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  1. Marcus Giaquinto. Visual Thinking in Mathematics: An Epistemological Study. [REVIEW]Jeremy Avigad - 2008 - 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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  2. The Phenomenological Spring: Husserl and the Göttingen Circle.Kimberly Baltzer-Jaray & Jeff Mitscherling - 2012 - Symposium: Canadian Journal of Continental Philosophy/Revue canadienne de philosophie continentale 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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  3. A Brentanian Philosophy of Arithmetic.D. Bell - 1989 - Brentano Studien 2:139-44.
  4. 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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  5. 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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  6. 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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  7. Husserl on the 'Totality of All Conceivable Arithmetical Operations'.Stefania Centrone - 2006 - 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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  8. Catégories formelles, nombres et conceptualisme. La première philosophie de l’arithmétique de Husserl.Arkadiusz Chrudzimski - 2009 - 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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  9. Husserl on Geometry and Spatial Representation.Jairo 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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  10. Husserl and Hilbert on Completeness, Still.Jairo Jose da Silva - forthcoming - Synthese:1-23.
    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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  11. Beyond Leibniz : Husserl's Vindication of Symbolic Knowledge.Jairo José da Silva - 2010 - In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer.
  12. Husserl's Two Notions Of Completeness.Jairo josé Da Silva - 2000 - 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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  13. Husserl Between Formalism and Intuitionism.James Dodd - 2007 - In Luciano Boi, Pierre Kerszberg & Frédéric Patras (eds.), Rediscovering Phenomenology: Phenomenological Essays on Mathematical Beings, Physical Reality, Perception and Consciousness (Phaenomenologica) (English and French Edition). Springer. pp. 267-308.
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  14. 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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  15. Arend Heyting and Phenomenology: Is the Meeting Feasible?Miriam Franchella - 2007 - 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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  16. Mark Van Atten. Brouwer Meets Husserl: On the Phenomenology of Choice Sequences.Miriam Franchella - 2007 - Philosophia Mathematica 16 (2):276-281.
    This book summarizes the intense research that the author performed for his Ph.D. thesis , revised and with the addition of an intuitionistic critique of Husserl's concept of number. His starting point consisted of a double conviction: 1) Brouwerian intuitionism is a valid way of doing mathematics but is grounded on a weak philosophy; 2) Husserlian phenomenology can provide a suitable philosophical ground for intuitionism. In order to let intuitionism and phenomenology match, he had to solve in general two problems: (...)
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  17. Review of Dr. E. Husserl's Philosophy of Arithmetic. [REVIEW]Gottlob Frege - 1977 - In Jitendranath Mohanty (ed.), Mind. M. Nijhoff. pp. 6--21.
  18. Mind, Meaning and Mathematics. Essays on the Philosophy of Husserl and Frege.L. Haaparanta (ed.) - 1994 - Kluwer Academic Publishers.
  19. On the Semantics of Mathematical Statements/Sobre a Semântica Dos Enunciados Matemáticos.Guillermo Haddock - 2007 - Manuscrito 30 (2):317-340.
    Husserl developed – independently of Frege – a semantics of sense and reference. There are, however, some important differences, specially with respect to the references of statements. According to Husserl, an assertive sentence refers to a state of affairs, which was its basis what he called a situation of affairs. Situations of affairs could also be considered as an alternative referent for statements on their own right, although for Husserl they were simply a sort of referential basis. Both Husserlian states (...)
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  20. Husserl's Philosophy of Mathematics: Its Origin and Relevance. [REVIEW]Guillermo E. Rosado Haddock - 2006 - 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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  21. Idealization in Mathematics: Husserl and Beyond.Guillermo E. Rosado Haddock - 2004 - 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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  22. Why and How Platonism?Guillermo Rosado Haddock - 2007 - Logic Journal of the IGPL 15 (5-6):621-636.
