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  1. A Few Historical-Critical Glances on Mathematical Ontology Through the Hermann Weyl and Edmund Husserl Works.Giuseppe Iurato - manuscript
    From the general history of culture, with a particular attention turned towards the personal and intellectual relationships between Hermann Weyl and Edmund Husserl, it will be possible to identify certain historical-critical moments from which a philosophical reflection concerning aspects of the ontology of mathematics may be carried out. In particular, a notable epistemological relevance of group theory methods will stand out.
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  2. Completeness, Categoricity and Imaginary Numbers: The Debate on Husserl.Víctor Aranda - 2020 - Bulletin of the Section of Logic 49 (2).
    Husserl's two notions of "definiteness" enabled him to clarify the problem of imaginary numbers. The exact meaning of these notions is a topic of much controversy. A "definite" axiom system has been interpreted as a syntactically complete theory, and also as a categorical one. I discuss whether and how far these readings manage to capture Husserl's goal of elucidating the problem of imaginary numbers, raising objections to both positions. Then, I suggest an interpretation of "absolute definiteness" as semantic completeness and (...)
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  3. Intuitionism in the Philosophy of Mathematics: Introducing a Phenomenological Account.Philipp Berghofer - 2020 - Philosophia Mathematica 28 (2):204-235.
    ABSTRACT The aim of this paper is to establish a phenomenological mathematical intuitionism that is based on fundamental phenomenological-epistemological principles. According to this intuitionism, mathematical intuitions are sui generis mental states, namely experiences that exhibit a distinctive phenomenal character. The focus is on two questions: what does it mean to undergo a mathematical intuition and what role do mathematical intuitions play in mathematical reasoning? While I crucially draw on Husserlian principles and adopt ideas we find in phenomenologically minded mathematicians such (...)
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  4. From Phenomenology to the Philosophy of the Concept: Jean Cavaillès as a Reader of Edmund Husserl.Jean-Paul Cauvin - 2020 - Hopos: The Journal of the International Society for the History of Philosophy of Science 10 (1):24-47.
    The article reconstructs Jean Cavaillès’s polemical engagement with Edmund Husserl’s phenomenological philosophy of mathematics. I argue that Cavaillès’s encounter with Husserl clarifies the scope and ambition of Cavaillès’s philosophy of the concept by identifying three interrelated epistemological problems in Husserl’s phenomenological method: (1) Cavaillès claims that Husserl denies a proper content to mathematics by reducing mathematics to logic. (2) This reduction obliges Husserl, in turn, to mischaracterize the significance of the history of mathematics for the philosophy of mathematics. (3) Finally, (...)
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  5. Skolem’s “Paradox” as Logic of Ground: The Mutual Foundation of Both Proper and Improper Interpretations.Vasil Penchev - 2020 - Epistemology eJournal (Elsevier: SSRN) 13 (19):1-16.
    A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather a metamathematical axiom about the relation of mathematics and reality. Its investigation needs philosophical (...)
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  6. All Science as Rigorous Science: The Principle of Constructive Mathematizability of Any Theory.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal 12 (12):1-15.
    A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather (...)
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  7. The Role of Intuition and Formal Thinking in Kant, Riemann, Husserl, Poincare, Weyl, and in Current Mathematics and Physics.Luciano Boi - 2019 - Kairos 22 (1):1-53.
    According to Kant, the axioms of intuition, i.e. space and time, must provide an organization of the sensory experience. However, this first orderliness of empirical sensations seems to depend on a kind of faculty pertaining to subjectivity, rather than to the encounter of these same intuitions with the real properties of phenomena. Starting from an analysis of some very significant developments in mathematical and theoretical physics in the last decades, in which intuition played an important role, we argue that nevertheless (...)
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  8. Phenomenological Ideas in the Philosophy of Mathematics. From Husserl to Gödel.Roman Murawski Thomas Bedürftig - 2018 - Studia Semiotyczne 32 (2):33-50.
    The paper is devoted to phenomenological ideas in conceptions of modern philosophy of mathematics. Views of Husserl, Weyl, Becker andGödel will be discussed and analysed. The aim of the paper is to show the influence of phenomenological ideas on the philosophical conceptions concerning mathematics. We shall start by indicating the attachment of Edmund Husserl to mathematics and by presenting the main points of his philosophy of mathematics. Next, works of two philosophers who attempted to apply Husserl’s phenomenological ideas to the (...)
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  9. Construction and Constitution in Mathematics.Mark Atten - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Springer Verlag.
