Results for 'Geometry'

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  1. Harald Schwaetzer.Bunte Geometrie - 2009 - In Klaus Reinhardt, Harald Schwaetzer & Franz-Bernhard Stammkötter (eds.), Heymericus de Campo: Philosophie Und Theologie Im 15. Jahrhundert. Roderer. pp. 28--183.
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  2. Vigier III.Spin Foam Spinors & Fundamental Space-Time Geometry - 2000 - Foundations of Physics 30 (1).
  3.  9
    D'Erehwon à l'Antre du Cyclope.Géométrie de L'Incommunicable & La Folie - 1994 - In Barry Smart (ed.), Michel Foucault: Critical Assessments. Routledge.
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  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.  7
    Geometrie und Erfahrung.Albert Einstein - 1921 - Akademie der Wissenschaften, in Kommission Bei W. De Gruyter.
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  6. Geometry as a Universal mental Construction.Véronique Izard, Pierre Pica, Danièle Hinchey, Stanislas Dehane & Elizabeth Spelke - 2011 - In Stanislas Dehaene & Elizabeth Brannon (eds.), Space, Time and Number in the Brain. Oxford University Press.
    Geometry, etymologically the “science of measuring the Earth”, is a mathematical formalization of space. Just as formal concepts of number may be rooted in an evolutionary ancient system for perceiving numerical quantity, the fathers of geometry may have been inspired by their perception of space. Is the spatial content of formal Euclidean geometry universally present in the way humans perceive space, or is Euclidean geometry a mental construction, specific to those who have received appropriate instruction? The (...)
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  7. The geometry of standard deontic logic.Alessio Moretti - 2009 - Logica Universalis 3 (1):19-57.
    Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic (both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”, “permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s “logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed a (...)
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  8.  91
    Logical Geometries and Information in the Square of Oppositions.Hans5 Smessaert & Lorenz6 Demey - 2014 - Journal of Logic, Language and Information 23 (4):527-565.
    The Aristotelian square of oppositions is a well-known diagram in logic and linguistics. In recent years, several extensions of the square have been discovered. However, these extensions have failed to become as widely known as the square. In this paper we argue that there is indeed a fundamental difference between the square and its extensions, viz., a difference in informativity. To do this, we distinguish between concrete Aristotelian diagrams and, on a more abstract level, the Aristotelian geometry. We then (...)
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  9.  6
    Geometry and Induction.Jean Nicod - 1970
  10. Fundamental and Emergent Geometry in Newtonian Physics.David Wallace - 2020 - British Journal for the Philosophy of Science 71 (1):1-32.
    Using as a starting point recent and apparently incompatible conclusions by Saunders and Knox, I revisit the question of the correct spacetime setting for Newtonian physics. I argue that understood correctly, these two versions of Newtonian physics make the same claims both about the background geometry required to define the theory, and about the inertial structure of the theory. In doing so I illustrate and explore in detail the view—espoused by Knox, and also by Brown —that inertial structure is (...)
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  11.  30
    Geometry and chronometry in philosophical perspective.Adolf Grünbaum - 1968 - Minneapolis,: University of Minnesota Press.
    Geometry and Chronometry in Philosophical Perspective was first published in 1968. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. In this volume Professor Grünbaum substantially extends and comments upon his essay "Geometry, Chronometry, and Empiricism," which was first published in Volume III of the Minnesota Studies in the Philosophy of Science. Commenting on the essay when it first appeared J. J. C. (...)
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  12. Non-Euclidean geometry and revolutions in mathematics.Yuxin Zheng - 1992 - In Donald Gillies (ed.), Revolutions in mathematics. New York: Oxford University Press. pp. 169--182.
     
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  13. Geometry and Monadology: Leibniz’s Analysis Situs and Philosophy of Space.Vincenzo De Risi - 2007 - Boston: Birkhäuser.
    This book reconstructs, both from the historical and theoretical points of view, Leibniz's geometrical studies, focusing in particular on the research Leibniz ...
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  14.  40
    "Mathesis of the Mind": A Study of Fichte’s Wissenschaftslehre and Geometry.David W. Wood - 2012 - New York, NY: New York/Amsterdam: Editions Rodopi (Brill Publishers). Fichte-Studien-Supplementa Vol. 29.
