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1 — 50 / 157
  1. added 2018-12-29
    Is Geometry Analytic?David Mwakima - 2017 - Dianoia 1 (4):66 - 78.
    In this paper I present critical evaluations of Ayer and Putnam's views on the analyticity of geometry. By drawing on the historico-philosophical work of Michael Friedman on the relativized apriori; and Roberto Torretti on the foundations of geometry, I show how we can make sense of the assertion that pure geometry is analytic in Carnap's sense.
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  2. added 2018-12-15
    The Value of Pi in the Bible (And What It Tells Us About Biblical Hermeneutics).James H. Cumming - manuscript
    This short two-page essay provides irrefutable evidence that the Bible was encoded by its original redactors. Critical scholarship on the Bible needs to take ancient Jewish hermeneutical methods seriously.
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  3. added 2018-12-12
    A Philosopher Looks at Non-Commutative Geometry.Nick Huggett - manuscript
    This paper introduces some basic ideas and formalism of physics in non-commutative geometry. My goals are three-fold: first to introduce the basic formal and conceptual ideas of non-commutative geometry, and second to raise and address some philosophical questions about it. Third, more generally to illuminate the point that deriving spacetime from a more fundamental theory requires discovering new modes of `physically salient' derivation.
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  4. added 2018-11-08
    A Priori Concepts in Euclidean Proof.Peter Fisher Epstein - forthcoming - Proceedings of the Aristotelian Society.
    With the discovery of consistent non-Euclidean geometries, the a priori status of Euclidean proof was radically undermined. In response, philosophers proposed two revisionary interpretations of the practice: some argued that Euclidean proof is a purely formal system of deductive logic; others suggested that Euclidean reasoning is empirical, employing concepts derived from experience. I argue that both interpretations fail to capture the true nature of our geometrical thought. Euclidean proof is not a system of pure logic, but one in which our (...)
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  5. added 2018-10-21
    Prolegomena to a Cognitive Investigation of Euclidean Diagrammatic Reasoning.Yacin Hamami & John Mumma - 2013 - Journal of Logic, Language and Information 22 (4):421-448.
    Euclidean diagrammatic reasoning refers to the diagrammatic inferential practice that originated in the geometrical proofs of Euclid’s Elements. A seminal philosophical analysis of this practice by Manders (‘The Euclidean diagram’, 2008) has revealed that a systematic method of reasoning underlies the use of diagrams in Euclid’s proofs, leading in turn to a logical analysis aiming to capture this method formally via proof systems. The central premise of this paper is that our understanding of Euclidean diagrammatic reasoning can be fruitfully advanced (...)
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  6. 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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  7. added 2018-03-30
    Fundamental Physics and the Fine-Structure Constant.Michael A. Sherbon - 2017 - International Journal of Physical Research 5 (2):46-48.
    From the exponential function of Euler’s equation to the geometry of a fundamental form, a calculation of the fine-structure constant and its relationship to the proton-electron mass ratio is given. Equations are found for the fundamental constants of the four forces of nature: electromagnetism, the weak force, the strong force and the force of gravitation. Symmetry principles are then associated with traditional physical measures.
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  8. added 2018-03-21
    A Survey of Geometric Algebra and Geometric Calculus.Alan Macdonald - 2017 - Advances in Applied Clifford Algebras 27:853-891.
    The paper is an introduction to geometric algebra and geometric calculus for those with a knowledge of undergraduate mathematics. No knowledge of physics is required. The section Further Study lists many papers available on the web.
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  9. added 2018-02-18
    John von Neumann's Mathematical “Utopia” in Quantum Theory.Giovanni Valente - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (4):860-871.
    This paper surveys John von Neumann's work on the mathematical foundations of quantum theories in the light of Hilbert's Sixth Problem concerning the geometrical axiomatization of physics. We argue that in von Neumann's view geometry was so tied to logic that he ultimately developed a logical interpretation of quantum probabilities. That motivated his abandonment of Hilbert space in favor of von Neumann algebras, specifically the type II1II1 factors, as the proper limit of quantum mechanics in infinite dimensions. Finally, we present (...)
