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  1. Kimberly Baltzer-Jaray & Jeff Mitscherling (2012). The Phenomenological Spring: Husserl and the Göttingen Circle. Symposium 16 (2):1-19.
    The article discusses research work of Heinrich Hofmann, who has completed doctoral studies in mathematics under Karl Weierstrass in Berlin. His first book "Philosophy of Arithmetic: Psychological and Logical Investigations With Supplementary Texts From 1887-1901" contains his thesis "In the Concept of Number: Psychological Analyses" completed in the guidance of Weierstrass.
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  2. Robert Brisart (2012). True Objects and Fulfilments Under Assumption in the Young Husserl. Axiomathes 22 (1):75-89.
    In the year 1894, Husserl had not been already contaminated by Bolzano’s realism. It was then that he conceived a theory of assumptions in order to “save an existence” for mathematical objects. Here we would like to explore this theory and show in what way it represented a convincing alternative to realistic ontology and its counterpart: the correspondence theory of truth. However, as soon as he designed it, Husserl shoved away all the implications for his theory of assumptions, and merely (...)
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  3. Stefania Centrone (2006). Husserl on the 'Totality of All Conceivable Arithmetical Operations'. History and Philosophy of Logic 27 (3):211-228.
    In the present paper, we discuss Husserl's deep account of the notions of ?calculation? and of arithmetical ?operation? which is found in the final chapter of the Philosophy of Arithmetic, arguing that Husserl is ? as far as we know ? the first scholar to reflect seriously on and to investigate the problem of circumscribing the totality of computable numerical operations. We pursue two complementary goals, namely: (i) to provide a formal reconstruction of Husserl's intuitions, and (ii) to demonstrate ? (...)
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  4. Arkadiusz Chrudzimski (2009). Catégories formelles, nombres et conceptualisme. La première philosophie de l’arithmétique de Husserl. Philosophiques 36 (2):427-445.
    Résumé -/- Dans son premier livre (Philosophie de l’arithmétique 1891), Husserl élabore une très intéressante philosophie des mathématiques. Les concepts mathématiques sont interprétés comme des concepts de « deuxième ordre » auxquels on accède par une réflexion sur nos opérations mentales de numération. Il s’ensuit que la vérité de la proposition : « il y a trois pommes sur la table » ne consiste pas dans une relation mythique quelconque avec la réalité extérieure au psychique (où le nombre trois doit (...)
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  5. Jairo da Silva (2012). Husserl on Geometry and Spatial Representation. Axiomathes 22 (1):5-30.
    Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of physical (...)
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  6. Jairo José da Silva (2010). Beyond Leibniz : Husserl's Vindication of Symbolic Knowledge. In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer.
  7. Jairo josé Da Silva (2000). Husserl's Two Notions Of Completeness. Synthese 125 (3):417-438.
    In this paper I discuss Husserl's solution of the problem of imaginary elements in mathematics as presented in the drafts for two lectures hegave in Göttingen in 1901 and other related texts of the same period,a problem that had occupied Husserl since the beginning of 1890, whenhe was planning a never published sequel to Philosophie der Arithmetik(1891). In order to solve the problem of imaginary entities Husserl introduced,independently of Hilbert, two notions of completeness (definiteness in Husserl'sterminology) for a formal axiomatic (...)
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  8. Miriam Franchella (2008). Mark Van Atten. Brouwer Meets Husserl: On the Phenomenology of Choice Sequences. Philosophia Mathematica 16 (2):276-281.
  9. Miriam Franchella (2007). Arend Heyting and Phenomenology: Is the Meeting Feasible? Bulletin d'Analyse Phénoménologique (2).
    La littérature témoigne d’une tendance croissante à soutenir l’intuitionisme par la phénoménologie. Le disciple de Brouwer Arend Heyting est considéré comme un précurseur de cette tendance, parce qu’il usait d’une terminologie phénoménologique en vue de définir la négation intuitioniste, en élaborant la première logique intuitioniste. Dans cet article, l’auteur tente d’explorer — en référence aux matériaux inédits conservés aux Archives Heyting — ce qui, dans la pensée de Heyting, est compatible avec la phénoménologie. Dans la conclusion, l’auteur suggère que Heyting (...)
