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  1. 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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  • (1 other version)Logic and formal ontology.B. Smith - 1989 - In Barry Smith (ed.), Constraints on Correspondence. Hölder/Pichler/Tempsky. pp. 29-67.
    The current resurgence of interest in cognition and in the nature of cognitive processing has brought with it also a renewed interest in the early work of Husserl, which contains one of the most sustained attempts to come to grips with the problems of logic from a cognitive point of view. Logic, for Husserl, is a theory of science; but it is a theory which takes seriously the idea that scientific theories are constituted by the mental acts of cognitive subjects. (...)
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  • Mathematizing phenomenology.Jeffrey Yoshimi - 2007 - Phenomenology and the Cognitive Sciences 6 (3):271-291.
    Husserl is well known for his critique of the “mathematizing tendencies” of modern science, and is particularly emphatic that mathematics and phenomenology are distinct and in some sense incompatible. But Husserl himself uses mathematical methods in phenomenology. In the first half of the paper I give a detailed analysis of this tension, showing how those Husserlian doctrines which seem to speak against application of mathematics to phenomenology do not in fact do so. In the second half of the paper I (...)
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  • Husserl’s Arguments for Psychologism.Filippo Piovesan - 2022 - Axiomathes 32 (4):659-685.
    The question of the psychologism of the theory of number developed by Husserl in his Philosophy of Arithmetic has long been debated, but it cannot be considered fully resolved. In this paper, I address the issue from a new point of view. My claim is that in the Philosophy of Arithmetic, Husserl made, albeit indirectly, a series of arguments that are worth reconstructing and clarifying since they are useful in shedding some light on the psychologism issue. More specifically, I maintain (...)
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  • O desenvolvimento da teoria semiótica de Husserl de 1890 a 1901.Daniel Peluso Guilhermino - 2020 - Kriterion: Journal of Philosophy 61 (147):649-674.
    RESUMO O artigo tem por objetivo analisar a mudança no regime do signo que ocorreu na filosofia de Husserl entre os anos de 1890 e 1901. Para tanto, partimos da reconstrução da teoria do simbolismo apresentada em Sobre a Lógica dos Signos, de 1890, e analisamos a recepção de algumas de suas teses centrais em Investigações Lógicas, de 1901. Querse, com isso, sublinhar a relevância histórica deste pequeno tratado de 1890 para a fenomenologia madura de Husserl. Ver-se-á, específicamente, que a (...)
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  • Husserl’s Early Genealogy of the Number System.Thomas Byrne - 2019 - Meta: Research in Hermeneutics, Phenomenology, and Practical Philosophy 2 (11):408-428.
    This article accomplishes two goals. First, the paper clarifies Edmund Husserl’s investigation of the historical inception of the number system from his early works, Philosophy of Arithmetic and, “On the Logic of Signs (Semiotic)”. The article explores Husserl’s analysis of five historical developmental stages, which culminated in our ancestor’s ability to employ and enumerate with number signs. Second, the article reveals how Husserl’s conclusions about the history of the number system from his early works opens up a fusion point with (...)
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  • Manifold, Intuition, and Synthesis in Kant and Husserl.Burt C. Hopkins - 2013 - History of Philosophy & Logical Analysis 16 (1):264-307.
    The problem of ‘collective unity’ in the transcendental philosophies of Kant and Husserl is investigated on the basis of number’s exemplary ‘collective unity’. To this end, the investigation reconstructs the historical context of the conceptuality of the mathematics that informs Kant’s and Husserl’s accounts of manifold, intuition, and synthesis. On the basis of this reconstruction, the argument is advanced that the unity of number – not the unity of the ‘concept’ of number – is presupposed by each transcendental philosopher in (...)
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  • Lógica y ontología formal.Barry Smith - 2004 - In . Grupo de Acción Filosófica (Gaf), Buenos Aires.
    La lógica es para Husserl una ciencia de la ciencia, una ciencia de lo que todas las ciencias tienen en común respecto de sus modos de validación. De este modo, la lógica trata por un lado con leyes universales relacionadas con la verdad, la deducción, la verificación y la falsación; y, por otro lado, con leyes relacionadas con la teoría como tal, y con lo que produce la unidad teorética. Ambos tipos de leyes se refieren por una parte a las (...)
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  • Surrogates and Empty Intentions: Husserl’s “On the Logic of Signs” as the Blueprint for his First Logical Investigation.Thomas Byrne - 2017 - Husserl Studies 33 (3):211-227.