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  10. added 2018-01-28
    On the Chow Ring of a Flag.Christian Wenzel - 1997 - Mathematische Nachrichten 188:293-310.
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  11. added 2018-01-28
    On the Structure of Non-Reduced Parabolic Subgroup-Schemes.Christian Wenzel - 1994 - Proceedings of Symposia in Pure Mathematics 56 (1):291-297.
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  12. added 2018-01-28
    Classification of All Parabolic Subgroup Schemes of a Reductive Linear Algebraic Group Over an Algebraically Closed Field.Christian Wenzel - 1993 - Transactions of the American Mathematical Society 337 (1):211-218.
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  13. added 2018-01-28
    Rationality of G/P for a Non-Reduced Parabolic Subgroup Scheme P.Christian Wenzel - 1993 - Proceedings of the American Mathematical Society 117 (4):899-904.
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  14. added 2018-01-22
    Géométrie pratique. Géomètres, ingénieurs, architectes, XVIe-XVIIIe siècles.Dominique Raynaud (ed.) - 2015 - Besançon: Presses universitaires de Franche-Comté.
    Actes du colloque de Grenoble (8-9 octobre 2009), avec les contributions de Samuel Gessner (Lisbone), Eberhard Knobloch (Berlin), Jorge Galindo Díaz (Bogotá), Joël Sakarovitch (Paris) et Dominique Raynaud (Grenoble).
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  15. added 2017-12-01
    Vitale Giordano: Un matematico bitontino nella Roma barocca.Francesco Tampoia - 2005 - Rome: Armando.
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  16. added 2017-11-25
    Iter Italicum and Leibniz/Giordano Correspondence.Francesco Tampoia - manuscript
    Letters exchanged by scientists are a crucial source by which to trace the process that accompanies their scientific evolution. In this paper -accomplished through a historical approach- I aim to throw new light on Leibniz's continuing interest in classical geometry and to stress the significance of his correspondence with the Italian mathematician Vitale Giordano.
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  17. added 2017-11-01
    Inequivalent Representations of Geometric Relation Algebras.Steven Givant - 2003 - Journal of Symbolic Logic 68 (1):267-310.
    It is shown that the automorphism group of a relation algebra ${\cal B}_P$ constructed from a projective geometry P is isomorphic to the collineation group of P. Also, the base automorphism group of a representation of ${\cal B}_P$ over an affine geometry D is isomorphic to the quotient of the collineation group of D by the dilatation subgroup. Consequently, the total number of inequivalent representations of ${\cal B}_P$ , for finite geometries P, is the sum of the numbers ${\mid Col(P)\mid\over (...)
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  18. added 2017-10-30
    Erratum and Addendum To: The BV-Energy of Maps Into a Manifold: Relaxation and Density Results.Mariano Giaquinta & Domenico Mucci - 2007 - Annali della Scuola Normale Superiore di Pisa 6 (1):185-194.
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  19. added 2017-10-30
    The BV-Energy of Maps Into a Manifold: Relaxation and Density Results.Mariano Giaquinta & Domenico Mucci - 2006 - Annali della Scuola Normale Superiore di Pisa 5 (4):483-548.
    Let ${\cal Y}$ be a smooth compact oriented riemannian manifoldwithout boundary, and assume that its $1$-homology group has notorsion. Weak limits of graphs of smooth maps $u_k:B^n\rightarrow {\cal Y}$ with equibounded total variation give riseto equivalence classes of cartesian currents in $\mathop {\rm cart}\nolimits ^{1,1}$ for which we introduce a natural$BV$-energy.Assume moreover that the first homotopy group of ${\cal Y}$ iscommutative. In any dimension $n$ we prove that every element $T$ in $\mathop {\rm cart}\nolimits ^{1,1}$ can be approximatedweakly in the (...)
