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  1. added 2020-05-29
    Slavoj Žižek, "Sex and the Failed Absolute". [REVIEW]Jakub Mácha - 2020 - Philosophy in Review 40 (2):88-90.
  2. added 2020-04-23
    The Strange Nature of Quantum Perception: To See a Photon, One Must Be a Photon.Steven M. Rosen - unknown
    This paper takes as its point of departure recent research into the possibility that human beings can perceive single photons. In order to appreciate what quantum perception may entail, we first explore several of the leading interpretations of quantum mechanics, then consider an alternative view based on the ontological phenomenology of Maurice Merleau-Ponty and Martin Heidegger. Next, the philosophical analysis is brought into sharper focus by employing a perceptual model, the Necker cube, augmented by the topology of the Klein bottle. (...)
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  3. added 2020-02-10
    Topological Models of Columnar Vagueness.Thomas Mormann - 2020 - Erkenntnis:1-24.
    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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  4. added 2020-01-05
    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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  5. added 2019-08-06
    Boundaries: A Brentanian Theory.Barry Smith - 2000 - Brentano Studien 8:107-114.
    According to Brentano's theory of boundaries, no boundary can exist without being connected with a continuum. But there is no specifiable part of the continuum, and no point, which is such that we may say that it is the existence of that part or of that point which conditions the boundary. - An adequate theory of the continuum must now recognize that boundaries be boundaries only in certain directions and not in others. This leads to consequences in other areas, too.
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  6. added 2019-07-04
    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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  7. added 2019-07-04
    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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  8. added 2019-06-11
    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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  9. added 2019-06-06
    Topology and Modality: The Topological Interpretation of First-Order Modal Logic: Topology and Modality.Steve Awodey - 2008 - Review of Symbolic Logic 1 (2):146-166.
    As McKinsey and Tarski showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for propositional modal logic, in which the “necessity” operation is modeled by taking the interior of an arbitrary subset of a topological space. In this article, the topological interpretation is extended in a natural way to arbitrary theories of full first-order logic. The resulting system of S4 first-order modal logic is complete with respect to such topological semantics.
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  10. added 2019-06-06
    Nonstandard Analysis in Topology: Nonstandard and Standard Compactifications.S. Salbany & Todor Todorov - 2000 - Journal of Symbolic Logic 65 (4):1836-1840.
    Let be a topological space and *X a nonstandard extension of X. Sets of the form *G, where G $\in$ T. form a base for the "standard" topology $^ST$ on *X. The topological space will be used to study compactifications of in a systematic way.
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  11. added 2019-06-06
    Science and God: The Topology of the Kantian World.Gerd Buchdahl - 1992 - Southern Journal of Philosophy 30 (Supplement):1-24.
    Kant maintains that in face of the failure of the traditional arguments for the existence of God it is necessary to provide an entirely fresh centre of gravity for the notion of religious consciousness. To explicate Kant's critique this paper develops, as a special hermeneutic device, the idea of a kind of Husserlian reduction and realization', in terms of which the various uses of Kant's concept of thing' or object' are given a new interpretation,using this to provide a novel approach (...)
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  12. added 2019-06-05
    New Foundations for Qualitative Physics.Jean Petitot & Barry Smith - 1990 - In J. E. Tiles, G. T. McKee & C. G. Dean (eds.), Evolving Knowledge in Natural Science and Artificial Intelligence. London: Pitman Publishing. pp. 231-49.
    Physical reality is all the reality we have, and so physical theory in the standard sense is all the ontology we need. This, at least, was an assumption taken almost universally for granted by the advocates of exact philosophy for much of the present century. Every event, it was held, is a physical event, and all structure in reality is physical structure. The grip of this assumption has perhaps been gradually weakened in recent years as far as the sciences of (...)
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  13. added 2019-04-07
    De amore.Andrej Poleev - 2018
  14. added 2019-02-04
    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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  15. added 2019-01-28
    What Is the Validity Domain of Einstein’s Equations? Distributional Solutions Over Singularities and Topological Links in Geometrodynamics.Elias Zafiris - 2016 - 100 Years of Chronogeometrodynamics: The Status of the Einstein's Theory of Gravitation in Its Centennial Year.
    The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the (...)
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  16. added 2019-01-28
    Rosen's Modelling Relations Via Categorical Adjunctions.Elias Zafiris - 2012 - International Journal of General Systems 41 (5):439-474.
    Rosen's modelling relations constitute a conceptual schema for the understanding of the bidirectional process of correspondence between natural systems and formal symbolic systems. The notion of formal systems used in this study refers to information structures constructed as algebraic rings of observable attributes of natural systems, in which the notion of observable signifies a physical attribute that, in principle, can be measured. Due to the fact that modelling relations are bidirectional by construction, they admit a precise categorical formulation in terms (...)