    I argue that Brouwer’s notion of the construction of purely mathematical objects and Husserl’s notion of their constitution by the transcendental subject coincide. Various objections to Brouwer’s intuitionism that have been raised in recent phenomenological literature are addressed. Then I present objections to Gödel’s project of founding classical mathematics on transcendental phenomenology. The problem for that project lies not so much in Husserl’s insistence on the spontaneous character of the constitution of mathematical objects, or in his refusal to allow an (...)
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  10. Geometric and Intuitive Space in Husserl.Vincenzo Costa - 2017 - In Felice Masi & Maria Catena (eds.), The Changing Faces of Space. Springer Verlag.
    Moving from the reformulation of the meaning of geometry, achieved in the first half of the Nineteenth Century, which also implied a new definition of the relationship between formal and empirical understanding of the space, Husserl starts, since the Philosophy of arithmetic, a deep reflection on the definition of space, which would have led to a new philosophical theory of Euclidean geometry. Husserl took the view that the clarification of scientific concepts must be made back to the intuitive ground from (...)
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  11. Mathematics and Its Applications, A Transcendental-Idealist Perspective.Jairo Da Silva - 2017 - Springer.
    This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal science, mathematical ontology: what (...)
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  12. Husserl and Hilbert.Mirja Hartimo - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Springer Verlag.
    The paper examines Husserl’s phenomenology and Hilbert’s view of the foundations of mathematics against the backdrop of their lifelong friendship. After a brief account of the complementary nature of their early approaches, the paper focuses on Husserl’s Formale und transzendentale Logik viewed as a response to Hilbert’s “new foundations” developed in the 1920s. While both Husserl and Hilbert share a “mathematics first,” nonrevisionist approach toward mathematics, they disagree about the way in which the access to it should be construed: Hilbert (...)
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  13. Husserl and Jacob Klein.Burt Hopkins - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Springer Verlag.
    The article explores the relationship between the philosopher and historian of mathematics Jacob Klein’s account of the transformation of the concept of number coincident with the invention of algebra and Husserl’s early investigations of the origin of the concept of number and his late account of the Galilean impulse to mathematize nature. Klein’s research is shown to present the historical context for Husserl’s twin failures in the Philosophy of Arithmetic, to provide a psychological foundation for the proper concept of number (...)
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  14. The Brentanist Philosophy of Mathematics in Edmund Husserl’s Early Works.Carlo Ierna - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Springer Verlag. pp. 147-168.
    A common analysis of Edmund Husserl’s early works on the philosophy of logic and mathematics presents these writings as the result of a combination of two distinct strands of influence: on the one hand a mathematical influence due to his teachers is Berlin, such as Karl Weierstrass, and on the other hand a philosophical influence due to his later studies in Vienna with Franz Brentano. However, the formative influences on Husserl’s early philosophy cannot be so cleanly separated into a philosophical (...)
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  15. Husserl and Boole.Pierluigi Minari & Stefania Centrone - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Springer Verlag.
    We aim at clarifying to what extent the work of the English mathematician George Boole on the algebra of logic is taken into consideration and discussed in the work of early Husserl, focusing in particular on Husserl’s lecture “Über die neueren Forschungen zur deduktiven Logik” of 1895, in which an entire section is devoted to Boole. We confront Husserl’s representation of the problem-solving processes with the analysis of “symbolic reasoning” proposed by George Boole in the Laws of Thought and try (...)
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  16. Husserl and Weyl.Jairo Silva - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Springer Verlag.
    In this paper, I carry out a comparative study of the philosophical views of Edmund Husserl and Hermann Weyl on issues such as mathematical existence and mathematical intuition, the validity of classical logic, the concept of logical definiteness, the nature of symbolic mathematics, the role of mathematics in empirical science, the relation of scientific theories with perception, space representation and the philosophy of geometry, and intentional constitution in general. My main goal is not simply to assess the extent of Husserl’s (...)
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  17. Husserl and His Alter Ego Kant.Judson Webb - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Springer Verlag.
    Husserl’s lifelong interest in Kant eventually becomes a preoccupation in his later years when he finds his phenomenology in competition with Neokantianism for the title of transcendental philosophy. Some issues that Husserl is concerned with in Kant are bound up with the works of Lambert. Kant believed that the role played by principles of sensibility in metaphysics should be determined by a “general phenomenology” on which Lambert had written. Kant initially believed that man is capable only of symbolic cognition, not (...)
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  18. Paradox, Harmony, and Crisis in Phenomenology.Judson Webb - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Springer Verlag.