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  10. Gottlob Frege & E. W. Kluge (1972). Review of Dr. E. Husserl's Philosophy of Arithmetic. [REVIEW] Mind 81 (323):321-337.
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  11. Guillermo E. Rosado Haddock (2006). Husserl's Philosophy of Mathematics: Its Origin and Relevance. [REVIEW] Husserl Studies 22 (3):193-222.
    This paper offers an exposition of Husserl's mature philosophy of mathematics, expounded for the first time in Logische Untersuchungen and maintained without any essential change throughout the rest of his life. It is shown that Husserl's views on mathematics were strongly influenced by Riemann, and had clear affinities with the much later Bourbaki school.
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  12. Guillermo E. Rosado Haddock (2004). Idealization in Mathematics: Husserl and Beyond. Poznan Studies in the Philosophy of the Sciences and the Humanities 82 (1):245-252.
    Husserl's contributions to the nature of mathematical knowledge are opposed to the naturalist, empiricist and pragmatist tendences that are nowadays dominant. It is claimed that mainstream tendences fail to distinguish the historical problem of the origin and evolution of mathematical knowledge from the epistemological problem of how is it that we have access to mathematical knowledge.
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  13. M. Hartimo (2010). Stefania Centrone. Logic and Philosophy of Mathematics in the Early Husserl. Synthese Library 345. Dordrecht: Springer, 2010. Pp. Xxii + 232. ISBN 978-90-481-3245-. [REVIEW] Philosophia Mathematica 18 (3):344-349.
    (No abstract is available for this citation).
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  14. Mirja Hartimo (2006). Mathematical Roots of Phenomenology: Husserl and the Concept of Number. History and Philosophy of Logic 27 (4):319-337.
    The paper examines the roots of Husserlian phenomenology in Weierstrass's approach to analysis. After elaborating on Weierstrass's programme of arithmetization of analysis, the paper examines Husserl's Philosophy of Arithmetic as an attempt to provide foundations to analysis. The Philosophy of Arithmetic consists of two parts; the first discusses authentic arithmetic and the second symbolic arithmetic. Husserl's novelty is to use Brentanian descriptive analysis to clarify the fundamental concepts of arithmetic in the first part. In the second part, he founds the (...)
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  15. Mirja Helena Hartimo (2008). From Geometry to Phenomenology. Synthese 162 (2):225 - 233.
    Richard Tieszen [Tieszen, R. (2005). Philosophy and Phenomenological Research, LXX(1), 153–173.] has argued that the group-theoretical approach to modern geometry can be seen as a realization of Edmund Husserl’s view of eidetic intuition. In support of Tieszen’s claim, the present article discusses Husserl’s approach to geometry in 1886–1902. Husserl’s first detailed discussion of the concept of group and invariants under transformations takes place in his notes on Hilbert’s Memoir Ueber die Grundlagen der Geometrie that Hilbert wrote during the winter 1901–1902. (...)
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  16. Kai Hauser (forthcoming). Intuition and Its Object. Axiomathes:1-29.
    The view that mathematics deals with ideal objects to which we have epistemic access by a kind of perception (’intuition’) has troubled many thinkers. Using ideas from Husserl’s phenomenology, I will take a different look at these matters. The upshot of this approach is that there are non-material objects and that they can be recognized in a process very closely related to sense perception. In fact, the perception of physical objects may be regarded as a special case of this more (...)
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  17. Claire Oritz Hill (1994). Frege's Attack on Husserl and Cantor. The Monist 77 (3):345-357.
  18. Claire Ortiz Hill (2010). Husserl on Axiomatization and Arithmetic. In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer.
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  19. Edmund Husserl (2005). Lecture on the Concept of Number (Ws 1889/90). New Yearbook for Phenomenology and Phenomenological Philosophy 5:279-309 recto.
