Results for 'geometry'

947 found
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  1. Harald Schwaetzer.Bunte Geometrie - 2009 - In Klaus Reinhardt, Harald Schwaetzer & Franz-Bernhard Stammkötter, Heymericus de Campo: Philosophie Und Theologie Im 15. Jahrhundert. Roderer. pp. 28--183.
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  2.  12
    D'Erehwon à l'Antre du Cyclope.Géométrie de L'Incommunicable & La Folie - 1988 - In Barry Smart, Michel Foucault: critical assessments. New York: Routledge.
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  3. Vigier III.Spin Foam Spinors & Fundamental Space-Time Geometry - 2000 - Foundations of Physics 30 (1).
  4. Instruction to Authors 279–283 Index to Volume 20 285–286.Christian Lotz, Corinne Painter, Sebastian Luft, Harry P. Reeder, Semantic Texture, Luciano Boi, Questions Regarding Husserlian Geometry, James R. Mensch & Postfoundational Phenomenology Husserlian - 2004 - Husserl Studies 20:285-286.
     
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  5.  13
    Analysis, constructions and diagrams in classical geometry.Panza Marco - 2021 - Metodo. International Studies in Phenomenology and Philosophy 9 (1):181-220.
    Greek ancient and early modern geometry necessarily uses diagrams. Among other things, these enter geometrical analysis. The paper distinguishes two sorts of geometrical analysis and shows that in one of them, dubbed “intra-confgurational” analysis, some diagrams necessarily enter as outcomes of a purely material gesture, namely not as result of a codifed constructive procedure, but as result of a free-hand drawing.
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  6. (1 other version)Philosophy of Geometry from Riemann to Poincaré.Roberto Torretti - 1978 - Revue Philosophique de la France Et de l'Etranger 172 (3):565-572.
     
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  7. Time and physical geometry.Hilary Putnam - 1967 - Journal of Philosophy 64 (8):240-247.
  8. Quantifying the subjective: Psychophysics and the geometry of color.Alistair M. C. Isaac - 2013 - Philosophical Psychology 26 (2):207 - 233.
    Early psychophysical methods as codified by Fechner motivate the development of quantitative theories of subjective experience. The basic insight is that just noticeable differences between experiences can serve as units for measuring a sensory domain. However, the methods described by Fechner tacitly assume that the experiences being investigated can be linearly ordered. This assumption is not true for all sensory domains; for example, there is no trivial linear order over all possible color sensations. This paper discusses key developments in the (...)
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  9. On the Foundations of Geometry.Henri Poincaré - 1898 - The Monist 9 (1):1-43.
  10.  10
    An expressive two-sorted spatial logic for plane projective geometry.Philippe Balbiani - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev, Advances in Modal Logic. CSLI Publications. pp. 49-68.
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  11. Geometrical Objects as Properties of Sensibles: Aristotle’s Philosophy of Geometry.Emily Katz - 2019 - Phronesis 64 (4):465-513.
    There is little agreement about Aristotle’s philosophy of geometry, partly due to the textual evidence and partly part to disagreement over what constitutes a plausible view. I keep separate the questions ‘What is Aristotle’s philosophy of geometry?’ and ‘Is Aristotle right?’, and consider the textual evidence in the context of Greek geometrical practice, and show that, for Aristotle, plane geometry is about properties of certain sensible objects—specifically, dimensional continuity—and certain properties possessed by actual and potential compass-and-straightedge drawings (...)
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  12. (1 other version)Recalcitrant Disagreement in Mathematics: An “Endless and Depressing Controversy” in the History of Italian Algebraic Geometry.Silvia De Toffoli & Claudio Fontanari - 2023 - Global Philosophy 33 (38):1-29.
    If there is an area of discourse in which disagreement is virtually absent, it is mathematics. After all, mathematicians justify their claims with deductive proofs: arguments that entail their conclusions. But is mathematics really exceptional in this respect? Looking at the history and practice of mathematics, we soon realize that it is not. First, deductive arguments must start somewhere. How should we choose the starting points (i.e., the axioms)? Second, mathematicians, like the rest of us, are fallible. Their ability to (...)
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  13.  19
    The Interaction between Logic and Geometry in Aristotelian Diagrams.Lorenz6 Demey & Hans5 Smessaert - 2016 - Diagrammatic Representation and Inference, Diagrams 9781:67 - 82.
