75 found
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  1.  31
    Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer.Robert Tragesser, Mark van Atten & Mark Atten (eds.) - 2015 - Springer Verlag.
    We compare Gödel’s and Brouwer’s explorations of mysticism and its relation to mathematics.
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  2.  63
    L.E.J. Brouwer's ‘Unreliability of the Logical Principles’: A New Translation, with an Introduction.Mark Van Atten & Göran Sundholm - 2017 - History and Philosophy of Logic 38 (1):24-47.
    We present a new English translation of L.E.J. Brouwer's paper ‘De onbetrouwbaarheid der logische principes’ of 1908, together with a philosophical and historical introduction. In this paper Brouwer for the first time objected to the idea that the Principle of the Excluded Middle is valid. We discuss the circumstances under which the manuscript was submitted and accepted, Brouwer's ideas on the principle of the excluded middle, its consistency and partial validity, and his argument against the possibility of absolutely undecidable propositions. (...)
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  3. On Brouwer.Mark Van Atten - unknown
    "On Brouwer", like other titles in the Wadsworth Philosopher's Series, offers a concise, yet comprehensive, introduction to this philosopher's most important ideas. Presenting the most important insights of well over a hundred seminal philosophers in both the Eastern and Western traditions, the Wadsworth Philosophers Series contains volumes written by scholars noted for their excellence in teaching and for their well-versed comprehension of each featured philosopher's major works and contributions. These titles have proven valuable in a number of ways. Serving as (...)
     
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  4.  57
    Brouwer Meets Husserl: On the Phenomenology of Choice Sequences.Markus Sebastiaan Paul Rogier van Atten - 2007 - Springer.
    Can the straight line be analysed mathematically such that it does not fall apart into a set of discrete points, as is usually done but through which its fundamental continuity is lost? And are there objects of pure mathematics that can change through time? Mathematician and philosopher L.E.J. Brouwer argued that the two questions are closely related and that the answer to both is "yes''. To this end he introduced a new kind of object into mathematics, the choice sequence. But (...)
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  5. On the Philosophical Development of Kurt Gödel.Mark Van Atten & Juliette Kennedy - 2003 - Bulletin of Symbolic Logic 9 (4):425-476.
    It is by now well known that Gödel first advocated the philosophy of Leibniz and then, since 1959, that of Husserl. This raises three questions:1.How is this turn to Husserl to be interpreted? Is it a dismissal of the Leibnizian philosophy, or a different way to achieve similar goals?2.Why did Gödel turn specifically to the later Husserl's transcendental idealism?3.Is there any detectable influence from Husserl on Gödel's writings?Regarding the first question, Wang [96, p.165] reports that Gödel ‘[saw] in Husserl's work (...)
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  6. Mysticism and Mathematics: Brouwer, Gödel, and the Common Core Thesis.Robert Tragesser, Mark van Atten & Mark Atten - 2015 - In Robert Tragesser, Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag.
  7.  45
    Brouwer and Weyl: The Phenomenology and Mathematics of the Intuitive Continuumt.Mark Van Atten, Dirk van Dalen & Richard Tieszen - 2002 - Philosophia Mathematica 10 (2):203-226.
    Brouwer and Weyl recognized that the intuitive continuum requires a mathematical analysis of a kind that set theory is not able to provide. As an alternative, Brouwer introduced choice sequences. We first describe the features of the intuitive continuum that prompted this development, focusing in particular on the flow of internal time as described in Husserl's phenomenology. Then we look at choice sequences and their logic. Finally, we investigate the differences between Brouwer and Weyl, and argue that Weyl's conception of (...)
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  8.  85
    Brouwer and Weyl: The Phenomenology and Mathematics of the Intuitive Continuumt.Mark van Atten, Dirk van Dalen & Richard Tieszen - 2002 - Philosophia Mathematica 10 (2):203-226.
    Brouwer and Weyl recognized that the intuitive continuum requires a mathematical analysis of a kind that set theory is not able to provide. As an alternative, Brouwer introduced choice sequences. We first describe the features of the intuitive continuum that prompted this development, focusing in particular on the flow of internal time as described in Husserl's phenomenology. Then we look at choice sequences and their logic. Finally, we investigate the differences between Brouwer and Weyl, and argue that Weyl's conception of (...)
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  9. The Proper Explanation of Intuitionistic Logic: On Brouwer's Demonstration of the Bar Theorem.Mark Van Atten & Göran Sundholm - unknown
    Brouwer's demonstration of his Bar Theorem gives rise to provocative questions regarding the proper explanation of the logical connectives within intuitionistic and constructivist frameworks, respectively, and, more generally, regarding the role of logic within intuitionism. It is the purpose of the present note to discuss a number of these issues, both from an historical, as well as a systematic point of view.
     
