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  1. 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.
  • Syntactic Reduction in Husserl’s Early Phenomenology of Arithmetic.Mirja Hartimo & Mitsuhiro Okada - 2016 - Synthese 193 (3):937-969.
    The paper traces the development and the role of syntactic reduction in Edmund Husserl’s early writings on mathematics and logic, especially on arithmetic. The notion has its origin in Hermann Hankel’s principle of permanence that Husserl set out to clarify. In Husserl’s early texts the emphasis of the reductions was meant to guarantee the consistency of the extended algorithm. Around the turn of the century Husserl uses the same idea in his conception of definiteness of what he calls “mathematical manifolds.” (...)
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  • Peirce and Diagrams: Two Contributors to an Actual Discussion Review Each Other.Frederik Stjernfelt & Ahti-Veikko Pietarinen - 2015 - Synthese 192 (4):1073-1088.
    The following two review papers have a common origin. Pietarinen’s book Signs of Logic and Stjernfelt’s book Diagrammatology were both published in the same Synthese Library Series being published by Springer. The two books also share the common topic of diagrammatic reasoning in Charles Peirce’s work. Beginning in a conference Applying Peirce held in Helsinki in conjunction with the World Congress of Semiotics in June 2007, two authors have commented upon these books under the headline of Synthese Library Book Session (...)
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  • Toward a Phenomenological Epistemology of Mathematical Logic.Manuel Isaac - 2018 - Synthese 195 (2):863-874.
    This paper deals with Husserl’s idea of pure logic as it is coined in the Logical Investigations. First, it exposes the formation of pure logic around a conception of completeness ; then, it presents intentionality as the keystone of such a structuring ; and finally, it provides a systematic reconstruction of pure logic from the semiotic standpoint of intentionality. In this way, it establishes Husserlian pure logic as a phenomenological epistemology of mathematical logic.
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  • 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 An Unpublished Manuscript From the Husserl-Archives.Carlo Ierna - 2011 - Husserl Studies 27 (3):217-226.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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  • Husserl on Completeness, Definitely.Mirja Hartimo - 2018 - Synthese 195 (4):1509-1527.
    The paper discusses Husserl’s notion of definiteness as presented in his Göttingen Mathematical Society Double Lecture of 1901 as a defense of two, in many cases incompatible, ideals, namely full characterizability of the domain, i.e., categoricity, and its syntactic completeness. These two ideals are manifest already in Husserl’s discussion of pure logic in the Prolegomena: The full characterizability is related to Husserl’s attempt to capture the interconnection of things, whereas syntactic completeness relates to the interconnection of truths. In the Prolegomena (...)
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  • 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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  • Husserl and Gödel’s Incompleteness Theorems.Mirja Hartimo - 2017 - Review of Symbolic Logic 10 (4):638-650.
    The paper examines Husserl’s interactions with logicians in the 1930s in order to assess Husserl’s awareness of Gödel’s incompleteness theorems. While there is no mention about the results in Husserl’s known exchanges with Hilbert, Weyl, or Zermelo, the most likely source about them for Husserl is Felix Kaufmann (1895–1949). Husserl’s interactions with Kaufmann show that Husserl may have learned about the results from him, but not necessarily so. Ultimately Husserl’s reading marks on Friedrich Waismann’s Einführung in das mathematische Denken: die (...)
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  • 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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  • 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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  • 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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