Hermann Weyl and L.E.J. Brouwer: Intuitive Continuum and Choice Sequences
Key Terms
- Hermann Weyl
- Intuitive Continuum
- Mathematical Continuum
- Phenomenology
- Intuitionistic Logic
- History of Mathematics
- Philosophy Of Mathematics
- Foundational Crisis in Mathematics
- Kant’s notion of the Primacy of Intuition
- Transcendental Idealism
- History of Continuity and Infinitesimals
- L. E. J. Brouwer
- Brouwer’s Intuitionism
- Infinitesimals
- Brouwer’s Choice Sequence
- Continuum
- Continuity Principle
- Atomistic Theory of Space and the Continuum
- Ur intuition
- Infinite Divisibility
- Indivisibility
- Principle of the Excluded Middle
- Topos
- Finite Logic and Infinite Logic
- Transfinite Logic
- Lawlike Sequence
- Lawless Sequence
- Free Choice Sequence
- Intuitive Mathematics
- Constructive Mathematics
- Constructivism
- Karl Menger – Menger Sponge (Assistant of L E J Brouwer)
- Cauchy Sequence
- Dedekind Cuts
- Intuitionism
- Logicism
- Formalism
- Non Cantorian Space
- Continuum
- Real Numbers
- Lattice
- Math and Music
- Boot Strapped Creation
- Awareness
- Consciousness
- Insight
- Intuition
- Imagination
- Theory of Karma
- Theory of Being
Key Scholars
- John L. Bell ( University of Western Ontario, Canada)
- Kati Kish Bar-On (MIT)
- Dirk van Dalen
- Solomon Feferman
- Arend Heyting
- Mark van Atten (SND, CNRS/Paris IV)
- Andrej Bauer (University of Ljubljana)
- Francesco Ciraulo (University of Padova)
- Martín Escardó (University of Birmingham)
- Michael Fourman (University of Edinburgh)
- Ieke Moerdijk (Radboud University, Nijmegen)
- Joan Rand Moschovakis (Occidental College, Los Angeles)
- Thomas Streicher (Technical University of Darmstadt)
- Göran Sundholm (University of Leiden)
- Anne S. Troelstra (University of Amsterdam)
- Wim Veldman (Radboud University)
- Steve Vickers (University of Birmingham)
Source: The Three Crises in Mathematics: Logicism, Intuitionism and Formalism
Source: The Three Crises in Mathematics: Logicism, Intuitionism and Formalism
Source: The Three Crises in Mathematics: Logicism, Intuitionism and Formalism
Source: The Three Crises in Mathematics: Logicism, Intuitionism and Formalism
Source: The Three Crises in Mathematics: Logicism, Intuitionism and Formalism
Source: The Three Crises in Mathematics: Logicism, Intuitionism and Formalism
Source: The Three Crises in Mathematics: Logicism, Intuitionism and Formalism
Source: The Three Crises in Mathematics: Logicism, Intuitionism and Formalism
Source: The Three Crises in Mathematics: Logicism, Intuitionism and Formalism
Source: The Three Crises in Mathematics: Logicism, Intuitionism and Formalism
Source: Gnomes in the Fog: The Reception of Brouwer’s Intuitionism in the 1920s
Source: Gnomes in the Fog: The Reception of Brouwer’s Intuitionism in the 1920s
Source: Gnomes in the Fog: The Reception of Brouwer’s Intuitionism in the 1920s
Source: Gnomes in the Fog: The Reception of Brouwer’s Intuitionism in the 1920s
Source: Gnomes in the Fog: The Reception of Brouwer’s Intuitionism in the 1920s
Source: Gnomes in the Fog: The Reception of Brouwer’s Intuitionism in the 1920s
Source: Gnomes in the Fog: The Reception of Brouwer’s Intuitionism in the 1920s
Source: The Return of the Flowing Continuum
Source: The Return of the Flowing Continuum
Source: The Return of the Flowing Continuum
Source: Choice Sequences and Their Uses
Source: Choice Sequences and Their Uses
Source: Choice Sequences and Their Uses
Source: Choice Sequences and Their Uses
Source: Choice Sequences and Their Uses
Source: Choice Sequences and Their Uses
Source: Choice Sequences and Their Uses
Source: Choice Sequences and Their Uses
Source: Choice Sequences and Their Uses