    This is an in-depth study of J.G. Fichte’s philosophy of mathematics and theory of geometry. It investigates both the external formal and internal cognitive parallels between the axioms, intuitions and constructions of geometry and the scientific methodology of the Fichtean system of philosophy. In contrast to “ordinary” Euclidean geometry, in his Erlanger Logik of 1805 Fichte posits a model of an “ursprüngliche” or original geometry – that is to say, a synthetic and constructivistic conception grounded in (...)
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  15. The Geometry of Meaning: Semantics Based on Conceptual Spaces.Peter Gärdenfors - 2014 - Cambridge, Massachusetts: MIT Press.
  16.  93
    Natural Geometry in Descartes and Kepler.Gary Hatfield - 2015 - Res Philosophica 92 (1):117-148.
    According to Kepler and Descartes, the geometry of the triangle formed by the two eyes when focused on a single point affords perception of the distance to that point. Kepler characterized the processes involved as associative learning. Descartes described the processes as a “ natural geometry.” Many interpreters have Descartes holding that perceivers calculate the distance to the focal point using angle-side-angle, calculations that are reduced to unnoticed mental habits in adult vision. This article offers a purely psychophysiological (...)
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  17. The Geometry of Conventionality.James Owen Weatherall & John Byron Manchak - 2014 - Philosophy of Science 81 (2):233-247.
    There is a venerable position in the philosophy of space and time that holds that the geometry of spacetime is conventional, provided one is willing to postulate a “universal force field.” Here we ask a more focused question, inspired by this literature: in the context of our best classical theories of space and time, if one understands “force” in the standard way, can one accommodate different geometries by postulating a new force field? We argue that the answer depends on (...)
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  18. Geometry and experience (1921).Albert Einstein - 2005 - Scientiae Studia 3 (4):665-675.
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  19.  14
    Space, Geometry, and Kant's Transcendental Deduction of the Categories.Thomas C. Vinci - 2014 - New York, US: Oup Usa.
    Thomas C. Vinci argues that Kant's Deductions demonstrate Kant's idealist doctrines and have the structure of an inference to the best explanation for correlated domains. With the Deduction of the Categories the correlated domains are intellectual conditions and non-geometrical laws of the empirical world. With the Deduction of the Concepts of Space, the correlated domains are the geometry of pure objects of intuition and the geometry of empirical objects.
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  20.  9
    Sacred geometry: your personal guide.Bernice Cockram - 2020 - New York, NY: Wellfleet Press.
    With In Focus Sacred Geometry, learn the fascinating history behind this ancient tradition as well as how to decipher the geometrical symbols, formulas, and patterns based on mathematical patterns. People have searched for the meaning behind mathematical patterns for thousands of years. At its core, sacred geometry seeks to find the universal patterns that are found and applied to the objects surrounding us, such as the designs found in temples, churches, mosques, monuments, art, architecture, and nature. Learn the (...)
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  21. Representational geometry: integrating cognition, computation, and the brain.Nikolaus Kriegeskorte & Rogier A. Kievit - 2013 - Trends in Cognitive Sciences 17 (8):401-412.
  22. The Geometry of Desert.Shelly Kagan - 2005 - New York, US: Oxford University Press.
    Moral desert -- Fault forfeits first -- Desert graphs -- Skylines -- Other shapes -- Placing peaks -- The ratio view -- Similar offense -- Graphing comparative desert -- Variation -- Groups -- Desert taken as a whole -- Reservations.
  23. Linguistic Geometry and its Applications.W. B. Vasantha Kandasamy, K. Ilanthenral & Florentin Smarandache - 2022 - Miami, FL, USA: Global Knowledge.
    The notion of linguistic geometry is defined in this book. It is pertinent to keep in the record that linguistic geometry differs from classical geometry. Many basic or fundamental concepts and notions of classical geometry are not true or extendable in the case of linguistic geometry. Hence, for simple illustration, facts like two distinct points in classical geometry always define a line passing through them; this is generally not true in linguistic geometry. Suppose (...)
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  24. Euclidean Geometry is a Priori.Boris Culina - manuscript
    In the article, an argument is given that Euclidean geometry is a priori in the same way that numbers are a priori, the result of modelling, not the world, but our activities in the world.
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  25.  25
    Differential Geometry, the Informational Surface and Oceanic Art: The Role of Pattern in Knowledge Economies.Susanne Küchler - 2017 - Theory, Culture and Society 34 (7-8):75-97.