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  20. added 2017-10-26
    Philosophy of Science and Scientific Controversy: A Variety of Physical Conceptions and of Philosophical Interpretations of Quantum Physics.Olival Freire Júnior - 2013 - Scientiae Studia 11 (4):937-962.
    Este ensaio introdutório faz uma breve apresentação do tratado de óptica atribuído a Euclides de Alexandria, inserindo-o no contexto das teorias sobre a visão formuladas pelas doutrinas filosóficas antigas. Ressalta-se o antagonismo entre a análise geométrica da visão, empreendida por Euclides, e as considerações filosóficas acerca dos processos físicos subjacentes à sensação visual. Pretende-se mostrar que o objeto da óptica euclidiana é a percepção visual daquilo que Aristóteles denomina "sensível comum". This introductory essay provides an abridged presentation of the optical (...)
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  21. added 2017-10-13
    The Point or the Primary Geometric Object.ZERARI Fathi - manuscript
    The definition of a point in geometry is primordial in order to understand the different elements of this branch of mathematics ( line, surface, solids…). This paper aims at shedding fresh light on the concept to demonstrate that it is related to another one named, here, the Primary Geometric Object; both concepts concur to understand the multiplicity of geometries and to provide hints as concerns a new understanding of some concepts in physics such as time, energy, mass….
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  22. added 2017-09-23
    Linear and Geometric Algebra.Alan Macdonald - 2012 - North Charleston, SC: CreateSpace.
    This textbook for the second year undergraduate linear algebra course presents a unified treatment of linear algebra and geometric algebra, while covering most of the usual linear algebra topics. -/- Geometric algebra and its extension to geometric calculus simplify, unify, and generalize vast areas of mathematics that involve geometric ideas. Geometric algebra is an extension of linear algebra. The treatment of many linear algebra topics is enhanced by geometric algebra, for example, determinants and orthogonal transformations. And geometric algebra does much (...)
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  23. added 2017-08-31
    Poincaré on the Foundations of Arithmetic and Geometry. Part 2: Intuition and Unity in Mathematics.Katherine Dunlop - 2017 - Hopos: The Journal of the International Society for the History of Philosophy of Science 7 (1):88-107.
    Part 1 of this article exposed a tension between Poincaré’s views of arithmetic and geometry and argued that it could not be resolved by taking geometry to depend on arithmetic. Part 2 aims to resolve the tension by supposing not merely that intuition’s role is to justify induction on the natural numbers but rather that it also functions to acquaint us with the unity of orders and structures and show practices to fit or harmonize with experience. I argue that in (...)
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  24. added 2017-08-04
    Le Tracé Continu des Sections Coniques À la Renaissance: Applications Optico-Perspectives, Héritage de la Tradition Mathématique Arabe.Dominique Raynaud - 2007 - Arabic Sciences and Philosophy 17 (2):299-345.
    The perfect compass, used by al-Qūhī, al-Sijzī and his successors for the continuous drawing of conic sections, reappeared after a long eclipse in the works of Renaissance mathematicians like Francesco Barozzi in Venice. The resurgence of this instrument seems to have depended on its interest to solve new optico-perspective problems. Having reviewed the various instruments designed for the drawing of conic sections, the article is focused on the sole conic compass. Theoretical and empirical applications are detailed. Contrarily to the common (...)
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  25. added 2017-07-12
    Aristotle's Hypotheses and the Euclidean Postulates.Alfonso Gómez-Lobo - 1977 - Review of Metaphysics 30 (3):430 - 439.
  26. added 2017-03-03
    Discourse on Method, Optics, Geometry, Meteorology, Translated by Paul J. Olscamp.Descartes René (ed.) - 1965 - New York: Bobbs-Merrill.