    Husserl’s first work formulated what proved to be an algorithmically complete arithmetic, lending mathematical clarity to Kronecker’s reduction of analysis to finite calculations with integers. Husserl’s critique of his nominalism led him to seek a philosophical justification of successful applications of symbolic arithmetic to nature, providing insight into the “wonderful affinity” between our mathematical thoughts and things without invoking a pre-established harmony. For this, Husserl develops a purely descriptive phenomenology for which he found inspiration in Mach’s proposal of a “universal (...)
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  19. Husserl and Hilbert on Completeness, Still.Jairo Jose da Silva - 2016 - Synthese 193 (6).
    In the first year of the twentieth century, in Gottingen, Husserl delivered two talks dealing with a problem that proved central in his philosophical development, that of imaginary elements in mathematics. In order to solve this problem Husserl introduced a logical notion, called “definiteness”, and variants of it, that are somehow related, he claimed, to Hilbert’s notions of completeness. Many different interpretations of what precisely Husserl meant by this notion, and its relations with Hilbert’s ones, have been proposed, but no (...)
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  20. Husserl and Jacob Klein.Burt C. Hopkins - 2016 - The European Legacy 21 (5-6):535-555.
    The article explores the relationship between the philosopher and historian of mathematics Jacob Klein’s account of the transformation of the concept of number coincident with the invention of algebra, together with Husserl’s early investigations of the origin of the concept of number and his late account of the Galilean impulse to mathematize nature. Klein’s research is shown to present the historical context for Husserl’s twin failures in the Philosophy of Arithmetic: to provide a psychological foundation for the proper concept of (...)
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  21. The Reception of Russell’s Paradox in Early Phenomenology and the School of Brentano: The Case of Husserl’s Manuscript A I 35α.Carlo Ierna - 2016 - In Guillermo E. Rosado Haddock (ed.), Husserl and Analytic Philosophy. De Gruyter. pp. 119-142.
    Edmund Husserl’s engagement with Bertrand Russell’s paradox stands in a continuum of reciprocal reception and discussions about impossible objects in the School of Brentano. Against this broader context, we will focus on Husserl’s discussion of Russell’s paradox in his manuscript A I 35α from 1912. This highly interesting and revealing manuscript has unfortunately remained unpublished, which probably explains the scant attention it has received. I will examine Husserl’s approach in A I 35α by relating it to earlier discussions of relevant (...)
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  22. The Shape of Things.Rajiv Kaushik - 2016 - Chiasmi International 18:313-331.
    This paper begins by pointing to an obvious difficulty in Merleau-Ponty’s late philosophy: undoing the decisive separation between linguistic connotation and the denotated, undoing the decisive separation between linguistic meaning and the sensible world. This difficulty demands that we understand how the sensible and the symbolic have a sort of spontaneous relation. How can this be? The history of this problem is then traced back to Husserl, and in particular to his The Origin of Geometry. For Husserl, ‘abstract geometry’ is (...)
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  23. Husserl’s Manuscript A I 35.Dieter Lohmar & Carlo Ierna - 2016 - In Guillermo E. Rosado Haddock (ed.), Husserl and Analytic Philosophy. De Gruyter. pp. 289-320.
    The following pages contain a partial edition of Husserl’s manuscript A I 35, pages 1a-28b. The first few pages are dated on May 1927 and are included mostly for completeness’ sake. The bulk of the manuscript convolute, however, is from 1912. Four pages of the convolute, 31a-34b, have been published as Beilage XII (210, 2–216, 2) in Hua XXXII. The manuscript was excluded from the text selection of Husserliana XXI3 based on its much later date of composition. A I 35/24a (...)
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  24. Mathematical Conception of Husserl’s Phenomenology.Seung-Ug Park - 2016 - Idealistic Studies 46 (2):183-197.
    In this paper, I have attempted to make the role of mathematical thinking clear in Husserl’s theory of sciences. Husserl believed that phenomenology could afford to provide a safe foundation for individual sciences. Hence, the first task of the project was reorganizing the system of sciences and to show the possibility of apodictic knowledge regarding the world. Husserl was inspired by the progress of mathematics at that time because mathematics is the most logical discipline and deals with abstract objects. It (...)
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  25. Intuition and Its Object.Kai Hauser - 2015 - Axiomathes 25 (3):253-281.
    The view that mathematics deals with ideal objects to which we have epistemic access by a kind of perception 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 universal (...)
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  26. Proof Phenomenon as a Function of the Phenomenology of Proving.Inês Hipólito - 2015 - Progress in Biophysics and Molecular Biology 119:360-367.
