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  1. Juliette Kennedy, Mark van Atten & Mark Atten (2015). On the Philosophical Development of Kurt Gödel. In Juliette Kennedy, Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer International Publishing
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  2. Mark van Atten & Mark Atten (2015). Two Draft Letters From Gödel on Self-Knowledge of Reason. In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer International Publishing 255-261.
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  3.  46
    Mark Van Atten & Juliette Kennedy (2003). On the Philosophical Development of Kurt Gödel. Bulletin of Symbolic Logic 9 (4):425-476.
  4. Mark van Atten (forthcoming). The Development of Intuitionistic Logic. 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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  5.  14
    M. van Atten (2013). 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] Philosophia Mathematica 21 (1):115-123.
  6.  39
    Markus Sebastiaan Paul Rogier van Atten (2007). Brouwer Meets Husserl: On the Phenomenology of Choice Sequences. 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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  7.  11
    Mark Van Atten, Dirk van Dalen & Richard Tieszen (2002). Brouwer and Weyl: The Phenomenology and Mathematics of the Intuitive Continuumt. Philosophia Mathematica 10 (2):203-226.
  8.  20
    Mark Van Atten, On Brouwer.
    "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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  9.  60
    Mark van Atten (2008). Thomas Ryckman: The Reign of Relativity. Philosophy in Physics 1915–1925. [REVIEW] Husserl Studies 24 (1):73-78.
  10.  49
    Mark van Atten, Dirk van Dalen & And Richard Tieszen (2002). Brouwer and Weyl: The Phenomenology and Mathematics of the Intuitive Continuumt. 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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  11.  12
    Juliette Kennedy & Mark van Atten (2004). Gödel's Modernism: On Set-Theoretic Incompleteness. Graduate Faculty Philosophy Journal 25 (2):289--349.
  12.  8
    Mark Van Atten & Göran Sundholm, The Proper Explanation of Intuitionistic Logic: On Brouwer's Demonstration of the Bar Theorem.
    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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  13.  9
    Mark van Atten (2005). Edmund Husserl, Logik. Vorlesung 1902/03, hg. von Elisabeth Schuhmann. Husserl Studies 21 (2):145-148.
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  14.  30
    Mark Van Atten, Kant and Real Numbers.
    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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  15.  2
    Mark Van Atten, The Development of Intuitionistic Logic.
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  16.  12
    M. van Atten (2006). Two Draft Letters From Godel on Self-Knowledge of Reason. 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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  17. Robert Tragesser, Mark van Atten & Mark Atten (2015). Mysticism and Mathematics: Brouwer, Gödel, and the Common Core Thesis. In Robert Tragesser, Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer International Publishing
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  18.  12
    Johannes Daubert, Mark van Atten & Karl Schuhmann (2004). Johannes Dauberts Notizen Zu Husserls Mathematisch-Philosophischen Übungen Vom SS 1905. New Yearbook for Phenomenology and Phenomenological Philosophy 4 (1):288-317.
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  19.  22
    Mark van Atten (2003). Brouwer, as Never Read by Husserl. 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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  20.  39
    Mark van Atten (2011). A Note on Leibniz's Argument Against Infinite Wholes. British Journal for the History of Philosophy 19 (1):121-129.
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  21.  30
    Gian-Carlo Rota & Mark van Atten (2008). Lectures on Being and Time (1998). New Yearbook for Phenomenology and Phenomenological Philosophy 8 (1):225-319.
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  22.  42
    Mark van Atten (2001). Gödel, Mathematics, and Possible Worlds. Axiomathes 12 (3-4):355-363.
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  23.  21
    Mark van Atten (2010). Construction and Constitution in Mathematics. 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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  24.  9
    Mark Van Atten, Intuitionism as Phenomenology.
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  25.  2
    Mark Van Atten, Göran Sundholm, Michel Bourdeau & Vanessa Van Atten (2014). « Que les Principes de la Logique Ne Sont Pas Fiables » : Nouvelle Traduction Française Annotée Et Commentée de l'Article de 1908 de L. E. J. Brouwer. [REVIEW] Revue d'Histoire des Sciences 67 (2):257.