    © Springer International Publishing Switzerland 2016. We develop a systematic approach for dealing with informationally equivalent Aristotelian diagrams, based on the interaction between the logical properties of the visualized information and the geometrical properties of the concrete polygon/polyhedron. To illustrate the account’s fruitfulness, we apply it to all Aristotelian families of 4-formula fragments that are closed under negation and to all Aristotelian families of 6-formula fragments that are closed under negation.
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  14. Edmund Husserl’s ‘Origin of Geometry’: An Introduction.Jacques Derrida - 1978 - University of Nebraska.
    Derrida's introduction to his French translation of Husserl's essay "The Origin of Geometry," arguing that although Husserl privileges speech over writing in an account of meaning and the development of scientific knowledge, this privilege is in fact unstable.
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  15.  42
    The quantized geometry of visual space: The coherent computation of depth, form, and lightness.Stephen Grossberg - 1983 - Behavioral and Brain Sciences 6 (4):625.
  16.  19
    Euclid and His Twentieth Century Rivals: Diagrams in the Logic of Euclidean Geometry.Nathaniel Miller - 2007 - Center for the Study of Language and Inf.
    Twentieth-century developments in logic and mathematics have led many people to view Euclid’s proofs as inherently informal, especially due to the use of diagrams in proofs. In _Euclid and His Twentieth-Century Rivals_, Nathaniel Miller discusses the history of diagrams in Euclidean Geometry, develops a formal system for working with them, and concludes that they can indeed be used rigorously. Miller also introduces a diagrammatic computer proof system, based on this formal system. This volume will be of interest to mathematicians, (...)
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  17. Kant's theory of geometry.Michael Friedman - 1985 - Philosophical Review 94 (4):455-506.
  18.  68
    Less cybernetics, more geometry….René Thom - 1985 - Behavioral and Brain Sciences 8 (1):166-167.
  19. Natural number and natural geometry.Elizabeth S. Spelke - 2011 - In Stanislas Dehaene & Elizabeth Brannon, Space, Time and Number in the Brain: Searching for the Foundations of Mathematical Thought. Oxford University Press. pp. 287--317.
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  20.  49
    On the Foundations of Geometry and Formal Theories of Arithmetic.John Corcoran - 1973 - Philosophy and Phenomenological Research 34 (2):283-286.
  21. The Primacy of Geometry.Meir Hemmo & Amit Hagar - 2013 - Studies in the History and Philosophy of Modern Physics 44 (3):357-364.
    We argue that current constructive approaches to the special theory of relativity do not derive the geometrical Minkowski structure from the dynamics but rather assume it. We further argue that in current physics there can be no dynamical derivation of primitive geometrical notions such as length. By this we believe we continue an argument initiated by Einstein.
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  22.  38
    A Proposition of Elementary Plane Geometry that Implies the Continuum Hypothesis.Frederick Bagemihl - 1961 - Mathematical Logic Quarterly 7 (1-5):77-79.
  23.  28
    Mathematizing Space: The Objects of Geometry from Antiquity to the Early Modern Age.Vincenzo De Risi (ed.) - 2015 - Birkhäuser.
    This book brings together papers of the conference on 'Space, Geometry and the Imagination from Antiquity to the Modern Age' held in Berlin, Germany, 27-29 August 2012. Focusing on the interconnections between the history of geometry and the philosophy of space in the pre-Modern and Early Modern Age, the essays in this volume are particularly directed toward elucidating the complex epistemological revolution that transformed the classical geometry of figures into the modern geometry of space. Contributors: Graciela (...)
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  24. What can geometry explain?Graham Nerlich - 1979 - British Journal for the Philosophy of Science 30 (1):69-83.
  25. (1 other version)On the Foundations of Geometry and Formal Theories of Arithmetic.Gottlob Frege - 1974 - Mind 83 (329):131-133.
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  26. Poincarés philosophy of geometry, or does geometric conventionalism deserve its name?E. G. Zahar - 1997 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 28 (2):183-218.
  27.  24
    Extension to Geometry of Principia Mathematica and Related Systems II.Martha Harrell - 1988 - Russell: The Journal of Bertrand Russell Studies 8 (1):140-160.
  28. Objectivity and Rigor in Classical Italian Algebraic Geometry.Silvia De Toffoli & Claudio Fontanari - 2022 - Noesis 38:195-212.
    The classification of algebraic surfaces by the Italian School of algebraic geometry is universally recognized as a breakthrough in 20th-century mathematics. The methods by which it was achieved do not, however, meet the modern standard of rigor and therefore appear dubious from a contemporary viewpoint. In this article, we offer a glimpse into the mathematical practice of the three leading exponents of the Italian School of algebraic geometry: Castelnuovo, Enriques, and Severi. We then bring into focus their distinctive (...)