    Probably the best arguments for Platonism are those directed against its rival philosophies of mathematics. Frege's arguments against formalism, Gödel's arguments against constructivism and those against the so-called syntactic view of mathematics, and an argument of Hodges against Putnam are expounded, as well as some arguments of the author. A more general criticism of Quine's views follows. The paper ends with some thoughts on mathematics as a sort of Platonism of structures, as conceived by Husserl and essentially endorsed by the (...)
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  23. Idealization in Mathematics: Husserl and Beyond.Guillermo Rosado Haddock - 2004 - Poznan Studies in the Philosophy of the Sciences and the Humanities 82:245-252.
    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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  24. 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]M. Hartimo - 2010 - Philosophia Mathematica 18 (3):344-349.
    (No abstract is available for this citation).
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  25. From Geometry to Phenomenology.Mirja Hartimo - 2008 - 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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  26. Towards Completeness: Husserl on Theories of Manifolds 1890–1901.Mirja Hartimo - 2007 - Synthese 156 (2):281-310.
    Husserl’s notion of definiteness, i.e., completeness is crucial to understanding Husserl’s view of logic, and consequently several related philosophical views, such as his argument against psychologism, his notion of ideality, and his view of formal ontology. Initially Husserl developed the notion of definiteness to clarify Hermann Hankel’s ‘principle of permanence’. One of the first attempts at formulating definiteness can be found in the Philosophy of Arithmetic, where definiteness serves the purpose of the modern notion of ‘soundness’ and leads Husserl to (...)
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  27. Mathematical Roots of Phenomenology: Husserl and the Concept of Number.Mirja Hartimo - 2006 - 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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  28. 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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  29. Frege's Attack on Husserl and Cantor.Claire Oritz Hill - 1994 - The Monist 77 (3):345-357.
  30. Husserl on Axiomatization and Arithmetic.Claire Ortiz Hill - 2010 - In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer.
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  31. Husserl and Jacob Klein.Burt C. Hopkins - 2016 - The European Legacy 21 (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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  32. Lecture on the Concept of Number (Ws 1889/90).Edmund Husserl - 2005 - 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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  33. Early Writings in the Philosophy of Logic and Mathematics.Edmund Husserl - 1994 - 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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  34. On the Concept of Number: Psychological Analysis.Edmund Husserl - 1972 - Philosophia Mathematica (1):44-52.
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  35. 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.
  36. Husserl’s Philosophy of Arithmetic in Reviews.Carlo Ierna - 2013 - 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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  37. Stefania Centrone: Logic and Philosophy of Mathematics in the Early Husserl. [REVIEW]Carlo Ierna - 2013 - Husserl Studies 29 (3):251-253.
  38. 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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  39. 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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  40. 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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  41. Edmund Husserl, Philosophy of Arithmetic, Translated by Dallas Willard.Carlo Ierna - 2008 - Husserl Studies 24 (1):53-58.
  42. The Beginnings of Husserl's Philosophy. Part 2: Mathematical and Philosophical Background.Carlo Ierna - 2006 - 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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  43. The Beginnings of Husserl's Philosophy. Part 1: From "Über den Begriff der Zahl" to "Philosophie der Arithmetik".Carlo Ierna - 2005 - New Yearbook for Phenomenology and Phenomenological Philosophy 5:1-56.
    The article examines the development of Husserl’s early philosophy from his Habilitationsschrift to the Philosophie der Arithmetik . An attempt will be made at reconstructing the lost Habilitationsschrift . 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 of these texts to illustrate the changes in Husserl’s position before and after February 1890. This date is (...)
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  44. Husserl and the Infinite.Carlo Ierna - 2003 - Studia Phaenomenologica 3 (1):179-192.
    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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  45. 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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  46. 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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  47. Geometry and Spatial Intuition: A Genetic Approach.Rene Jagnow - unknown
    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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  48. 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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  49. Review of Dr. E. Husserl's Philosophy of Arithmetic. [REVIEW]E. W. Kluge - 1972 - Mind 81 (323):321 - 337.
  50. I.—Review of Dr. E. Husserl's Philosophy of Arithmetic. [REVIEW]E. W. Kluge - 1972 - Mind 81 (323):321-337.
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