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Hermann WEYL

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  1. (1 other version)‘But one must not legalize the mentioned sin’: Phenomenological vs. dynamical treatments of rods and clocks in Einstein׳s thought.Marco Giovanelli - 2014 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 48 (1):20-44.
    The paper offers a historical overview of Einstein's oscillating attitude towards a "phenomenological" and "dynamical" treatment of rods and clocks in relativity theory. Contrary to what it has been usually claimed in recent literature, it is argued that this distinction should not be understood in the framework of opposition between principle and constructive theories. In particular Einstein does not seem to have plead for a "dynamical" explanation for the phenomenon rods contraction and clock dilation which was initially described only "kinematically". (...)
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  • (1 other version)Talking at cross-purposes: how Einstein and the logical empiricists never agreed on what they were disagreeing about.Marco Giovanelli - 2013 - Synthese 190 (17):3819-3863.
    By inserting the dialogue between Einstein, Schlick and Reichenbach into a wider network of debates about the epistemology of geometry, this paper shows that not only did Einstein and Logical Empiricists come to disagree about the role, principled or provisional, played by rods and clocks in General Relativity, but also that in their lifelong interchange, they never clearly identified the problem they were discussing. Einstein’s reflections on geometry can be understood only in the context of his ”measuring rod objection” against (...)
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  • Objectivity Sans Intelligibility. Hermann Weyl's Symbolic Constructivism.Iulian D. Toader - 2011 - Dissertation, University of Notre Dame
    A new form of skepticism is described, which holds that objectivity and understanding are incompossible ideals of modern science. This is attributed to Weyl, hence its name: Weylean skepticism. Two general defeat strategies are then proposed, one of which is rejected.
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  • The origins of the spacetime Metric: Bell’s Lorentzian Pedagogy and its significance in general relativity.Harvey R. Brown & Oliver Pooley - 2001 - In Craig Callender & Nick Huggett (eds.), Physics Meets Philosophy at the Planck Scale: Contemporary Theories in Quantum Gravity. Cambridge University Press. pp. 256--72.
    The purpose of this paper is to evaluate the `Lorentzian Pedagogy' defended by J.S. Bell in his essay ``How to teach special relativity'', and to explore its consistency with Einstein's thinking from 1905 to 1952. Some remarks are also made in this context on Weyl's philosophy of relativity and his 1918 gauge theory. Finally, it is argued that the Lorentzian pedagogy---which stresses the important connection between kinematics and dynamics---clarifies the role of rods and clocks in general relativity.
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  • On the role of virtual work in Levi-Civita’s parallel transport.Giuseppe Iurato & Giuseppe Ruta - 2016 - Archive for History of Exact Sciences 70 (5):1-13 (provisional).
    The current literature on history of science reports that Levi-Civita’s parallel transport was motivated by his attempt to provide the covariant derivative of the absolute differential calculus with a geometrical interpretation (For instance, see Scholz in ''The intersection of history and mathematics'', Birkhäuser, Basel, pp 203-230, 1994, Sect. 4). Levi-Civita’s memoir on the subject was explicitly aimed at simplifying the geometrical computation of the curvature of a Riemannian manifold. In the present paper, we wish to point out the possible role (...)
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  • Hilbert's program then and now.Richard Zach - 2002 - In Dale Jacquette (ed.), Philosophy of Logic. Malden, Mass.: North Holland. pp. 411–447.
    Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial (...)
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  • Wittgenstein on Weyl: the law of the excluded middle and the natural numbers.Jann Paul Engler - 2023 - Synthese 201 (6):1-23.
    In one of his meetings with members of the Vienna Circle, Wittgenstein discusses Hermann Weyl’s brief conversion to intuitionism and criticizes his arguments against applying the law of the excluded middle to generalizations over the natural numbers. Like Weyl, however, Wittgenstein rejects the classical model theoretic conception of generality when it comes to infinite domains. Nonetheless, he disagrees with him about the reasons for doing so. This paper provides an account of Wittgenstein’s criticism of Weyl that is based on his (...)
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  • Towards a new philosophical perspective on Hermann Weyl’s turn to intuitionism.Kati Kish Bar-On - 2021 - Science in Context 34 (1):51-68.
    The paper explores Hermann Weyl’s turn to intuitionism through a philosophical prism of normative framework transitions. It focuses on three central themes that occupied Weyl’s thought: the notion of the continuum, logical existence, and the necessity of intuitionism, constructivism, and formalism to adequately address the foundational crisis of mathematics. The analysis of these themes reveals Weyl’s continuous endeavor to deal with such fundamental problems and suggests a view that provides a different perspective concerning Weyl’s wavering foundational positions. Building on a (...)
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  • Uniform distribution and algorithmic randomness.Jeremy Avigad - 2013 - Journal of Symbolic Logic 78 (1):334-344.
    A seminal theorem due to Weyl [14] states that if $(a_n)$ is any sequence of distinct integers, then, for almost every $x \in \mathbb{R}$, the sequence $(a_n x)$ is uniformly distributed modulo one. In particular, for almost every $x$ in the unit interval, the sequence $(a_n x)$ is uniformly distributed modulo one for every computable sequence $(a_n)$ of distinct integers. Call such an $x$ UD random. Here it is shown that every Schnorr random real is UD random, but there are (...)