    Kurt Gödel wrote (1964, p. 272), after he had read Husserl, that the notion of objectivity raises a question: “the question of the objective existence of the objects of mathematical intuition (which, incidentally, is an exact replica of the question of the objective existence of the outer world)”. This “exact replica” brings to mind the close analogy Husserl saw between our intuition of essences in Wesensschau and of physical objects in perception. What is it like to experience a mathematical proving (...)
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  27. L'idée de la Logique Formelle Dans les Appendices VI À X du Volume 12 des Husserliana.Manuel Gustavo Isaac - 2015 - History and Philosophy of Logic 36 (4):321-345.
    Au terme des Prolégomènes, Husserl formule son idée de la logique pure en la structurant sur deux niveaux: l'un, supérieur, de la logique formelle fondé transcendantalement et d'un point de vue épistémologique par l'autre, inférieur, d'une morphologie des catégories. Seul le second de ces deux niveaux est traité dans les Recherches logiques, tandis que les travaux théoriques en logique formelle menés par Husserl à la même époque en paraissent plutôt indépendants. Cet article est consacré à ces travaux tels que recueillis (...)
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  28. The First Gestures of Knowledge.Pierre Kerszberg - 2014 - Tijdschrift Voor Filosofie 76 (2):277-306.
    Husserl credited Riemann for bringing the modern idea of “mathesis universalis‘ to its realization. Going beyond the logical ideal of a theory of all possible forms of theories, this paper explores the phenomenological sense of intrinsically physical geometry. Starting from Kant, how can we follow the thread of transcendental idealism in the search for the hidden presuppositions of this kind of geometry? This is achieved by reflecting on the paradigmatic experience of the earth at rest in our primary lifeworld.
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  29. Dummett and the Problem of Abstract Objects.George Duke - 2013 - Teorema: International Journal of Philosophy 32 (1):61-75.
    One major difficulty confronting attempts to clarify the epistemological and ontological status of abstract objects is determining the sense, if any, in which such entities may be characterised as mind and language independent. Our contention is that the tolerant reductionist position of Michael Dummett can be strengthened by drawing on Husserl's mature account of the constitution of ideal objects and mathematical objectivity. According to the Husserlian position we advocate, abstract singular terms pick out weakly mind-independent sedimented meaning-contents. These meaning-contents serve (...)
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  30. Stefania Centrone: Logic and Philosophy of Mathematics in the Early Husserl : Synthese Library 345, Springer, Dordrecht, 2010, Pp Xxii + 232, ISBN 978-90-481-3245-4. [REVIEW]Carlo Ierna - 2013 - Husserl Studies 29 (3):251-253.
  31. Husserl’s Philosophy of Arithmetic in Reviews.Carlo Ierna - 2013 - The New Yearbook for Phenomenology and Phenomenological Philosophy 12:198-242.
    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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  32. Vers une genèse a-subjective des idéalités mathématiques. Cavaillès critique de Husserl.Dominique Pradelle - 2013 - Archives de Philosophie 76 (2):239-270.
    In this paper our purpose is to explane and discuss the essential objections Cavaillès raised to Husserlian phenomenology in his last text “On Logic and Theory of Science”. In this text Cavaillès questioned the foundational status of cogito and the capacity of consciousness to produce new ideal objects.; and he replaced this capacity with an anonymous generating necessity that would be dialectical and would take place intin the ideal domains of objects. We have to determine if such objections question every (...)
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  33. The Phenomenological Spring: Husserl and the Göttingen Circle.Kimberly Baltzer-Jaray & Jeff Mitscherling - 2012 - 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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  34. True Objects and Fulfilments Under Assumption in the Young Husserl.Robert Brisart - 2012 - 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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  35. Husserl on Geometry and Spatial Representation.Jairo José da Silva - 2012 - 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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  36. La notion husserlienne de multiplicité : au-delà de Cantor et Riemann.Carlo Ierna - 2012 - Methodos 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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  37. Husserl's Psychology of Arithmetic.Carlo Ierna - 2012 - 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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  38. La notion husserlienne de multiplicité : au-delà de Cantor et Riemann.Carlo Ierna - 2012 - 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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  39. Wogegen wandte sich Husserl 1891?: Ein Beitrag zur neueren Rezeption des Verhältnisses von Husserl und Frege.Deodáth Zuh - 2012 - Husserl Studies 28 (2):95-120.