    René Descartes, Discourse on Method, Optics, Geometry, and Meteorology. Trans., with an Introduction, by Paul J. Olscamp. Indianapolis: The Bobbs-Merrill Co., 1965. Pp. xxxvi + 361. = The Library of Liberal Arts, 211. Paper, $2.25. -/- From the notice in Journal of the History of Philosophy 5 (1967), 311: "In the introduction, Professor Olscamp calls attention to the fact that Descartes intended the other three pieces in this volume to serve as examples of the method set forth in the Discourse. (...)
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  27. added 2016-12-08
    The Epistemology of Geometry I: The Problem of Exactness.Anne Newstead & Franklin James - 2010 - Proceedings of the Australasian Society for Cognitive Science 2009.
    We show how an epistemology informed by cognitive science promises to shed light on an ancient problem in the philosophy of mathematics: the problem of exactness. The problem of exactness arises because geometrical knowledge is thought to concern perfect geometrical forms, whereas the embodiment of such forms in the natural world may be imperfect. There thus arises an apparent mismatch between mathematical concepts and physical reality. We propose that the problem can be solved by emphasizing the ways in which the (...)
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  28. added 2016-12-01
    Practical Geometry in the High Middle Ages. Artis Cuiuslibet Consummatio, and the Pratike de Geometrie. [REVIEW]Joann Morse - 1983 - British Journal for the History of Science 16 (2):211-212.
  29. added 2016-11-09
    Topological Paradoxes of Time Measurement.Roy Lisker - unknown
    This paper applies the ideas presented in "Time, Euclidean Geometry and Relativity" ID 1290 , to a specific problem in temporal measurement. It is shown that, under very natural assumptions, that if there is a minimum time interval T in ones collection of clocks, it is impossible to measure an interval of time 1/2T save by the accidental construction of a clock which pulses in that interval. This situation is contrasted to that for length, in which either the Euclidean Algorithm (...)
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  30. added 2016-10-29
    The Idea of a Diagram.Desmond Fearnley-Sander - 1989 - In Hassan Ait-Kaci & Maurice Nivat (eds.), Resolution of Equations in Algebraic Structures. Academic Press.
    A detailed axiomatisation of diagrams (in affine geometry) is presented, which supports typing of geometric objects, calculation of geometric quantities and automated proof of theorems.
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  31. added 2016-10-03
    Aristotelian Continua.Øystein Linnebo, Stewart Shapiro & Geoffrey Hellman - 2016 - Philosophia Mathematica 24 (2):214-246.
    In previous work, Hellman and Shapiro present a regions-based account of a one-dimensional continuum. This paper produces a more Aristotelian theory, eschewing the existence of points and the use of infinite sets or pluralities. We first show how to modify the original theory. There are a number of theorems that have to be added as axioms. Building on some work by Linnebo, we then show how to take the ‘potential’ nature of the usual operations seriously, by using a modal language, (...)
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  32. added 2016-08-27
    A Newtonian Tale Details on Notes and Proofs in Geneva Edition of Newton's Principia.Raffaele Pisano & Paolo Bussotti - 2016 - BSHM-Journal of the British Society for the History of Mathematics:1-19.
    Based on our research regarding the relationship between physics and mathematics in HPS, and recently on Geneva Edition of Newton's Philosophiae Naturalis Principia Mathematica (1739–42) by Thomas Le Seur (1703–70) and François Jacquier (1711–88), in this paper we present some aspects of such Edition: a combination of editorial features and scientific aims. The proof of Proposition XLIII is presented and commented as a case study.
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  33. added 2016-08-27
    Review of Poincaré, Philosopher of Science. [REVIEW]Nathan Lackey & Cory Wright - 2016 - Philosophy in Review 36 (4):157–159.
  34. added 2016-06-04
    Thomas Reid’s Geometry of Visibles and the Parallel Postulate.Giovanni Grandi - 2005 - Studies in History and Philosophy of Science Part A 36 (1):79-103.