    Among the various lecture courses that Edmund Husserl held during his time as a Privatdozent at the University of Halle (1887-1901), there was one on "Ausgewählte Fragen aus der Philosophie der Mathematik" (Selected Questions from the Philosophy of Mathematics), which he gave twice, once in the WS 1889/90 and again in WS 1890/91. As Husserl reports in his letter to Carl Stumpf of February 1890, he lectured mainly on “spatial-logical questions” and gave an extensive critique of the Riemann-Helmholtz theories. Indeed, (...)
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  20. Edmund Husserl (1994). Early Writings in the Philosophy of Logic and Mathematics. Kluwer Academic Publishers.
    This book makes available to the English reader nearly all of the shorter philosophical works, published or unpublished, that Husserl produced on the way to the phenomenological breakthrough recorded in his Logical Investigations of 1900-1901. Here one sees Husserl's method emerging step by step, and such crucial substantive conclusions as that concerning the nature of Ideal entities and the status the intentional `relation' and its `objects'. Husserl's literary encounters with many of the leading thinkers of his day illuminates both the (...)
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  21. Edmund Husserl (1972). On the Concept of Number: Psychological Analysis. Philosophia Mathematica (1):44-52.
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  22. Carlo Ierna (2013). Husserl’s Philosophy of Arithmetic in Reviews. The New Yearbook for Phenomonology and Phenomenological Philosophy:198-242.
    This present collection of (translations of) reviews is intended to help obtain a more balanced picture of the reception and impact of Edmund Husserl’s first book, the 1891 Philosophy of Arithmetic. One of the insights to be gained from this non-exhaustive collection of reviews is that the Philosophy of Arithmetic had a much more widespread reception than hitherto assumed: in the present collection alone there already are fourteen, all published between 1891 and 1895. Three of the reviews appeared in mathematical (...)
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  23. Carlo Ierna (2013). Stefania Centrone: Logic and Philosophy of Mathematics in the Early Husserl. [REVIEW] Husserl Studies 29 (3):251-253.
  24. Carlo Ierna (2012). Husserl's Psychology of Arithmetic. Bulletin d'Analyse Phénoménologique 8 (1):97-120.
    In 1913, in a draft for a new Preface for the second edition of the Logical Investigations, Edmund Husserl reveals to his readers that "The source of all my studies and the first source of my epistemological difficul­ties lies in my first works on the philosophy of arithmetic and mathematics in general", i.e. his Habilitationsschrift and the Philosophy of Arithmetic: "I carefully studied the consciousness constituting the amount, first the collec­tive consciousness (consciousness of quantity, of multiplicity) in its simplest and (...)
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  25. Carlo Ierna (2012). La notion husserlienne de multiplicité : au-delà de Cantor et Riemann. Methodos. Savoirs Et Textes 12 (12).
    The concept of a Mannigfaltigkeit in Husserl has been given various interpretations, due to its shifting role in his works. Many authors have been misled by this term, placing it in the context of Husserl’s early period in Halle, while writing the Philosophy of Arithmetic, as a friend and colleague of Georg Cantor.Yet at the time, Husserl distanced himself explicitly from Cantor’s definition and rather took Bernhard Riemann as example, having studied and lectured extensively on Riemann’s theories of space. Husserl’s (...)
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  26. Carlo Ierna (2011). Der Durchgang Durch Das Unmögliche . An Unpublished Manuscript From the Husserl-Archives. Husserl Studies 27 (3):217-226.
    The article introduces and discusses an unpublished manuscript by Edmund Husserl, conserved at the Husserl-Archives Leuven with signature K I 26, pp. 73a–73b. The article is followed by the text of the manuscript in German and in an English translation. The manuscript, titled “The Transition through the Impossible” ( Der Durchgang durch das Unmögliche ), was part of the material Husserl used for his 1901 Doppelvortrag in Göttingen. In the manuscript, the impossible is characterized as the “sphere of objectlessness” ( (...)
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  27. Carlo Ierna (2008). Edmund Husserl, Philosophy of Arithmetic, Translated by Dallas Willard. Husserl Studies 24 (1):53-58.