    Graphic pattern (e.g. geometric design) and number-based code (e.g. digital sequencing) can store and transmit complex information more efficiently than referential modes of representation. The analysis of the two genres and their relation to one another has not advanced significantly beyond a general classification based on motion-centred geometries of symmetry. This article examines an intriguing example of patchwork coverlets from the maritime societies of Oceania, where information referencing a complex genealogical system is lodged in geometric designs. By drawing attention to (...)
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  26.  40
    The geometry of state space.M. Adelman, J. V. Corbett & C. A. Hurst - 1993 - Foundations of Physics 23 (2):211-223.
    The geometry of the state space of a finite-dimensional quantum mechanical system, with particular reference to four dimensions, is studied. Many novel features, not evident in the two-dimensional space of a single spin, are found. Although the state space is a convex set, it is not a ball, and its boundary contains mixed states in addition to the pure states, which form a low-dimensional submanifold. The appropriate language to describe the role of the observer is that of flag manifolds.
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  27.  8
    Geometrie und Erfahrung: Erweiterte Fassung des Festvortrages Gehalten an der Preussischen Akademie der Wissenschaften zu Berlin am 27. Januar 1921.Albert Einstein - 1921 - Springer.
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  28. Core Knowledge of Geometry in an Amazonian Indigene Group.Stanislas Dehaene, Véronique Izard, Pierre Pica & Elizabeth Spelke - 2006 - Science 311 (5759)::381-4.
    Does geometry constitues a core set of intuitions present in all humans, regarless of their language or schooling ? We used two non verbal tests to probe the conceptual primitives of geometry in the Munduruku, an isolated Amazonian indigene group. Our results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms.
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  29.  74
    Finsler Geometry and Relativistic Field Theory.R. G. Beil - 2003 - Foundations of Physics 33 (7):1107-1127.
    Finsler geometry on the tangent bundle appears to be applicable to relativistic field theory, particularly, unified field theories. The physical motivation for Finsler structure is conveniently developed by the use of “gauge” transformations on the tangent space. In this context a remarkable correspondence of metrics, connections, and curvatures to, respectively, gauge potentials, fields, and energy-momentum emerges. Specific relativistic electromagnetic metrics such as Randers, Beil, and Weyl can be compared.
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  30.  12
    Geometrie.Jens Lemanski - 2018 - In Daniel Schubbe & Matthias Koßler (eds.), Schopenhauer-Handbuch: Leben – Werk – Wirkung. Springer. pp. 330–335.
    In mathematics textbooks and special mathematical treatises, themes and theses of Arthur Schopenhauer's elementary geometry appear again and again. Since Schopenhauer's geometry or philosophy of geometry was considered exemplary in the 19th and early 20th centuries in its relation to figures and thus to the intuition, the two-hundred-year reception history sketched in this paper also follows the evaluation of intuition-related geometries, which depends on the mathematical paradigms.
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  31.  8
    Geometrie.Jens Lemanski - 2018 - In Daniel Schubbe & Matthias Koßler (eds.), Schopenhauer-Handbuch: Leben – Werk – Wirkung. Springer. pp. 329-333.
    In Mathematiklehrbüchern und mathematischen Spezialabhandlungen tauchen bis heute immer wieder Themen und Thesen der Schopenhauerschen Elementargeometrie auf. Da Schopenhauers Geometrie bzw. Philosophie der Geometrie in ihrer Figuren- und damit Anschauungsbezogenheit im 19. und frühen 20. Jahrhundert exemplarisch galt, folgt die hier skizzenhaft dargestellte zweihundertjährige Rezeptionsgeschichte auch der von den mathematischen Paradigmen abhängenden Bewertung anschauungsbezogener Geometrien.
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  32.  77
    Oppositional Geometry in the Diagrammatic Calculus CL.Jens Lemanski - 2017 - South American Journal of Logic 3 (2):517-531.
    The paper presents the diagrammatic calculus CL, which combines features of tree, Euler-type, Venn-type diagrams and squares of opposition. In its basic form, `CL' (= Cubus Logicus) organizes terms in the form of a square or cube. By applying the arrows of the square of opposition to CL, judgments and inferences can be displayed. Thus CL offers on the one hand an intuitive method to display ontologies and on the other hand a diagrammatic tool to check inferences. The paper focuses (...)
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  33.  40
    The Ethics of Geometry: A Genealogy of Modernity.David Rapport Lachterman - 1989 - Routledge.