Source: Choice Sequences and Their Uses
Source: Choice Sequences and Their Uses
Source: Choice Sequences and Their Uses
Source: HERMANN WEYL ON INTUITION AND THE CONTINUUM
Source: HERMANN WEYL ON INTUITION AND THE CONTINUUM
Source: HERMANN WEYL ON INTUITION AND THE CONTINUUM
Source: HERMANN WEYL ON INTUITION AND THE CONTINUUM
Source: HERMANN WEYL ON INTUITION AND THE CONTINUUM
Source: HERMANN WEYL ON INTUITION AND THE CONTINUUM
Source: HERMANN WEYL ON INTUITION AND THE CONTINUUM
Source: HERMANN WEYL ON INTUITION AND THE CONTINUUM
Source: HERMANN WEYL ON INTUITION AND THE CONTINUUM
Source: HERMANN WEYL ON INTUITION AND THE CONTINUUM
Source: HERMANN WEYL ON INTUITION AND THE CONTINUUM
Source: HERMANN WEYL ON INTUITION AND THE CONTINUUM
Source: HERMANN WEYL ON INTUITION AND THE CONTINUUM
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Key Sources of Research
The Continuum: A Critical Examination of the Foundation of Analysis
By Hermann Weyl
HERMANN WEYL ON INTUITION AND THE CONTINUUM*
John L. Bell
Divergent conceptions of the continuum in 19th and early 20th century mathematics and philosophy.
Bell, J.L.
Axiomathes 15, 63–84 (2005).
https://doi.org/10.1007/s10516-004-7108-4
Towards a new philosophical perspective on Hermann Weyl’s turn to intuitionism
Kati Kish Bar-On
Cohn Institute for the History and Philosophy of Science and Ideas, Tel Aviv University
Email: katikish@gmail.com
Science in Context (2021), 34, 51–68
doi:10.1017/S0269889722000047
Click to access Latest_version_Weyl.pdf
Hermann Weyl and his Phenomenological Research within Infinitesimal Geometry
Flavio Baracco
28th March 2019
UNIMI
DIPARTIMENTO DI FILOSOFIA “PIERO MARTINETTI”
DOCTORAL SCHOOL IN PHILOSOPHY AND HUMAN SCIENCES
Hermann Weyl
SEP
https://plato.stanford.edu/Archives/win2021/entries/weyl/
Mathematical modernity, goal or problem? The opposing views of Felix Hausdorff and Hermann Weyl
Erhard Scholz∗
Hermann Weyl: From Trascendental Phenomenology to String Theory
Val Dusek
https://www.academia.edu/53213018/Hermann_Weyl_From_Trascendental_Phenomenology_to_String_Theory
UNITY & DIVERSITY IN TAO
Val Dusek
The significance of Hermann Weyl’s Das Kontinuum
Solomon Feferman
https://www.academia.edu/160344/The_significance_of_Hermann_Weyls_Das_Kontinuum
Weyl’s Conception of the Continuum in a Husserlian Transcendental Perspective
Stathis Livadas
2017, Studia Philosophica Estonica
https://doi.org/10.12697/spe.2017.10.1.07
Intuitionism in the Philosophy of Mathematics: Introducing a Phenomenological Account
Philipp Berghofer
https://doi.org/10.1093/philmat/nkaa011
Weyl’s Phenomenological Constructivism
Flavio Baracco
2019, Meta: Research in Hermeneutics, Phenomenology, and Practical Philosophy
https://www.academia.edu/41544999/Weyls_Phenomenological_Constructivism
Brouwer and Weyl: The Phenomenology and Mathematics of the Intuitive Continuumt
Mark van Atten
2002, Philosophia Mathematica
Weyl and intuitionistic infinitesimals
Mark van Atten
https://www.academia.edu/36150214/Weyl_and_intuitionistic_infinitesimals
Introducing choice sequences into mathematical ontology
Josiano Nereu
Published 2011
https://www.academia.edu/70140230/Introducing_choice_sequences_into_mathematical_ontology
Notions of choice sequence
Michael Fourman
1982, Studies in Logic and the Foundations of Mathematics
https://www.academia.edu/68558265/Notions_of_choice_sequence
Weyl’s appropriation of Husserl’s and Poincaré’s thought
Richard Feist
https://www.academia.edu/67375668/Weyls_appropriation_of_Husserls_and_Poincarés_thought
‘Heidegger and Weyl on the Question of Continuity’
https://www.academia.edu/1034062/Heidegger_and_Weyl_on_the_Question_of_Continuity
Conceptions of the Continuum.