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  10.  4
    One Hundred Years of Intuitionism : The Cerisy Conference.M. van Atten, P. Boldini, M. Bourdeau & G. Heinzmann - 2008 - Birkhäuser Basel.
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  11.  52
    A Note on Leibniz's Argument Against Infinite Wholes.Mark van Atten - 2011 - British Journal for the History of Philosophy 19 (1):121-129.
  12.  6
    Two Draft Letters From Gödel on Self-Knowledge of Reason.Mark van Atten & Mark Atten - 2015 - In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag. pp. 255-261.
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  13. The Development of Intuitionistic Logic.Mark Van Atten - unknown
     
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  14.  39
    Gödel’s Modernism: On Set-Theoretic Incompleteness.Juliette Cara Kennedy & Mark van Atten - 2004 - Graduate Faculty Philosophy Journal 25 (2):289-349.
    On Friday, November 15, 1940, Kurt Gödel gave a talk on set theory at Brown University. The topic was his recent proof of the consistency of Cantor’s Continuum Hypothesis with the axiomatic system ZFC for set theory. His friend from their days in Vienna, Rudolf Carnap, was in the audience, and afterward wrote a note to himself in which he raised a number of questions on incompleteness.
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  15.  62
    Arguments for the Continuity Principle.Mark van Atten & Dirk van Dalen - 2002 - Bulletin of Symbolic Logic 8 (3):329-347.
  16.  16
    Gödel’s Modernism: On Set-Theoretic Incompleteness.Mark van Atten - 2004 - Graduate Faculty Philosophy Journal 25 (2):289-349.
    On Friday, November 15, 1940, Kurt Gödel gave a talk on set theory at Brown University. The topic was his recent proof of the consistency of Cantor’s Continuum Hypothesis with the axiomatic system ZFC for set theory. His friend from their days in Vienna, Rudolf Carnap, was in the audience, and afterward wrote a note to himself in which he raised a number of questions on incompleteness.
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  17.  57
    Two Draft Letters From Godel on Self-Knowledge of Reason.M. van Atten - 2006 - Philosophia Mathematica 14 (2):255-261.
    In his text ‘The modern development of the foundations of mathematics in the light of philosophy’ from around 1961, Gödel announces a turn to Husserl's phenomenology to find the foundations of mathematics. In Gödel's archive there are two draft letters that shed some further light on the exact strategy that he formulated for himself in the early 1960s. Transcriptions of these letters are presented, together with some comments.
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  18. Monads and Sets: On Gödel, Leibniz, and the Reflection Principle.Mark van Atten & Mark Atten - 2015 - In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag.
    Gödel once offered an argument for the general reflection principle in set theory that took the form of an analogy with Leibniz' Monadology. I discuss the mathematical and philosophical background to Gödel's argument, reconstruct the proposed analogy in detail, and argue that it has no justificatory force.
     