    Thomas Reid (1710–1796) presented a two-dimensional geometry of the visual field in his Inquiry into the human mind (1764), whose axioms are different from those of Euclidean plane geometry. Reid’s ‘geometry of visibles’ is the same as the geometry of the surface of the sphere, described without reference to points and lines outside the surface itself. Interpreters of Reid seem to be divided in evaluating the significance of his geometry of visibles in the history of the discovery of non-Euclidean geometries. (...)
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  35. added 2016-04-02
    Imagination in Mathematics.Andrew Arana - 2016 - In Amy Kind (ed.), Routledge Handbook on the Philosophy of Imagination. Routledge. pp. 463-477.
    This article will consider imagination in mathematics from a historical point of view, noting the key moments in its conception during the ancient, modern and contemporary eras.
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  36. added 2016-03-12
    Writing, Embodiment, Deferral: Merleau-Ponty and Derrida on The Origin of Geometry.Emmanuel Alloa - 2014 - Philosophy Today 58 (2):219-239.
    A simplistic image of twentieth century French philosophy sees Merleau-Ponty’s death in 1961 as the line that divides two irreconcilable moments in its history: existentialism and phenomenology, on the one hand, and structuralism on the other. The structuralist generation claimed to recapture the dimension of objectivity and impersonality, which the previous generation was supposedly incapable of. As a matter of fact, in 1962, Derrida’s edition of Husserl’s The Origin of Geometry was taken to be a turning point that announced the (...)
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  37. added 2016-02-25
    Wittgenstein e as teorias semânticas do a priori visual: Observações Filosóficas , cap. XVI & XX.Ludovic Soutif - 2009 - Doispontos 6 (1):13-34.
    Neste artigo, tentamos mostrar que um problema comum aos capítulos XVI e XX das Observações filosóficas é o da aplicabilidade dos conceitos e «proposições» da geometria à realidade física e perceptiva (visual, em particular), e que o modo pelo qual Wittgenstein aborda esse problema nessa obra difere radicalmente, a despeito de aparentes similitudes, daquele que caracteriza as teorias semânticas do a priori visual em termos de estipulações (notadamente, o de Carnap em 1922). O esclarecimento do estatuto dos enunciados sobre os (...)
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  38. added 2015-10-29
    Where Does It All End? Boundaries Beyond Euclidean Space.Jonathan Thompson - 2005 - Inquiry: The University of Arkansas Undergraduate Research Journal 6.
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  39. added 2015-10-18
    Unified Fields in the Universe.John Linus O'Sullivan - forthcoming - Gsjournal 1 (May).
    Abstract: Space is from two kinds of energy in standing waves; (1) energy with mass which is finite energy and (2) energy without mass which is infinite energy. Given light speed is equal to frequency times wavelength C = f λ then photon half waves are twice light speed on contraction before reversal expansion at light speed. Light speed is a constant relative to mass in Special Relativity but photon half waves are twice light speed on contraction from the fundamental (...)
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  40. added 2015-09-21
    Origin of Matter with Time.John Linus O'sullivan - forthcoming - GsJournal.
    Abstract: Space is from two kinds of energy in standing waves; (1) energy with mass which is finite energy and (2) energy without mass which is infinite energy. Given light speed is equal to frequency times wavelength C = f λ then photon half waves are twice light speed on contraction before reversal expansion at light speed. Light speed is a constant relative to mass in Special Relativity but photon half waves are twice light speed on contraction from the fundamental (...)
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  41. added 2015-09-08
    Empirical Conditions for a Reidean Geometry of Visual Experience.Hannes Ole Matthiessen - 2016 - Topoi 35 (2):511-522.
    Thomas Reid's Geometry of Visibles, according to which the geometrical properties of an object's perspectival appearance equal the geometrical properties of its projection on the inside of a sphere with the eye in its centre allows for two different interpretations. It may (1) be understood as a theory about phenomenal visual space – i.e. an account of how things appear to human observers from a certain point of view – or it may (2) be seen as a mathematical model of (...)
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  42. added 2015-08-30
    Les débats sur les fondements de la perspective linéaire de Piero della Francesca à Egnatio Danti: un cas de mathématisation à rebours.Dominique Raynaud - 2010 - Early Science and Medicine 15 (4):474-504.