Feferman Solomon.
In: Intellectica. Revue de l’Association pour la Recherche Cognitive, n°51, 2009/1. Le continu mathématique. Nouvelles conceptions, nouveaux enjeux. pp. 169-189;
doi : https://doi.org/10.3406/intel.2009.1737
https://www.persee.fr/doc/intel_0769-4113_2009_num_51_1_1737
Bernhard Riemann’s Conceptual Mathematics and the Idea of Space
Arkady Plotnitsky
Purdue University
From philosophical traditions to scientific developments: reconsidering the response to Brouwer’s intuitionism
Kati Kish Bar-On
Received: 2 February 2022 / Accepted: 24 September 2022
Synthese (2022) 200:521
https://doi.org/10.1007/s11229-022-03908-3
https://dspace.mit.edu/bitstream/handle/1721.1/146907/11229_2022_Article_3908.pdf?sequence=1
WEYL REEXAMINED: “DAS KONTINUUM” 100 YEARS LATER
ARNON AVRON*
SCHOOL OF COMPUTER SCIENCE
TEL AVIV UNIVERSITY, TEL AVIV 6997801, ISRAEL
Bulletin of Symbolic Logic , Volume 26 , Issue 1 , March 2020 , pp. 26 – 79
DOI: https://doi.org/10.1017/bsl.2020.23
Weyl vindicated: Das Kontinuum 70 years later
Feferman, S.,
Remi e Prospettive Della Logica e Della Scienza Contemporanee , vol. I (1988), pp. 59–93,
Mathematical Intuitionism
Posy, C. (2020).
(Elements in the Philosophy of Mathematics). Cambridge: Cambridge University Press. doi:10.1017/9781108674485
Hermann Weyl’s Intuitionistic Mathematics.
Van Dalen, D. (1995).
Bulletin of Symbolic Logic, 1(2), 145-169. doi:10.2307/421038
Labyrinth of Continua
Patrick Reeder,
Philosophia Mathematica, Volume 26, Issue 1, February 2018, Pages 1–39, https://doi.org/10.1093/philmat/nkx018
Herman Weyl on the Concept of Continuum.
Scholz, E. (2000).
In: Hendricks, V.F., Pedersen, S.A., Jørgensen, K.F. (eds) Proof Theory. Synthese Library, vol 292. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2796-9_9
https://link.springer.com/chapter/10.1007/978-94-017-2796-9_9
Intuitionism in the Philosophy of Mathematics
SEP
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The Development of Intuitionistic Logic
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Intuitionistic Logic
SEP
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Connecting the revolutionary with the conventional: Rethinking the differences between the works of Brouwer, Heyting, and Weyl
Kati Kish Bar-On
Massachusetts Institute of Technology (Forthcoming in Philosophy of Science)
https://philarchive.org/archive/BARCTR-5
Computational Complexity and Brouwer’s Continuum
Robert L. Constable
Cornell University USA
February 26, 2020
Weyl and intuitionistic infinitesimals
Mark van Atten∗ July 2, 2018
dedicated to the memory of Richard Tieszen, 1951–2017
L. E. J. Brouwer
https://en.wikipedia.org/wiki/L._E._J._Brouwer
Luitzen Egbertus Jan Brouwer
SEP
https://plato.stanford.edu/entries/brouwer/
Mystic, Geometer, and Intuitionist, 2 volumes
van Dalen, D., 1999/2005,
Oxford: Clarendon Press.