    This paper accomplishes two tasks. First, I examine in detail Edmund Husserl’s earliest philosophy of surrogates, as it is found in his 1890 “On the Logic of Signs ”. I analyze his psychological and logical investigations of surrogates, where the former is concerned with explaining how these signs function and the latter with how they do so reliably. His differentiation of surrogates on the basis of their genetic origins and degrees of necessity is discussed. Second, the historical importance of this (...)
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  • Husserl’s Early Semiotics and Number Signs: Philosophy of Arithmetic through the Lens of “On the Logic of Signs ”.Thomas Byrne - 2017 - Journal of the British Society for Phenomenology 48 (4):287-303.
    This paper demonstrates that Edmund Husserl’s frequently overlooked 1890 manuscript, “On the Logic of Signs,” when closely investigated, reveals itself to be the hermeneutical touchstone for his seminal 1891 Philosophy of Arithmetic. As the former comprises Husserl’s earliest attempt to account for all of the different kinds of signitive experience, his conclusions there can be directly applied to the latter, which is focused on one particular type of sign; namely, number signs. Husserl’s 1890 descriptions of motivating and replacing signs will (...)
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  • Burt C. Hopkins. The Origin of the Logic of Symbolic Mathematics: Edmund Husserl and Jacob Klein. Studies in Continental Thought. Bloomington: University of Indiana Press, 2011. ISBN 978-0-253-35671-0 (hbk). Pp. xxxi + 559. [REVIEW]Carlo Ierna - 2014 - Philosophia Mathematica 22 (2):249-262.
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  • Jean-Michel Salanskis. Philosophie des mathématiques. Problèmes & Controverses. Paris: Vrin, 2008. ISBN 978-2-7116-1988-7. Pp. 304. [REVIEW]André Lebel - 2014 - Philosophia Mathematica 22 (2):262-270.
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  • Husserl's Psychology of Arithmetic.Carlo Ierna - 2012 - Bulletin d'Analyse Phénoménologique 8:97-120.
    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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  • (1 other version)Logic and formal ontology.Barry Smith - 2000 - Manuscrito 23 (2):275-323.
    Revised version of chapter in J. N. Mohanty and W. McKenna (eds.), Husserl’s Phenomenology: A Textbook, Lanham: University Press of America, 1989, 29–67. -/- Logic for Husserl is a science of science, a science of what all sciences have in common in their modes of validation. Thus logic deals with universal laws relating to truth, to deduction, to verification and falsification, and with laws relating to theory as such, and to what makes for theoretical unity, both on the side of (...)
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  • Parts and Moments. Studies in Logic and Formal Ontology.Barry Smith (ed.) - 1982 - Philosophia Verlag.
    A collection of material on Husserl's Logical Investigations, and specifically on Husserl's formal theory of parts, wholes and dependence and its influence in ontology, logic and psychology. Includes translations of classic works by Adolf Reinach and Eugenie Ginsberg, as well as original contributions by Wolfgang Künne, Kevin Mulligan, Gilbert Null, Barry Smith, Peter M. Simons, Roger A. Simons and Dallas Willard. Documents work on Husserl's ontology arising out of early meetings of the Seminar for Austro-German Philosophy.
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  • Dallas Willard’s Contribution to Phenomenology.Burt C. Hopkins - 2019 - Husserl Studies 35 (2):117-130.
    Dallas Willard’s contribution to phenomenology is presented in terms of his articles on, and translations into English of, Edmund Husserl’s early philosophical writings, which single-handedly prevented them from falling into oblivion, both literally and philosophically. Willard’s account of Husserl’s “negative critique” of formalized logic in those writings, and argument for its contemporary relevance, is presented and largely endorsed.
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  • Hilbert mathematics versus (or rather “without”) Gödel mathematics: V. Ontomathematics!Vasil Penchev - 2024 - Metaphysics eJournal (Elsevier: SSRN) 17 (10):1-57.
    The paper is the final, fifth part of a series of studies introducing the new conceptions of “Hilbert mathematics” and “ontomathematics”. The specific subject of the present investigation is the proper philosophical sense of both, including philosophy of mathematics and philosophy of physics not less than the traditional “first philosophy” (as far as ontomathematics is a conservative generalization of ontology as well as of Heidegger’s “fundamental ontology” though in a sense) and history of philosophy (deepening Heidegger’s destruction of it from (...)
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  • Psicologismo Logico E Logiche Psicologistiche.Massimo Libardi - 1997 - Axiomathes 8 (1-3):307-366.
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