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  17. added 2019-01-28
    Categorical Modeling of Natural Complex Systems. Part II: Functorial Process of Localization-Globalization.Elias Zafiris - 2008 - Advances in Systems Science and Applications 8 (3):367-387.
    We develop a general covariant categorical modeling theory of natural systems' behavior based on the fundamental functorial processes of representation and localization-globalization. In the second part of this study we analyze the semantic bidirectional process of localization-globalization. The notion of a localization system of a complex information structure bears a dual role: Firstly, it determines the appropriate categorical environment of base reference contexts for considering the operational modeling of a complex system's behavior, and secondly, it specifies the global compatibility conditions (...)
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  18. added 2019-01-28
    Generalized Topological Covering Systems on Quantum Events' Structures.Elias Zafiris - 2006 - Journal of Physics A: Mathematics and Applications 39 (6):1485-1505.
    Homologous operational localization processes are effectuated in terms of generalized topological covering systems on structures of physical events. We study localization systems of quantum events' structures by means of Gtothendieck topologies on the base category of Boolean events' algebras. We show that a quantum events algebra is represented by means of a Grothendieck sheaf-theoretic fibred structure, with respect to the global partial order of quantum events' fibres over the base category of local Boolean frames.
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  19. added 2019-01-28
    Sheaf-Theoretic Representation of Quantum Measure Algebras.Elias Zafiris - 2006 - Journal of Mathematical Physics 47 (9).
    We construct a sheaf-theoretic representation of quantum probabilistic structures, in terms of covering systems of Boolean measure algebras. These systems coordinatize quantum states by means of Boolean coefficients, interpreted as Boolean localization measures. The representation is based on the existence of a pair of adjoint functors between the category of presheaves of Boolean measure algebras and the category of quantum measure algebras. The sheaf-theoretic semantic transition of quantum structures shifts their physical significance from the orthoposet axiomatization at the level of (...)
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  20. added 2019-01-28
    Interpreting Observables in a Quantum World From the Categorial Standpoint.Elias Zafiris - 2004 - International Journal of Theoretical Physics 43 (1):265-298.
    We develop a relativistic perspective on structures of quantum observables, in terms of localization systems of Boolean coordinatizing charts. This perspective implies that the quantum world is comprehended via Boolean reference frames for measurement of observables, pasted together along their overlaps. The scheme is formalized categorically, as an instance of the adjunction concept. The latter is used as a framework for the specification of a categorical equivalence signifying an invariance in the translational code of communication between Boolean localizing contexts and (...)
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  21. added 2019-01-27
    Concept and Formalization of Constellatory Self-Unfolding: A Novel Perspective on the Relation Between Quantum and Relativistic Physics.Albrecht Von Müller & Elias Zafiris - 2018 - Springer.
    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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  22. added 2019-01-27
    Boolean Localization Of Quantum Events: A Processual Sheaf-Theoretic Approach.Elias Zafiris - 2016 - In David Ray Griffin, Michael Epperson & Timothy E. Eastman (eds.), Physics and Speculative Philosophy: Potentiality in Modern Science. De Gruyter. pp. 107-126.
  23. added 2019-01-27
    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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  24. 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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  25. 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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  26. added 2018-11-10
    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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  27. added 2018-11-03
    Topological Foundations of Cognitive Science.Carola Eschenbach, Christopher Habel & Barry Smith (eds.) - 1984 - 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 the Geometry of Solids, Almerindo E. Ojeda (...)
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  28. 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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  29. 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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  30. 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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  31. 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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  32. 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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  33. added 2017-11-24
    Putting the World Back Into Semantics.Barry Smith - 1993 - Grazer Philosophische Studien 44 (1):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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  34. 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.
  35. 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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  36. 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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  37. added 2017-08-23
    Envisioning Transformations – The Practice of Topology.Silvia De Toffoli & Valeria Giardino - 2016 - In Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 2012--2014. 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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  38. 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. 315-336.
    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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  39. added 2017-01-26
    Some Remarks on Abstract Distance in General Topology.Z. P. Mamuzic - 1979 - Eleutheria 2:433-446.
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  40. 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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  41. 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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  42. 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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  43. 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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  44. added 2017-01-16
    Tilings, Tiling Spaces and Topology.L. Sadun - 2006 - Philosophical Magazine 86 (6-8):875-881.
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  45. 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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  46. 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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  47. 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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  48. 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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  49. 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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  50. 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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