The standard biography of Brouwer. Volume 1, The Dawning Revolution, covers the years 1881–1928, volume 2, Hope and Disillusion, covers 1929–1966.
The Return of the Flowing Continuum
Dirk van Dalen
Intellectica, 2009/1, 51, pp.
From philosophical traditions to scientific developments: reconsidering the response to Brouwer’s intuitionism.
Kish Bar-On, K.
Synthese 200, 521 (2022). https://doi.org/10.1007/s11229-022-03908-3
https://link.springer.com/article/10.1007/s11229-022-03908-3
The Mathematical Continuum: From Intuition to Logic
Giuseppe Longo
Peirce and Brouwer
Conor Mayo-Wilson
September 5, 2011
IDEAS AND EXPLORATIONS
Brouwer’s Road to Intuitionism
Johannes John Carel Kuiper
PhD Thesis, 2004, Universiteit Utrecht
INTUITIONISTIC MATHEMATICS AND LOGIC
JOAN RAND MOSCHOVAKIS AND GARYFALLIA VAFEIADOU
Cornell Univ.
Click to access intuitionistic-math2.pdf
Choice Sequences and the Continuum
Casper Storm Hansen∗
Click to access choicesequences.pdf
Constructivity, Computability, and the Continuum
Michael Beeson
Intuitionism and Infinity
Sean Richardson
Philosophical Methods
December 2017
https://www.seanhrichardson.com/files/philosophy_intuitionism.pdf
Classical and intuitionistic mathematical languages shape our understanding of time in physics
Nicolas Gisin
Group of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
May 3, 2022
https://www.arxiv-vanity.com/papers/2002.01653/
What is a Line?
D. F. M. Strauss
Axiomathes (2014) 24:181–205
DOI 10.1007/s10516-013-9224-5
Click to access What-is-a-Line-Axiomathes.pdf
MIND AND NATURE
Selected Writings on Philosophy, Mathematics, and Physics
HERMANN WEYL
Edited and with an introduction by Peter Pesic
PRINCETON UNIVERSITY PRESS
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INTUITIONISTIC, FREE, AND MANY-VALUED LOGICS
Intuitionism
DIRK VAN DALEN AND MARK VAN ATTEN
Weyl’s Phenomenological Constructivism
Flavio Baracco
Université Paris 7
META: RESEARCH IN HERMENEUTICS, PHENOMENOLOGY, AND PRACTICAL PHILOSOPHY VOL. XI, NO. 2 / DECEMBER 2019: 589-617, ISSN 2067-3655, www.metajournal.org
Click to access 589-617-baracco-meta-2019-no2-rev.pdf
The Crisis in the Foundations of Mathematics
Jos ́e Ferreiro ́s
Phenomenology, Logic, and the Philosophy of Mathematics
By Richard L. Tieszen
The Continuum: A Constructive Approach to Basic Concepts of Real Analysis
By Rudolf Taschner
One Hundred Years of Intuitionism (1907-2007): The Cerisy Conference
edited by Mark van Atten, Pascal Boldini, Michel Bourdeau, Gerhard Heinzmann
From Foundations to Philosophy of Mathematics: An Historical Account of their development in XX Century and Beyond
By Joan Roselló
L.E.J. Brouwer – Topologist, Intuitionist, Philosopher
How Mathematics Is Rooted in Life
Dirk Dalen
2013
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Mystic, Geometer, and Intuitionist : the Life of L.E.J. Brouwer
Dalen, D. van (Dirk).
Oxford: Clarendon Press, 1999. Print.
Brouwer’s Intuitionism
Stigt, Walter P. van.
Walter P. van Stigt. Amsterdam ;: North-Holland, 1990. Print.
Mathematical Intuitionism and Intersubjectivity. A Critical Exposition of Arguments for Intuitionism.
Horsten, Leon & Placek, Tomasz. (2002).