    Eine vollständige Darstellung von Edmund Husserls Verhältnis zu Gottlob Frege steht noch aus, so dass es nicht verwundert, einige Missverständnisse, dieses Verhältnis betreffend, im Umlauf zu finden. Selbst scheinbar längst überwundene systematische Dogmen tauchen wieder auf, so z.B. die Auffassung, dass Husserl nicht nur entscheidend von Gottlob Frege beeinflusst wurde, sondern darüber hinaus auch seine schärfste Frege-Kritik 1891 zurückgenommen habe. Mein Beitrag enthält eine überwiegend historisch vorgehende Entgegnung auf solche fälschlich vertretenen Ansichten wie sie sich auch in dem neu erschienenen (...)
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  40. Begründungen bei Bolzano und beim frühen Husserl.Stefania Centrone - 2011 - Zeitschrift für Philosophische Forschung 65 (1):5-27.
    Two hundred years ago Bernard Bolzano published a booklet on the philosophy of mathematics that is the first major step forward in this area since Pascal’s De l’esprit géométrique. Following Aristotelian lines Bolzano distinguishes in his opusculum two kinds of proofs, those that simply show that something is the case, and those that explain why something is the case. In his Wissenschaftslehre this contrast reappears as that between derivability and consecutivity . Husserl takes up some of Bolzano’s key concepts in (...)
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  41. Der Durchgang Durch Das Unmögliche . An Unpublished Manuscript From the Husserl-Archives.Carlo Ierna - 2011 - 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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  42. Logic and Philosophy of Mathematics in the Early Husserl - By Stefania Centrone.Matteo Plebani - 2011 - Dialectica 65 (3):477-482.
  43. Seeing Meaning: Frege and Derrida on Ideality and the Limits of Husserlian Intuitionism.Hans Ruin - 2011 - 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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  44. Beyond Leibniz : Husserl's Vindication of Symbolic Knowledge.Jairo José da Silva - 2010 - In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer.
  45. Stefania Centrone. Logic and Philosophy of Mathematics in the Early Husserl. Synthese Library 345. Dordrecht: Springer, 2010. Pp. Xxii + 232. ISBN 978-90-481-3245-4. [REVIEW]Mirja Hartimo - 2010 - Philosophia Mathematica 18 (3):344-349.
    It is beginning to be rather well known that Edmund Husserl, the founder of phenomenological philosophy, was originally a mathematician; he studied with Weierstrass and Kronecker in Berlin, wrote his doctoral dissertation on the calculus of variations, and was then a colleague of Cantor in Halle until he moved to the Göttingen of Hilbert and Klein in 1901. Much of Husserl’s writing prior to 1901 was about mathematics, and arguably the origin of phenomenology was in Husserl’s attempts to give philosophical (...)
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  46. Husserl on Axiomatization and Arithmetic.Claire Ortiz Hill - 2010 - In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer.
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  47. 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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  48. The Content and Meaning of the Transition From the Theory of Relations in Philosophy of Arithmetic to the Mereology of the Third Logical Investigation.Fotini Vassiliou - 2010 - Research in Phenomenology 40 (3):408-429.
    In the third Logical Investigation Husserl presents an integrated theory of wholes and parts based on the notions of dependency, foundation ( Fundierung ), and aprioricity. Careful examination of the literature reveals misconceptions regarding the meaning and scope of the central axis of this theory, especially with respect to its proper context within the development of Husserl's thought. The present paper will establish this context and in the process correct a number of these misconceptions. The presentation of mereology in the (...)
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  49. Marcus Giaquinto. Visual Thinking in Mathematics: An Epistemological Study. [REVIEW]Jeremy Avigad - 2009 - Philosophia Mathematica 17 (1):95-108.
    Published in 1891, Edmund Husserl's first book, Philosophie der Arithmetik, aimed to ‘prepare the scientific foundations for a future construction of that discipline’. His goals should seem reasonable to contemporary philosophers of mathematics: "…through patient investigation of details, to seek foundations, and to test noteworthy theories through painstaking criticism, separating the correct from the erroneous, in order, thus informed, to set in their place new ones which are, if possible, more adequately secured. 1"But the ensuing strategy for grounding mathematical knowledge (...)
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  50. La théorie des assomptions chez le jeune Husserl.Robert Brisart - 2009 - Philosophiques 36 (2):399-425.
    Afin de « sauver une existence » pour les objets dont il est question dans les représentations mathématiques, le jeune Husserl invente en 1894 une théorie des assomptions. Notre but est d’explorer cette théorie pour montrer en quoi elle constituait une alternative probante par rapport à l’ontologie réaliste et à la conception correspondantiste de la vérité. De celles-ci, pourtant, Husserl ne parviendra pas à se départir à l’époque, comme en témoigne la dichotomie qu’il opère entre la signification et la perception, (...)
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