    The Ethics of Geometry is a study of the relationship between philosophy and mathematics. Essential differences in the ethos of mathematics, for example, the customary ways of undertaking and understanding mathematical procedures and their objects, provide insight into the fundamental issues in the quarrel of moderns with ancients. Two signal features of the modern ethos are the priority of problem-solving over theorem-proving, and the claim that constructability by human minds or instruments establishes the existence of relevant entities. These figures (...)
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  34.  4
    Geometry driven statistics.Ian L. Dryden & John T. Kent (eds.) - 2015 - Chichester, West Sussex: Wiley.
    A timely collection of advanced, original material in the area of statistical methodology motivated by geometric problems, dedicated to the influential work of Kanti V. Mardia This volume celebrates Kanti V. Mardia's long and influential career in statistics. A common theme unifying much of Mardia’s work is the importance of geometry in statistics, and to highlight the areas emphasized in his research this book brings together 16 contributions from high-profile researchers in the field. Geometry Driven Statistics covers a (...)
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  35.  43
    Inconsistent geometry.C. Mortensen - unknown
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  36. Affine geometry, visual sensation, and preference for symmetry of things in a thing.Birgitta Dresp-Langley - 2016 - Symmetry 127 (8).
    Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of advantage. Geometry is ideally suited for expressing the logic of evolutionary selection for symmetry, which is found in the shape curves of vein systems and other natural objects such as leaves, cell membranes, or tunnel systems built by ants. The topology and (...) of symmetry is controlled by numerical parameters, which act in analogy with a biological organism’s DNA. The introductory part of this paper reviews findings from experiments illustrating the critical role of two-dimensional (2D) design parameters, affine geometry and shape symmetry for visual or tactile shape sensation and perception-based decision making in populations of experts and non-experts. It will be shown that 2D fractal symmetry, referred to herein as the “symmetry of things in a thing”, results from principles very similar to those of affine projection. Results from experiments on aesthetic and visual preference judgments in response to 2D fractal trees with varying degrees of asymmetry are presented. In a first experiment (psychophysical scaling procedure), non-expert observers had to rate (on a scale from 0 to 10) the perceived beauty of a random series of 2D fractal trees with varying degrees of fractal symmetry. In a second experiment (two-alternative forced choice procedure), they had to express their preference for one of two shapes from the series. The shape pairs were presented successively in random order. Results show that the smallest possible fractal deviation from “symmetry of things in a thing” significantly reduces the perceived attractiveness of such shapes. The potential of future studies where different levels of complexity of fractal patterns are weighed against different degrees of symmetry is pointed out in the conclusion. (shrink)
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  37. Geometry of logic and truth approximation.Thomas Mormann - 2005 - Poznan Studies in the Philosophy of the Sciences and the Humanities 83 (1):431-454.
    In this paper it is argued that the theory of truth approximation should be pursued in the framework of some kind of geometry of logic. More specifically it is shown that the theory of interval structures provides a general framework for dealing with matters of truth approximation. The qualitative and the quantitative accounts of truthlikeness turn out to be special cases of the interval account. This suggests that there is no principled gap between the qualitative and quantitative approach. Rather, (...)
     
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  38. The Geometry of Partial Understanding.Colin Allen - 2013 - American Philosophical Quarterly 50 (3):249-262.
    Wittgenstein famously ended his Tractatus Logico-Philosophicus (Wittgenstein 1922) by writing: "Whereof one cannot speak, one must pass over in silence." (Wovon man nicht sprechen kann, darüber muss man schweigen.) In that earliest work, Wittgenstein gives no clue about whether this aphorism applied to animal minds, or whether he would have included philosophical discussions about animal minds as among those displaying "the most fundamental confusions (of which the whole of philosophy is full)" (1922, TLP 3.324), but given his later writings on (...)
     
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  39.  3
    Metric Geometry in a Tame Setting.Erik Walsberg - 2018 - Bulletin of Symbolic Logic 24 (4):460-460.
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  40. Geometry and generality in Frege's philosophy of arithmetic.Jamie Tappenden - 1995 - Synthese 102 (3):319 - 361.
    This paper develops some respects in which the philosophy of mathematics can fruitfully be informed by mathematical practice, through examining Frege's Grundlagen in its historical setting. The first sections of the paper are devoted to elaborating some aspects of nineteenth century mathematics which informed Frege's early work. (These events are of considerable philosophical significance even apart from the connection with Frege.) In the middle sections, some minor themes of Grundlagen are developed: the relationship Frege envisions between arithmetic and geometry (...)