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  • Mathematics and phenomenology: The correspondence between O. Becker and H. Weyl.Paolo Mancosu & T. A. Ryckman - 2002 - Philosophia Mathematica 10 (2):130-202.
    Recently discovered correspondence from Oskar Becker to Hermann Weyl sheds new light on Weyl's engagement with Husserlian transcendental phenomenology in 1918-1927. Here the last two of these letters, dated July and August, 1926, dealing with issues in the philosophy of mathematics are presented, together with background and a detailed commentary. The letters provide an instructive context for re-assessing the connection between intuitionism and phenomenology in Weyl's foundational thought, and for understanding Weyl's term ‘symbolic construction’ as marking his own considered position (...)
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  • Divergent conceptions of the continuum in 19th and early 20th century mathematics and philosophy.John L. Bell - 2005 - Axiomathes 15 (1):63-84.
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  • (1 other version)Mathematical Analogies in Physics: the Curious Case of Gauge Symmetries.Guy Hetzroni & Noah Stemeroff - 2023 - In Carl Posy & Yemima Ben-Menahem (eds.), Mathematical Knowledge, Objects and Applications: Essays in Memory of Mark Steiner. Springer. pp. 229-262.
    Gauge symmetries provide one of the most puzzling examples of the applicability of mathematics in physics. The presented work focuses on the role of analogical reasoning in the gauge argument, motivated by Mark Steiner's claim that the application of the gauge principle relies on a Pythagorean analogy whose success undermines naturalist philosophy. In this paper, we present two different views concerning the analogy between gravity, electromagnetism, and nuclear interactions, each providing a different philosophical response to the problem of the applicability (...)
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  • Lectures on Jacques Herbrand as a Logician.Claus-Peter Wirth, Jörg Siekmann, Christoph Benzmüller & Serge Autexier - 2009 - Seki Publications (Issn 1437-4447).
    We give some lectures on the work on formal logic of Jacques Herbrand, and sketch his life and his influence on automated theorem proving. The intended audience ranges from students interested in logic over historians to logicians. Besides the well-known correction of Herbrand’s False Lemma by Goedel and Dreben, we also present the hardly known unpublished correction of Heijenoort and its consequences on Herbrand’s Modus Ponens Elimination. Besides Herbrand’s Fundamental Theorem and its relation to the Loewenheim-Skolem-Theorem, we carefully investigate Herbrand’s (...)
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  • The use of useless knowledge: Bergson against the pragmatists.Barry Allen - 2013 - Canadian Journal of Philosophy 43 (1):37-59.
    Henri Bergson and William James were great admirers of each other, and James seemed to think he got valuable ideas from Bergson. But early critics were right to see in Bergson the antithesis of pragmatism. Unfolding this antithesis is a convenient way to study important concepts and innovations in Bergson's philosophy. I concentrate on his ideas of duration and intuition, and show how they prove the necessity of going beyond pragmatism. The reason is because knowledge itself goes beyond the utilitarian (...)
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  • Weyl’s Appropriation of Husserl’s and Poincar“s Thought.Richard Feist - 2002 - Synthese 132 (3):273 - 301.
    This article locates Weyl''s philosophy of mathematics and its relationship to his philosophy of science within the epistemological and ontological framework of Husserl''s phenomenology as expressed in the Logical Investigations and Ideas. This interpretation permits a unified reading of Weyl''s scattered philosophical comments in The Continuum and Space-Time-Matter. But the article also indicates that Weyl employed Poincaré''s predicativist concerns to modify Husserl''s semantics and trim Husserl''s ontology. Using Poincaré''s razor to shave Husserl''s beard leads to limitations on the least upper (...)
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  • The prehistory of the subsystems of second-order arithmetic.Walter Dean & Sean Walsh - 2017 - Review of Symbolic Logic 10 (2):357-396.
    This paper presents a systematic study of the prehistory of the traditional subsystems of second-order arithmetic that feature prominently in the reverse mathematics program of Friedman and Simpson. We look in particular at: (i) the long arc from Poincar\'e to Feferman as concerns arithmetic definability and provability, (ii) the interplay between finitism and the formalization of analysis in the lecture notes and publications of Hilbert and Bernays, (iii) the uncertainty as to the constructive status of principles equivalent to Weak K\"onig's (...)
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  • How Weyl stumbled across electricity while pursuing mathematical justice.Alexander Afriat - 2009 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 40 (1):20-25.
    It is argued that Weyl’s theory of gravitation and electricity came out of ‘mathematical justice’: out of the equal rights direction and length. Such mathematical justice was manifestly at work in the context of discovery, and is enough to derive all of source-free electromagnetism. Weyl’s repeated references to coordinates and gauge are taken to express equal treatment of direction and length.