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  19.  39
    Construction and Constitution in Mathematics.Mark van Atten - 2010 - New Yearbook for Phenomenology and Phenomenological Philosophy 10:43-90.
    In the following, I argue that L. E. J. Brouwer's notion of the construction of purely mathematical objects and Edmund Husserl's notion of their constitution coincide.
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  20.  75
    Thomas Ryckman: The Reign of Relativity. Philosophy in Physics 1915–1925. [REVIEW]Mark van Atten - 2008 - Husserl Studies 24 (1):73-78.
  21.  66
    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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  22.  22
    Gödel's Logic.Mark van Atten & Juliette Kennedy - 2009 - In Dov Gabbay (ed.), The Handbook of the History of Logic. Elsevier. pp. 449-509.
  23.  12
    A Note on Leibniz’s Argument Against Infinite Wholes.Mark van Atten & Mark Atten - 2015 - In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag. pp. 121-129.
  24.  46
    Fabrizio Palombi, the Star & the Whole: Gian-Carlo Rota on Mathematics and Phenomenology. Boca Raton: Crc Press, 2011. Isbn 978-1-56881-583-1 (Pbk). Pp. XIV + 124. English Translation of la Stella E L'Intero: La Ricerca di Gian-Carlo Rota Tra Matematica E Fenomenologia. 2nd Rev. Ed. Torino: Bollati Boringhieri, 2003. [REVIEW]M. van Atten - 2013 - Philosophia Mathematica 21 (1):115-123.
  25.  38
    Anne-Marie Décaillot, Cantor et la France. Correspondance du mathématicien allemand avec les Français à la fin du xixe siècle, Paris, Éditions Kimé, 2008, 347 p.Anne-Marie Décaillot, Cantor et la France. Correspondance du mathématicien allemand avec les Français à la fin du xixe siècle, Paris, Éditions Kimé, 2008, 347 p. [REVIEW]Mark van Atten - 2010 - Philosophiques 37 (1):262-265.
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  26.  32
    Johannes Dauberts Notizen Zu Husserls Mathematisch-Philosophischen Übungen Vom SS 1905.Johannes Daubert, Mark van Atten & Karl Schuhmann - 2004 - New Yearbook for Phenomenology and Phenomenological Philosophy 4 (1):288-317.
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  27.  64
    Gödel, Mathematics, and Possible Worlds.Mark van Atten - 2001 - Axiomathes 12 (3-4):355-363.
  28.  32
    Why Husserl Should Have Been a Strong Revisionist in Mathematics.M. van Atten - 2002 - Husserl Studies 18 (1):1-18.
    Husserl repeatedly has claimed that (1) mathematics without a philosophical foundation is not a science but a mere technique; (2) philosophical considerations may lead to the rejection of parts of mathematical practice; but (3) they cannot lead to mathematical innovations. My thesis is that Husserl's third claim is wrong, by his own standards.
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  29.  17
    On Gödel's Awareness of Skolem's Helsinki Lecture.Mark van Atten - 2005 - History and Philosophy of Logic 26 (4):321-326.
    Gödel always claimed that he did not know Skolem's Helsinki lecture when writing his dissertation. Some questions and doubts have been raised about this claim, in particular on the basis of a library slip showing that he had requested Skolem's paper in 1928. It is shown that this library slip does not constitute evidence against Gödel's claim, and that, on the contrary, the library slip and other archive material actually corroborate what Gödel said.
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  30.  26
    The Irreflexivity of Brouwer's Philosophy.Mark van Atten - 2002 - Axiomathes 13 (1):65-77.
    I argue that Brouwer''s general philosophy cannot accountfor itself, and, a fortiori, cannot lend justification tomathematical principles derived from it. Thus it cannot groundintuitionism, the jobBrouwer had intended it to do. The strategy is to ask whetherthat philosophy actually allows for the kind of knowledge thatsuch an account of itself would amount to.
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  31. Construction and Constitution in Mathematics.Mark van Atten & Mark Atten - 2015 - In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag.
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  32. Erratum.Mark van Atten & Mark Atten - 2015 - In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag.
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  33. Gödel and Brouwer: Two Rivalling Brothers.Mark van Atten & Mark Atten - 2015 - In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag.
     