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  29.  53
    The application of mereology to grounding of elementary geometry.Edmund Glibowski - 1969 - Studia Logica 24 (1):109-129.
  30. The Problem of Universality, Necessity, and Cognitive Precision Viewed in the Light of Kant’s Constructivist Approach to Geometry.Saša Laketa - 2024 - Filozofska Istrazivanja 44 (2):311-330.
    Kant claims that the cognitive consensus about the deductive consistency and coherence of constructive geometric concepts, and their subsequent precise application in the realm of experience, results from the transcendental ideality of space and time and the distinction based on it; the distinction between phenomenal reality and reality as it is. All objects of possible experience are necessarily perceived in universal and necessary space-time relations, and this is also the condition for the possibility of universal, necessary, and precise application of (...)
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  31. (1 other version)Frege and Kant on geometry.Michael Dummett - 1982 - Inquiry: An Interdisciplinary Journal of Philosophy 25 (2):233 – 254.
    In his Grundlagen, Frege held that geometrical truths.are synthetic a priori, and that they rest on intuition. From this it has been concluded that he thought, like Kant, that space and time are a priori intuitions and that physical objects are mere appearances. It is plausible that Frege always believed geometrical truths to be synthetic a priori; the virtual disappearance of the word ‘intuition’ from his writings from after 1885 until 1924 suggests, on the other hand, that he became dissatisfied (...)
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  32. The constructible and the intelligible in Newton's philosophy of geometry.Mary Domski - 2003 - Philosophy of Science 70 (5):1114-1124.
    In the preface to the Principia (1687) Newton famously states that “geometry is founded on mechanical practice.” Several commentators have taken this and similar remarks as an indication that Newton was firmly situated in the constructivist tradition of geometry that was prevalent in the seventeenth century. By drawing on a selection of Newton's unpublished texts, I hope to show the faults of such an interpretation. In these texts, Newton not only rejects the constructivism that took its birth in (...)
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    Analysis in greek geometry.Richard Robinson - 1936 - Mind 45 (180):464-473.
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  34. Kant on real definitions in geometry.Jeremy Heis - 2014 - Canadian Journal of Philosophy 44 (5-6):605-630.
    This paper gives a contextualized reading of Kant's theory of real definitions in geometry. Though Leibniz, Wolff, Lambert and Kant all believe that definitions in geometry must be ‘real’, they disagree about what a real definition is. These disagreements are made vivid by looking at two of Euclid's definitions. I argue that Kant accepted Euclid's definition of circle and rejected his definition of parallel lines because his conception of mathematics placed uniquely stringent requirements on real definitions in (...). Leibniz, Wolff and Lambert thus accept definitions that Kant rejects because they assign weaker roles to real definitions. (shrink)
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  35. On the reality of space-time geometry and the wavefunction.Jeeva Anandan & Harvey R. Brown - 1995 - Foundations of Physics 25 (2):349--60.
    The action-reaction principle (AR) is examined in three contexts: (1) the inertial-gravitational interaction between a particle and space-time geometry, (2) protective observation of an extended wave function of a single particle, and (3) the causal-stochastic or Bohm interpretation of quantum mechanics. A new criterion of reality is formulated using the AR principle. This criterion implies that the wave function of a single particle is real and justifies in the Bohm interpretation the dual ontology of the particle and its associated (...)
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  36. How euclidean geometry has misled metaphysics.Graham Nerlich - 1991 - Journal of Philosophy 88 (4):169-189.
  37. Space–time philosophy reconstructed via massive Nordström scalar gravities? Laws vs. geometry, conventionality, and underdetermination.J. Brian Pitts - 2016 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 53:73-92.
    What if gravity satisfied the Klein-Gordon equation? Both particle physics from the 1920s-30s and the 1890s Neumann-Seeliger modification of Newtonian gravity with exponential decay suggest considering a "graviton mass term" for gravity, which is _algebraic_ in the potential. Unlike Nordström's "massless" theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman-Cunningham conformal group. It therefore exhibits the whole of Minkowski space-time structure, albeit only indirectly concerning volumes. Massive (...)
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  38.  16
    An expressive two-sorted spatial logic for plane projective geometry.Philippe Balbiani - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev, Advances in Modal Logic. CSLI Publications. pp. 49-68.