The Bulletin of Symbolic Logic – BSL. 8. 10.2307/797955.
Mathematical Intuitionism and Intersubjectivity
T Placek,
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Construction, Solipsism, and Intuitionistic Mathematics
Kevin Blum
Macalester Journal of Philosophy
Volume 14
Issue 1 Spring 2005
How Much Change is Too Much Change? Rethinking the Reasons Behind the Lack of Reception to Brouwer’s Intuitionism
Kati Kish Bar-On
The Cohn Institute for the History and Philosophy of Science and Ideas, Tel Aviv University katikish@gmail.com
Click to access To%20upload_PSA.pdf
Brouwer meets Husserl: On the Phenomenology of Choice Sequences
By Mark van Atten
The Three Crises in Mathematics: Logicism, Intuitionism and Formalism
Snapper, Ernst
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From Foundations to Philosophy of Mathematics
An Historical Account of their Development
in the XX Century and Beyond
Joan Roselló
Gnomes in the Fog: The Reception of Brouwer’s Intuitionism in the 1920s
by Dennis E. Hesseling
Basel, Birkh ̈auser, 2003
ISBN 3-7643-6536-6
Reviewed by Jeremy Avigad
Individual choice sequences in the work of L. E. J. Brouwer
Philosophia Scientiae, Volume 9 (2005) no. S2, pp. 217-232.
http://www.numdam.org/item/PHSC_2005__9_S2_217_0/
The grounding for Continuum
Stanislaw Ambroszkiewicz
2019
Institute of Computer Science, Polish Academy of Sciences, al. Jana Kazimierza 5, 01-248 Warsaw, Poland
E-mail: sambrosz@gmail.com
A Bibliography of L.E.J. Brouwer.
van Dalen, D. (2008b).
Birkhäuser Basel.
Choice Sequences
Troelstra, Anne S.
Oxford: Clarendon Press, 1977.
On the Origin and Development of Brouwer’s Concept of Choice Sequences
Troelstra, Anne S.
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Studies in Logic and the Foundations of Mathematics
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Troelstra, A.S.
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https://doi.org/10.1007/BF00247189
Consciousness, Philosophy, and Mathematics
L E J Brouwer
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The Modal Logic of Potential Infinity, With an Application to Free Choice Sequences
Ethan Brauer, B.A.
PhD Thesis
≁ ̸
Graduate Program in Philosophy
The Ohio State University 2020
Intuitionistic Logic: A View of its Evolution
Ann Kathrin Peters
Technische Universität Kaiserslautern, Department of Computer Science
seminar report
Seminar: Embedded Systems Seminar in Summer term 2019
Choice Sequences and Their Uses
Joan Rand Moschovakis
MPLA and Occidental College (Emerita)
Workshop on Spreads and Choice Sequences
Mittag-Lefler Institute
June 8-10, 2015
What is a choice sequence?
How a solution of Troelstra’s paradox shows the way to an answer to this question
Joop Niekus
“Informal Theory of Choice Sequences.”
Troelstra, A. S.
Studia Logica: An International Journal for Symbolic Logic 25 (1969): 31–54. http://www.jstor.org/stable/20014544.
Brouwer’s Cambridge Lectures on Intuitionism
Luitzen Egbertus Jan Brouwer
Cambridge University Press, 1981
Spreads or choice sequences?
H.C.M. De Swart (1992)
History and Philosophy of Logic, 13:2, 203-213,
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“Chapter Five. Intuitionism”
Linnebo, Øystein.
Philosophy of Mathematics,
Princeton: Princeton University Press, 2017, pp. 73-87. https://doi.org/10.1515/9781400885244-007
Über die neue Grundlagenkrise der Mathematik.
Weyl, H.
Math Z 10, 39–79 (1921). https://doi.org/10.1007/BF02102305
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Crosilla, L., & Linnebo, Ø. (2023).
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Continuity in Intuitionism
Charles McCarty,
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DOI: 10.1093/oso/9780198809647.003.0013
HERMANN WEYL ON INTUITION AND THE CONTINUUM*
John L. Bell
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