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  41. Kant on geometry and spatial intuition.Michael Friedman - 2012 - Synthese 186 (1):231-255.
    I use recent work on Kant and diagrammatic reasoning to develop a reconsideration of central aspects of Kant’s philosophy of geometry and its relation to spatial intuition. In particular, I reconsider in this light the relations between geometrical concepts and their schemata, and the relationship between pure and empirical intuition. I argue that diagrammatic interpretations of Kant’s theory of geometrical intuition can, at best, capture only part of what Kant’s conception involves and that, for example, they cannot explain why (...)
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  42.  27
    Constructive geometry and the parallel postulate.Michael Beeson - 2016 - Bulletin of Symbolic Logic 22 (1):1-104.
    Euclidean geometry, as presented by Euclid, consists of straightedge-and-compass constructions and rigorous reasoning about the results of those constructions. We show that Euclidean geometry can be developed using only intuitionistic logic. This involves finding “uniform” constructions where normally a case distinction is used. For example, in finding a perpendicular to line L through point p, one usually uses two different constructions, “erecting” a perpendicular when p is on L, and “dropping” a perpendicular when p is not on L, (...)
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  43. The geometry of visual space and the nature of visual experience.Farid Masrour - 2015 - Philosophical Studies 172 (7):1813-1832.
    Some recently popular accounts of perception account for the phenomenal character of perceptual experience in terms of the qualities of objects. My concern in this paper is with naturalistic versions of such a phenomenal externalist view. Focusing on visual spatial perception, I argue that naturalistic phenomenal externalism conflicts with a number of scientific facts about the geometrical characteristics of visual spatial experience.
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  44. The geometry of visual space.Robert French - 1987 - Noûs 21 (2):115-133.
  45.  7
    The geometry of burning mirrors in Greek antiquity. Analysis, heuristic, projections, lemmatic fragmentation.Fabio Acerbi - 2011 - Archive for History of Exact Sciences 65 (5):471-497.
    The article analyzes in detail the assumptions and the proofs typical of the research field of the geometry of burning mirrors. It emphasizes the role of two propositions of the Archimedean Quadratura parabolae, never brought to bear on this subject, and of a complex system of projections reducing a sumptōma of a parabola to some specific linear lemmas. On the grounds of this case-study, the much-debated problem of the heuristic role of analysis is also discussed.
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  46.  54
    Projective Geometry in Logical Space: Rethinking Tractarian Thoughts.Pablo Acuña - 2018 - International Journal of Philosophical Studies 26 (1):1-23.
    Customary interpretations state that Tractarian thoughts are pictures, and, a fortiori, facts. I argue that important difficulties are unavoidable if we assume this standard view, and I propose a reading of the concept taking advantage of an analogy that Wittgenstein introduces, namely, the analogy between thoughts and projective geometry. I claim that thoughts should be understood neither as pictures nor as facts, but as acts of geometric projection in logical space. The interpretation I propose thus removes the root of (...)
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  47.  37
    Geometry and Structure of Quantum Phase Space.Hoshang Heydari - 2015 - Foundations of Physics 45 (7):851-857.
    The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry. The geometry also plays an important role in foundations of quantum mechanics and quantum information. In this work we discuss a geometric framework for mixed quantum states represented by density matrices, where the quantum phase space of density matrices is equipped with a symplectic structure, an almost complex structure, and a compatible (...)
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  48.  86
    The geometry of visibles.R. B. Angell - 1974 - Noûs 8 (2):87-117.
  49. Physical Geometry and Fundamental Metaphysics.Cian Dorr - 2011 - Proceedings of the Aristotelian Society 111 (1pt1):135-159.
    I explore some ways in which one might base an account of the fundamental metaphysics of geometry on the mathematical theory of Linear Structures recently developed by Tim Maudlin (2010). Having considered some of the challenges facing this approach, Idevelop an alternative approach, according to which the fundamental ontology includes concrete entities structurally isomorphic to functions from space-time points to real numbers.
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  50. From Geometry to Conceptual Relativity.Thomas William Barrett & Hans Halvorson - 2017 - Erkenntnis 82 (5):1043-1063.
    The purported fact that geometric theories formulated in terms of points and geometric theories formulated in terms of lines are “equally correct” is often invoked in arguments for conceptual relativity, in particular by Putnam and Goodman. We discuss a few notions of equivalence between first-order theories, and we then demonstrate a precise sense in which this purported fact is true. We argue, however, that this fact does not undermine metaphysical realism.
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