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  34. Gödel and Intuitionism.Mark van Atten & Mark Atten - 2015 - In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag.
     
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  35. Gödel’s Dialectica Interpretation and Leibniz.Mark van Atten & Mark Atten - 2015 - In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag.
  36. Gödel, Mathematics, and Possible Worlds.Mark van Atten & Mark Atten - 2015 - In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag.
     
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  37. Introduction.Mark van Atten & Mark Atten - 2015 - In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag.
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  38. Phenomenology of Mathematics.Mark van Atten & Mark Atten - 2015 - In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag.
     
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  39. The Development of Intuitionistic Logic.Mark van Atten - forthcoming - Stanford Encyclopedia of Philosophy. The Meta-27here I Am Assuming That’Evidence’Provides the Basis for One’s Doxastic Justification. Additionally, I.
     
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  40. On Gödel's Logic.Juliette Kennedy & Mark van Atten - 2009 - In Dov Gabbay (ed.), The Handbook of the History of Logic. Elsevier.
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  41. On the Philosophical Development of Kurt Gödel.Juliette Kennedy & Mark van Atten - 2015 - In Juliette Kennedy & Mark van Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag.
  42.  48
    Lectures on Being and Time (1998).Gian-Carlo Rota & Mark van Atten - 2008 - New Yearbook for Phenomenology and Phenomenological Philosophy 8 (1):225-319.
  43.  5
    Author's Notice.Mark van Atten - 2003 - New Yearbook for Phenomenology and Phenomenological Philosophy 3:335-336.
  44.  15
    Brouwer’s Argument for the Unity of Scientific Theories.Mark van Atten - 2002 - Vienna Circle Institute Yearbook 9:95-102.
    The Dutch mathematician and philosopher L.E.J. Brouwer is well known for his ground-breaking work in topology and his iconoclastic philosophy of mathematics, intuitionism. What is far less well known is that Brouwer mused on the philosophy of the natural sciences as well. Later in life he also taught courses in physics at the University of Amsterdam.
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  45. Brouwer and the Hypothetical Judgement. Second Thoughts on John Kuiper's Ideas and Explorations: Brouwer's Road to Intuitionism.Mark Van Atten - 2004 - Revue Internationale de Philosophie 58 (4):501-516.
     
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  46.  13
    Bespr. Van: Husserl or Frege? Meaning, Objectivity, and Mathematics (Claire Ortiz Hill and Guillermo E. Rosado Haddock). [REVIEW]Markus Van Atten - 2003 - Philosophia Mathematica 11 (2):241-244.
  47.  10
    Carl Stumpf, Über die Grundsätze der Mathematik. Herausgegeben von Wolfgang Ewen. Würzburg, Könighausen & Neumann 2008Carl Stumpf, Über die Grundsätze der Mathematik. Herausgegeben von Wolfgang Ewen. Würzburg, Könighausen & Neumann 2008. [REVIEW]Mark van Atten - 2011 - Philosophiques 38 (2):623-626.
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  48.  32
    Review of C. O. Hill and G. E. Rosado Haddock, Husserl or Frege? Meaning, Objectivity, and Mathematics[REVIEW]Mark van Atten - 2003 - Philosophia Mathematica 11 (2):241-244.
  49.  16
    Dennis E. Hesseling. Gnomes in the Fog. The Reception of Brouwer's Intuitionism in the 1920s. Science Networks. Historical Studies, Vol. 28. Birkhäuser, Boston, 2003, Xxiii + 447 Pp. [REVIEW]Mark van Atten - 2004 - Bulletin of Symbolic Logic 10 (3):423-427.
  50.  3
    Die Mathematik Und Das Synthetische Apriori. [REVIEW]Mark van Atten - 2009 - Bulletin of Symbolic Logic 15 (1):91-94.
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