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  39. R. Buccheri (ed.), The Nature of Time: Geometry, Physics and Perception.Stuart R. Hameroff - 2003
     
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  40.  13
    Sakha world model: semantics considered in terms of geometry of forms.M. T. Satanar & V. V. Illarionov - 2018 - Liberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitarnyj Zhurnalrossiiskii Gumanitarnyi Zhurnal 7 (6):471.
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  41. On Models of Elementary Elliptic Geometry.W. Schwabhauser - 1965 - In J. W. Addison, The theory of models. Amsterdam,: North-Holland Pub. Co..
     
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  42.  30
    A Symmetric Primitive notion for Euclidean Geometry.Dana Scott - 1968 - Journal of Symbolic Logic 33 (2):288-289.
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  43.  52
    The simplest axiom system for plane hyperbolic geometry.Victor Pambuccian - 2004 - Studia Logica 77 (3):385 - 411.
    We provide a quantifier-free axiom system for plane hyperbolic geometry in a language containing only absolute geometrically meaningful ternary operations (in the sense that they have the same interpretation in Euclidean geometry as well). Each axiom contains at most 4 variables. It is known that there is no axiom system for plane hyperbolic consisting of only prenex 3-variable axioms. Changing one of the axioms, one obtains an axiom system for plane Euclidean geometry, expressed in the same language, (...)
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  44.  38
    Frege and the origins of model theory in nineteenth century geometry.Günther Eder - 2019 - Synthese 198 (6):5547-5575.
    The aim of this article is to contribute to a better understanding of Frege’s views on semantics and metatheory by looking at his take on several themes in nineteenth century geometry that were significant for the development of modern model-theoretic semantics. I will focus on three issues in which a central semantic idea, the idea of reinterpreting non-logical terms, gradually came to play a substantial role: the introduction of elements at infinity in projective geometry; the study of transfer (...)
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  45. The c-aplpha Non Exclusion Principle and the vastly different internal electron and muon center of charge vacuum fluctuation geometry.Jim Wilson - forthcoming - Physics Essays.
    The electronic and muonic hydrogen energy levels are calculated very accurately [1] in Quantum Electrodynamics (QED) by coupling the Dirac Equation four vector (c ,mc2) current covariantly with the external electromagnetic (EM) field four vector in QED’s Interactive Representation (IR). The c -Non Exclusion Principle(c -NEP) states that, if one accepts c as the electron/muon velocity operator because of the very accurate hydrogen energy levels calculated, the one must also accept the resulting electron/muon internal spatial and time coordinate operators (ISaTCO) (...)
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  46. The cognitive geometry of war.Barry Smith - 1989 - In Constraints on Correspondence. Hölder/Pichler/Tempsky. pp. 394--403.
    When national borders in the modern sense first began to be established in early modern Europe, non-contiguous and perforated nations were a commonplace. According to the conception of the shapes of nations that is currently preferred, however, nations must conform to the topological model of circularity; their borders must guarantee contiguity and simple connectedness, and such borders must as far as possible conform to existing topographical features on the ground. The striving to conform to this model can be seen at (...)
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  47.  30
    Currents in a theory of strong interaction based on a fiber bundle geometry.W. Drechsler - 1977 - Foundations of Physics 7 (9-10):629-671.
    A fiber bundle constructed over spacetime is used as the basic underlying framework for a differential geometric description of extended hadrons. The bundle has a Cartan connection and possesses the de Sitter groupSO(4, 1) as structural group, operating as a group of motion in a locally defined space of constant curvature (the fiber) characterized by a radius of curvatureR≈10−13 cm related to the strong interactions. A hadronic matter field ω(x, ζ) is defined on the bundle space, withx the spacetime coordinate (...)
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  48. Against Pointillisme about Geometry.Jeremy Butterfield - 2006 - In Friedrich Stadler & Michael Stöltzner, Time and History: Proceedings of the 28. International Ludwig Wittgenstein Symposium, Kirchberg Am Wechsel, Austria 2005. Frankfurt, Germany: De Gruyter. pp. 181-222.
    This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. More specifically, this paper argues against pointillisme about the structure of space and-or spacetime itself, especially a paper by Bricker (1993). (...)
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  49. John Wesley Young: Lectures on Fundamental Concepts of Algebra and Geometry.William Wells Denton - 1912 - Mind 21 (83):445-448.
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  50.  30
    Orienting in virtual environments: How are surface features and environmental geometry weighted in an orientation task?Debbie M. Kelly & Walter F. Bischof - 2008 - Cognition 109 (1):89-104.
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