacitly subverted by the semiotic structure of conventional phenomenological writing. First it is demonstrated that the three components of the sign—sign-vehicle, object, and interpretant (C. S. Peirce)—bear an external relationship to each other when treated conventionally. This is linked to the abstractness of alphabetic language, which objectifies nature and splits subject and object. It is the subject-object divide that phenomenology must surmount if (...)
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