  28. Carlo Ierna (2006). The Beginnings of Husserl's Philosophy. Part 2: Mathematical and Philosophical Background. New Yearbook for Phenomenology and Phenomenological Philosophy 6 (1):23-71.
    The article examines the development of Husserl’s early philosophy from his Habilitationsschrift (1887) to the Philosophie der Arithmetik (1891). -/- An attempt will be made at reconstructing the lost Habilitationsschrift (of which only the first chapter survives, which we know as Über den Begriff der Zahl). The examined sources show that the original version of the Habilitationsschrift was by far broader than the printed version, and included most topics of the PA. -/- The article contains an extensive and detailed comparison (...)
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  29. Carlo Ierna (2005). The Beginnings of Husserl's Philosophy. Part 1: From "Über den Begriff der Zahl" to "Philosophie der Arithmetik&Quot;. New Yearbook for Phenomenology and Phenomenological Philosophy 5:1-56.
    The article examines the development of Husserl’s early philosophy from his Habilitationsschrift (1887) to the Philosophie der Arithmetik (1891). -/- An attempt will be made at reconstructing the lost Habilitationsschrift (of which only the first chapter survives, which we know as Über den Begriff der Zahl). The examined sources show that the original version of the Habilitationsschrift was by far broader than the printed version, and included most topics of the PA. -/- The article contains an extensive and detailed comparison (...)
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  30. Carlo Ierna (2003). Husserl and the Infinite. Studia Phaenomenologica 3 (1-2):179-194.
    In the article Husserl’s view of the infinite around 1890 is analysed. I give a survey of his mathematical background and other important influences (especially Bolzano). The article contains a short exposition on Husserl's distinction between proper and symbolic presentations in the "Philosophie der Arithmetik" and between finite and infinite symbolic collections. Subsequently Husserl’s conception of surrogate presentations in his treatise "Zur Logik der Zeichen (Semiotik)" is discussed. In this text Husserl gives a detailed account of infinity, using surrogate presentations. (...)
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  31. René Jagnow, Geometry and Spatial Intuition: A Genetic Approach.
    In this thesis, I investigate the nature of geometric knowledge and its relationship to spatial intuition. My goal is to rehabilitate the Kantian view that Euclid's geometry is a mathematical practice, which is grounded in spatial intuition, yet, nevertheless, yields a type of a priori knowledge about the structure of visual space. I argue for this by showing that Euclid's geometry allows us to derive knowledge from idealized visual objects, i.e., idealized diagrams by means of non-formal logical inferences. By developing (...)
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  32. E. W. Kluge (1972). Review of Dr. E. Husserl's Philosophy of Arithmetic. [REVIEW] Mind 81 (323):321 - 337.
  33. Mary Leng (2002). Claire Ortiz Hill and Guillenno E. Rosado Haddock, Husserl or Frege? Meaning, Objectivity, and Mathematics Reviewed By. Philosophy in Review 22 (5):325-327.
  34. Dietrich Mahnke (1977). From Hilbert to Husserl: First Introduction to Phenomenology, Especially That of Formal Mathematics. Studies in History and Philosophy of Science Part A 8 (1):71-84.
  35. Ulrich Majer (1997). Husserl and Hilbert on Completeness. Synthese 110 (1):37-56.
  36. J. Philip Miller (1982). Numbers in Presence and Absence: A Study of Husserl's Philosophy of Mathematics. Distributors for the U.S. And Canada, Kluwer Boston, Inc..
    CHAPTER I THE EMERGENCE AND DEVELOPMENT OF HUSSERL'S 'PHILOSOPHY OF ARITHMETIC'. HISTORICAL BACKGROUND: WEIERSTRASS AND THE ARITHMETIZATION OF ANALYSIS In ...
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  37. Claire Ortiz Hill & Jairo Jose da Silva (eds.) (1997). The Road Not Taken. On Husserl's Philosophy of Logic and Mathematics. College Publications.
  38. Alberto Peruzzi (1989). Towards a Real Phenomenology of Logic. Husserl Studies 6 (1):1-24.
  39. E. Pivcevic (1967). Husserl Versus Frege. Mind 76 (302):155-165.
  40. Matteo Plebani (2011). Review of S. Centrone, Logic and Philosophy of Mathematics in the Early Husserl. [REVIEW] Dialectica 65 (3):477-482.