    L'essor de la perspective linéaire a suscité de nombreuses polémiques tout au long du Quattrocento et du Cinquecento, opposant les partisans d'une géométrisation artificialiste de la vision à ceux qui vantaient les qualités du dessin d'après nature ou invoquaient des arguments de nature physiologique. Ces débats peuvent être retracés à partir des quatre alternatives qui en constituent le noyau dur : champ de vision restreint vs. large ; immobilité vs. mobilité oculaire ; tableau plan vs. curviligne ; vision monoculaire vs. (...)
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  43. added 2015-08-30
    Debates on the Foundations of Linear Perspective From Piero Della Francesca to Egnatio Danti: A Case of Upside-Down Mathematics.Dominique Raynaud - 2010 - Early Science and Medicine 15 (4-5):474-504.
    In the Quattrocento and Cinquecento the rise of linear perspective caused many polemics which opposed the supporters of an artificial geometrisation of sight to those who were praising the qualities of the drawing according to nature, or were invoking some arguments on a physiological basis. ese debates can be grouped according to the four alternatives that form their central concerns: restricted vs. broad field of vision; ocular immobility vs. mobility; curvilinear vs. planar picture; monocular vs. binocular vision. By retaining the (...)
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  44. added 2015-08-25
    Has Poincaré's Conventionalism Been Refuted?John Preston - 1995 - Ratio 8 (2):193-200.
  45. added 2015-08-12
    Eternal Geometry: Nelson and Non-Euclidean Geometries.Renato Pettoello - 2010 - Rivista di Storia Della Filosofia 65 (3):483-506.
  46. added 2015-08-12
    Another Constructive Axiomatization of Euclidean Planes.Victor Pambuccian - 2000 - Mathematical Logic Quarterly 46 (1):45-48.
    H. Tietze has proved algebraically that the geometry of uniquely determined ruler and compass constructions coincides with the geometry of ruler and set square constructions. We provide a new proof of this result via new universal axiom systems for Euclidean planes of characteristic ≠ 2 in languages containing only operation symbols.
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  47. added 2015-08-10
    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, computer (...)
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  48. added 2015-07-07
    Analysis and Synthesis in John Playfair's Elements of Geometry.Amy Ackerberg-Hastings - 2002 - British Journal for the History of Science 35 (1):43-72.
    John Playfair , professor of mathematics and natural philosophy at the University of Edinburgh, is a relatively obscure figure today, best known as the popularizer of James Hutton's theory of geology. However, Playfair was also involved in mathematics for most of his active career, with his most widely distributed publication, Elements of Geometry , shaping the mathematics education for at least thirteen thousand British students during the nineteenth century. This study focuses on the mathematical context surrounding Elements of Geometry. Specifically, (...)
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  49. added 2015-06-23
    Epistemological Aspects of Modern Painting.L. Kvasz - 2000 - Filozofia 55 (8):601-619.
    The aim of the paper is to analyse the geometrical aspects of a series of modern paintings and to show the parallel between them and the development of modern geometry. It starts with El Greco, offering a geometrical explanation of his painting the figures in a prolonged manner. Further the analogy between the impressionist way of creating space and the geometrical idea of Cayley to use projective space as a basis for non-Euclidean geometry is reconstructed. Next the paper describes the (...)
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  50. added 2015-06-23
    Prolegomena K Formálnej Epistemológii.Ladislav Kvasz - 1999 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 6 (1999):223-239.
    The aim of this paper is a philosophical generalisation of the results, which we obtained through the analysis of the development of synthetic geometry. I our papers Náčrt analytickej teórie subjektu and Topológia versus teória množín we proposed a method of analysis of the development of geometry based on Wittgensteinś Picture theory of meaning from the Tractatus. It turned out, that the concept of the form of language can be effectively used to characterise the changes, which occured in the course (...)
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1 — 50 / 157