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  • On the Relationship between Parts and Wholes in Husserl's Phenomenology.Ettore Casari - 2007 - In Luciano Boi, Pierre Kerszberg & Frédéric Patras (eds.), Rediscovering Phenomenology. Phenomenological Essays on Mathematical Beings, Physical Reality, Perception and Consciousness. Hal Ccsd. pp. 67-102.
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  • Logic of Gauge.Alexander Afriat - 2019 - In Carlos Lobo & Julien Bernard (eds.), Weyl and the Problem of Space: From Science to Philosophy. Springer Verlag.
    The logic of gauge theory is considered by tracing its development from general relativity to Yang-Mills theory, through Weyl's two gauge theories. A handful of elements---which for want of better terms can be called \emph{geometrical justice}, \emph{matter wave}, \emph{second clock effect}, \emph{twice too many energy levels}---are enough to produce Weyl's second theory; and from there, all that's needed to reach the Yang-Mills formalism is a \emph{non-Abelian structure group} (say $\mathbb{SU}\textrm{(}N\textrm{)}$).
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  • Martinetti e il concetto di numero.Umberto Bottazzini - 2022 - Rivista di Storia Della Filosofia 3:373-383.
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  • A Raum with a View.Neil Dewar & Joshua Eisenthal - 2020 - In Claus Beisbart, Tilman Sauer & Christian Wüthrich (eds.), Thinking About Space and Time: 100 Years of Applying and Interpreting General Relativity. Cham: Birkhäuser. pp. 111-132.
    A central issue in the philosophical debates over general relativity concerns the status of the metric field: should it be regarded as part of the background arena in which physical fields evolve, or as a physical field itself? In this paper, we approach this debate through its relationship to the so-called "Problem of Space": the problem of determining which abstract, mathematical geometries are candidate descriptions of physical space. In particular, we explore the way that Hermann Weyl tackled the Problem of (...)
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  • Geometrization Versus Transcendent Matter: A Systematic Historiography of Theories of Matter Following Weyl.Norman Sieroka - 2010 - British Journal for the Philosophy of Science 61 (4):769-802.
    This article investigates an intertwined systematic and historical view on theories of matter. It follows an approach brought forward by Hermann Weyl around 1925, applies it to recent theories of matter in physics (including geometrodynamics and quantum gravity), and embeds it into a more general philosophical framework. First, I shall discuss the physical and philosophical problems of a unified field theory on the basis of Weyl's own abandonment of his 1918 ‘pure field theory’ in favour of an ‘agent theory’ of (...)
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  • Brouwer, as never read by Husserl.Mark van Atten - 2003 - Synthese 137 (1-2):3-19.
    Even though Husserl and Brouwer have never discussed each other's work, ideas from Husserl have been used to justify Brouwer's intuitionistic logic. I claim that a Husserlian reading of Brouwer can also serve to justify the existence of choice sequences as objects of pure mathematics. An outline of such a reading is given, and some objections are discussed.
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  • Jacques Herbrand: life, logic, and automated deduction.Claus-Peter Wirth, Jörg Siekmann, Christoph Benzmüller & Serge Autexier - 2009 - In Dov Gabbay (ed.), The Handbook of the History of Logic. Elsevier. pp. 195-254.
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  • Análisis de la relación entre el continuo intuitivo y el matemático en "Das Kontinuum".Victor Gonzalez Rojo - 2021 - Revista de Filosofía 46 (2):255-270.
    En este artículo pretendo discutir la conclusión a la que llega Weyl en su libro _El continuo_ sobre la relación entre el continuo intuitivo y el matemático. Esto me sirve a su vez para analizar más profundamente estas ideas, y postular la propiedad de ausencia de espacios vacíos [_Lückenlosigkeit_] como fundamento del continuo intuitivo y, en consecuencia, del matemático. Proponiendo además una alternativa idealista para el tratamiento del problema del continuo.
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  • Philosophy as a cultural resource and medium of reflection for Hermann Weyl.Erhard Scholz - 2005 - Revue de Synthèse 126 (2):331-351.
    Dans un discours prononcé à Zurich vers la fin des années 1940, Hermann Weyl a examiné l'épistémologie dialectique de Ferdinand Gonseth et l'a considérée comme trop strictement limitée aux aspects de changement historique. Son expérience de la philosophie diaclectique post-kantienne, en particulier la dérivation du concept de l'espace et de la matière chez Johann Gottlieb Fichte, avait constitué une base dialectique solide pour ses propres études de 1918 en une géométrie purement infinitésimale et la théorie antérieure d'un champ de matière (...)
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  • (1 other version)Collision of Traditions. The Emergence of Logical Empiricism Between the Riemannian and Helmholtzian Traditions.Marco Giovanelli - 2013 - .
    This paper attempts to explain the emergence of the logical empiricist philosophy of space and time as a collision of mathematical traditions. The historical development of the ``Riemannian'' and ``Helmholtzian'' traditions in 19th century mathematics is investigated. Whereas Helmholtz's insistence on rigid bodies in geometry was developed group theoretically by Lie and philosophically by Poincaré, Riemann's Habilitationsvotrag triggered Christoffel's and Lipschitz's work on quadratic differential forms, paving the way to Ricci's absolute differential calculus. The transition from special to general relativity (...)
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