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Mark van Atten [85]Markus Van Atten [1]Markus Sebastiaan Paul Rogier van Atten [1]
  1.  42
    Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer.Robert Tragesser, Mark van Atten & Mark Atten (eds.) - 2015 - Cham: Springer Verlag.
    We compare Gödel’s and Brouwer’s explorations of mysticism and its relation to mathematics.
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  2. On Brouwer.Mark van Atten - 2004 - Wadsworth Publishing Company.
    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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  3.  69
    Brouwer meets Husserl: on the phenomenology of choice sequences.Markus Sebastiaan Paul Rogier van Atten - 2007 - Dordrecht: 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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  4. 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.
  5.  2
    The development of intuitionistic logic.Mark van Atten - 2008 - Stanford Encyclopedia of Philosophy. The Meta-27here I Am Assuming That’Evidence’Provides the Basis for One’s Doxastic Justification. Additionally, I:en ligne.
  6.  83
    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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  7. 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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  8.  63
    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.  92
    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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  10.  37
    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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  11. 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.
  12.  11
    The development of intuitionistic logic.Mark van Atten - unknown
  13.  71
    Arguments for the continuity principle.Mark van Atten & Dirk van Dalen - 2002 - Bulletin of Symbolic Logic 8 (3):329-347.
    There are two principles that lend Brouwer's mathematics the extra power beyond arithmetic. Both are presented in Brouwer's writings with little or no argument. One, the principle of bar induction, will not concern us here. The other, the continuity principle for numbers, occurs for the first time in print in [4]. It is formulated and immediately applied to show that the set of numerical choice sequences is not enumerable. In fact, the idea of the continuity property can be dated fairly (...)
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  14.  35
    Why Husserl should have been a strong revisionist in mathematics.Mark 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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  15.  9
    One Hundred Years of Intuitionism : The Cerisy Conference.Mark van Atten, Pascal Boldini, Michel Bourdeau & Gerhard Heinzmann - 2008 - Birkhäuser Basel.
    Intuitionism is one of the main foundations for mathematics proposed in the twentieth century and its views on logic have also notably become important with the development of theoretical computer science. This book reviews and completes the historical account of intuitionism. It also presents recent philosophical work on intuitionism and gives examples of new technical advances and applications. It brings together 21 contributions from today's leading authors on intuitionism.
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  16.  41
    Gödel’s Modernism.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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  17.  57
    A Note on Leibniz's Argument Against Infinite Wholes.Mark van Atten - 2011 - British Journal for the History of Philosophy 19 (1):121-129.
    Leibniz had a well-known argument against the existence of infinite wholes that is based on the part-whole axiom: the whole is greater than the part. The refutation of this argument by Russell and others is equally well known. In this note, I argue (against positions recently defended by Arthur, Breger, and Brown) for the following three claims: (1) Leibniz himself had all the means to devise and accept this refutation; (2) This refutation does not presuppose the consistency of Cantorian set (...)
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  18.  44
    Construction and Constitution in Mathematics.Mark van Atten - 2010 - New Yearbook for Phenomenology and Phenomenological Philosophy 10 (1):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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  19. 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.
  20.  61
    Two Draft Letters from Godel on Self-knowledge of Reason.Mark 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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  21.  17
    Gödel’s Modernism.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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  22.  26
    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.  9
    Two Draft Letters from Gödel on Self-Knowledge of Reason.Mark van Atten & Mark Atten - 2006 - In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag. pp. 255-261.
    In his text 'The modern development of the foundations of mathematics in the light of philosophy' from around 1961, Go¨del announces a turn to Husserl's phenomenology to find the foundations of mathematics. In Go¨del'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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  24.  74
    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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  25.  78
    Thomas Ryckman: The reign of relativity. Philosophy in physics 1915–1925. [REVIEW]Mark van Atten - 2008 - Husserl Studies 24 (1):73-78.
  26.  24
    Monads and Sets: On Gödel, Leibniz, and the Reflection Principle.Mark van Atten & Mark Atten - 2009 - In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag. pp. 3-33.
    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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  27. Gödel and Intuitionism.Mark van Atten & Mark Atten - 2006 - In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag.
    Joint Session of the two Divisions of the International Union for History and Philosophy of Science.
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  28.  86
    Edmund Husserl, Logik. Vorlesung 1902/03, hg. von Elisabeth Schuhmann.Mark van Atten - 2005 - Husserl Studies 21 (2):145-148.
  29.  62
    Kant and real numbers.Mark van Atten - unknown
    Kant held that under the concept of √2 falls a geometrical magnitude, but not a number. In particular, he explicitly distinguished this root from potentially infinite converging sequences of rationals. Like Kant, Brouwer based his foundations of mathematics on the a priori intuition of time, but unlike Kant, Brouwer did identify this root with a potentially infinite sequence. In this paper I discuss the systematical reasons why in Kant's philosophy this identification is impossible.
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  30.  2
    Gödel, Mathematics, and Possible Worlds.Mark van Atten & Mark Atten - 2001 - In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag. pp. 355-363.
  31.  2
    Gödel and German Idealism.Mark van Atten - unknown
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  32.  2
    Intuitionistic interpretations of the hypothetical judgement.Mark van Atten - unknown
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  33.  2
    Why did Kurt Gödel turn to transcendental idealism?Mark van Atten - unknown
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  34.  30
    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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  35. Construction and Constitution in Mathematics.Mark van Atten & Mark Atten - 2010 - In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag. pp. 43-90.
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  36. 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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  37. 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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  38. 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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  39. 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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  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.  1
    Brouwer meets Husserl. On the Phenomenology of Choice Sequences.Mark van Atten (ed.) - 2006 - 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? The 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. (...)
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  42. Further intuitionistic comments.Mark van Atten - unknown
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  43. Gödel's philosophical developments.Mark Van Atten & Juliette Kennedy - 2003 - Bulletin of Symbolic Logic 9:470-92.
     
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  44. On the philosophical development of Kurt Gödel.Mark van Atten & Juliette Kennedy - 2010 - In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: essays for his centennial. Association for Symbolic Logic.
     
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  45. Some closing comments.Mark van Atten - unknown
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  46.  29
    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.
  47.  30
    Intuitionism as Phenomenology.Mark van Atten - unknown
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  48.  39
    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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  49.  20
    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.  19
    Dummett's objection to the ontological route to intuitionistic logic: a rejoinder.Mark van Atten - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 65 (6):725-742.
    ABSTRACT In ‘The philosophical basis of intuitionistic logic’, Michael Dummett discusses two routes towards accepting intuitionistic rather than classical logic in number theory, one meaning-theoretical and the other ontological. He concludes that the former route is open, but the latter is closed. I reconstruct Dummett's argument against the ontological route and argue that it fails. Call a procedure ‘investigative’ if that in virtue of which a true proposition stating its outcome is true exists prior to the execution of that procedure; (...)
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