  41. Dominique Pradelle (2013). Vers une genèse a-subjective des idéalités mathématiques. Archives de Philosophie 2:239-270.
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  42. Hans Ruin (2011). Seeing Meaning: Frege and Derrida on Ideality and the Limits of Husserlian Intuitionism. [REVIEW] Husserl Studies 27 (1):63-81.
    The article seeks to challenge the standard accounts of how to view the difference between Husserl and Frege on the nature of ideal objects and meanings. It does so partly by using Derrida’s deconstructive reading of Husserl to open up a critical space where the two approaches can be confronted in a new way. Frege’s criticism of Husserl’s philosophy of mathematics (that it was essentially psychologistic) was partly overcome by the program of transcendental phenomenology. But the original challenge to the (...)
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  43. Denis Seron (2003). Identification et tautologie: l'identité chez Husserl et Wittgenstein. Revue Philosophique De Louvain 101 (4):593-609.
    Une question commune à la sixième Recherche logique de Husserl et au Tractatus de Wittgenstein est la question du statut des équations mathématiques, et plus largement des jugements d’identité. Elle est de savoir si le mathématicien énonce des propositions, pourvues comme telles d’un caractère de vérité possible, ou au contraire de simples règles de substitution destinées au calcul. Telle que l’a formulée Frege, cette question peut se résumer ainsi: existe-t- il une connaissance mathématique? Sur ce point, la position de Husserl (...)
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  44. R. Tieszen (2006). Revisiting Husserl's Philosophy of Arithmetic Edmund Husserl. Philosophy of Arithmetic: Psychological and Logical Investigations with Supplementary Texts From 1887–1901. Translated by Dallas Willard. Dordrecht: Kluwer, 2003. Pp. Lxiv + 513. ISBN 1-4020-1546-1. [REVIEW] Philosophia Mathematica 14 (1):112-130.
  45. Richard Tieszen (2005). Free Variation and the Intuition of Geometric Essences: Some Reflections on Phenomenology and Modern Geometry. Philosophy and Phenomenological Research 70 (1):153–173.
    Edmund Husserl has argued that we can intuit essences and, moreover, that it is possible to formulate a method for intuiting essences. Husserl calls this method 'ideation'. In this paper I bring a fresh perspective to bear on these claims by illustrating them in connection with some examples from modern pure geometry. I follow Husserl in describing geometric essences as invariants through different types of free variations and I then link this to the mapping out of geometric invariants in modern (...)
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  46. Richard Tieszen (2002). Gödel and the Intuition of Concepts. Synthese 133 (3):363 - 391.
    Gödel has argued that we can cultivate the intuition or perception of abstractconcepts in mathematics and logic. Gödel's ideas about the intuition of conceptsare not incidental to his later philosophical thinking but are related to many otherthemes in his work, and especially to his reflections on the incompleteness theorems.I describe how some of Gödel's claims about the intuition of abstract concepts are related to other themes in his philosophy of mathematics. In most of this paper, however,I focus on a central (...)
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  47. Richard Tieszen (1995). Mathematics. In Barry Smith & David Woodruff Smith (eds.), The Cambridge Companion to Husserl (Cambridge Companions to Philosophy). Cambridge University Press.
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  48. Richard Tieszen (1990). Frege and Husserl on Number. Ratio 3 (2):150-164.
  49. Richard Tieszen & Dorothy Leland (1989). Book Reviews. [REVIEW] Husserl Studies 6 (2):69-81.
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  50. Iulian D. Toader (2012). An Outline of Weylean Skepticism. In Concha Martínez Vidal (ed.), Proceedings of the 7th Conference of the Spanish Society for Logic, Methodology and Philosophy of Science.
    This paper introduces Weylean skepticism, the view that objectivity and intelligibility are opposite ideals of science, explains the motivation for it and the argument that justifies it. The paper indicates also a couple of ways in which this skepticism could be resisted.
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