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  26.  16
    Mark Van Atten, Different Times: Kant and Brouwer on Real Numbers.
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  27.  15
    Mark Van Atten, On the Fulfillment of Categorial Intentions.
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  28.  11
    Mark van Atten (2012). The Adventure of Reason. Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900–1940. History and Philosophy of Logic 33 (2):191-193.
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  29.  27
    Mark van Atten & Dirk van Dalen (2002). Arguments for the Continuity Principle. Bulletin of Symbolic Logic 8 (3):329-347.
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  30.  30
    Mark van Atten (2005). Edmund Husserl, Logik. Vorlesung 1902/03, Hg. Von Elisabeth Schuhmann. Husserl Studies 21 (2):145-148.
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  31.  7
    Mark Van Atten & Juliette Kennedy (2009). Göodel's Logic. In Dov Gabbay (ed.), The Handbook of the History of Logic. Elsevier 449-509.
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  32.  14
    Mark van Atten & Karl Schuhmann (2004). Introduction Johannes Daubert's Transcript of Husserl's Mathematical-Philosophical Exercises (Summer Semester 1905). New Yearbook for Phenomenology and Phenomenological Philosophy 4:284-287.
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  33.  9
    Mark Van Atten, Phenomenology and Transcendental Argument in Mathematics: The Case of Brouwer's Bar Theorem.
    On the intended interpretation of intuitionistic logic, Heyting's Proof Interpretation, a proof of a proposition of the form p -> q consists in a construction method that transforms any possible proof of p into a proof of q. This involves the notion of the totality of all proofs in an essential way, and this interpretation has therefore been objected to on grounds of impredicativity (e.g. Gödel 1933). In fact this hardly ever leads to problems as in proofs of implications usually (...)
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  34.  16
    M. van Atten (2002). Why Husserl Should Have Been a Strong Revisionist in Mathematics. 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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  35.  20
    Mark van Atten (2002). The Irreflexivity of Brouwer's Philosophy. 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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  36.  7
    Mark van Atten & Mark Atten (2015). Monads and Sets: On Gödel, Leibniz, and the Reflection Principle. In Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer International Publishing
    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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  37.  6
    Mark van Atten (2010). 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] Philosophiques 37 (1):262-265.
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  38.  2
    Mark van Atten (2002). Brouwer’s Argument for the Unity of Scientific Theories. 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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  39.  5
    Mark van Atten (2003). Author's Notice. New Yearbook for Phenomenology and Phenomenological Philosophy 3:335-336.
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  40.  7
    Mark Van Atten & Göran Sundholm, The Proper Interpretation of Intuitionistic Logic.
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  41.  5
    Mark van Atten (2011). 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] Philosophiques 38 (2):623-626.
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  42.  6
    Mark Van Atten, Gödel and Platonism.
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  43.  13
    Mark van Atten (2005). On Gödel's Awareness of Skolem's Helsinki Lecture. 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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  44.  7
    Mark Van Atten, The Interpretation of Ex Falso.
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  45.  4
    Mark van Atten (2004). Hesseling Dennis E.. 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] Bulletin of Symbolic Logic 10 (3):423-427.
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  46.  4
    Mark van Atten (2004). Gödel's Modernism. Graduate Faculty Philosophy Journal 25 (2):289-349.
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  47.  7
    Mark Van Atten, Monads and Sets: On Leibniz, Gödel, and the Reflection Principle.
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  48.  12
    Mark van Atten (2003). Review of C. O. Hill and G. E. Rosado Haddock, Husserl or Frege? Meaning, Objectivity, and Mathematics. [REVIEW] Philosophia Mathematica 11 (2):241-244.
  49.  3
    Mark Van Atten (2004). Brouwer and the Hypothetical Judgement. Second Thoughts on John Kuiper's Ideas and Explorations: Brouwer's Road to Intuitionism. Revue Internationale de Philosophie 58 (4):501-516.
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  50.  12
    Mark van Atten, Luitzen Egbertus Jan Brouwer. Stanford Encyclopedia of Philosophy.
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