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  1. Abduction and Conjecturing in Mathematics.Ferdinando Arzarello, Valeria Andriano, Federica Olivero & Ornella Robutti - 1998 - Philosophica 61 (1):77-94.
    The logic of discovering and that of justifying have been a permanent source of debate in mathematics, because of their different and apparently contradictory features within the processes of production of mathematical sentences. In fact, a fundamental unity appears as soon as one investigates deeply the phenomenology of conjecturing and proving using concrete examples. In this paper it is shown that abduction, in the sense of Peirce, is an essential unifying activity, ruling such phenomena. Abduction is the major ingredient in (...)
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  2. Hermann Weyl's Later Philosophical Views: His Divergence From Husserl.John Bell - manuscript
    In what seems to have been his last paper, Insight and Reflection (1954), Hermann Weyl provides an illuminating sketch of his intellectual development, and describes the principal influences—scientific and philosophical—exerted on him in the course of his career as a mathematician. Of the latter the most important in the earlier stages was Husserl’s phenomenology. In Weyl’s work of 1918-22 we find much evidence of the great influence Husserl’s ideas had on Weyl’s philosophical outlook—one need merely glance through the pages of (...)
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  3. Towards a Merleau-Pontean Epistemology in Mathematics (Abstract).Pierre Cassou-Nogues - 1999 - Chiasmi International 1:300-300.
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  4. Review of M. Hartimo (Ed.), Phenomenology and Mathematics[REVIEW]Stefania Centrone - 2014 - Philosophia Mathematica 22 (1):126-129.
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  5. Logic and Philosophy of Mathematics in the Early Husserl.Stefania Centrone - 2010 - Springer.
    This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to ...
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  6. Numbers in Presence and Absence. A Study of Husserl's Philosophy of Mathematics.Richard Cobb-Stevens - 1983 - Review of Metaphysics 37 (1):136-138.
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  7. WEYL, HERMANN. "Philosophy of Mathematics and Natural Science". [REVIEW]Brian Coffey - 1949 - Modern Schoolman 27:232.
  8. Mathematical Symbols as Epistemic Actions.De Cruz Helen & De Smedt Johan - 2013 - Synthese 190 (1):3-19.
    Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols are not only used to (...)
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  9. Review of R. S. Tragesser, Husserl and Realism in Logic and Mathematics[REVIEW]John J. Drummond - 1985 - Review of Metaphysics 38 (4):913-916.
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  10. The Surd.Aden Evens - 2006 - In Simon B. Duffy (ed.), Virtual Mathematics: The Logic of Difference. Clinamen.
    This article explores the question of what number is, demonstrating parallels between the Deleuzian notion of the differential as a dynamic moment of number and the intuitionist definition of number as a choice sequence. One conclusion offers a theory of mathematical progress, and suggests that this theory might be extended to domains outside of mathematics.
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  11. Towards a Phenomenological Mathematics.J. G. Fauvel - 1975 - Philosophy and Phenomenological Research 36 (1):16-24.
  12. 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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  13. Traduzione di Friedrich Waismann, Introduzione al pensiero matematico.Ludovico Geymonat - 1942 - Einaudi.
  14. Phenomenology and the Infinite in Mathematics. [REVIEW]D. A. Gillies - 1980 - British Journal for the Philosophy of Science 31 (3):289-298.
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  15. Book Review: Logic, Mathematics, and the Mind: A Critical Study of Richard Tieszen's Phenomenology, Logic, and the Philosophy of Mathematics. [REVIEW]Robert Hanna - 2009 - Notre Dame Journal of Formal Logic 50 (3):339-361.
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  16. Husserl's Pluralistic Phenomenology of Mathematics.M. Hartimo - 2012 - Philosophia Mathematica 20 (1):86-110.
    The paper discusses Husserl's phenomenology of mathematics in his Formal and Transcendental Logic (1929). In it Husserl seeks to provide descriptive foundations for mathematics. As sciences and mathematics are normative activities Husserl's attempt is also to describe the norms at work in these disciplines. The description shows that mathematics can be given in several different ways. The phenomenologist's task is to examine whether a given part of mathematics is genuine according to the norms that pertain to the approach in question. (...)
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  17. Phenomenology and Mathematics.Mirja Hartimo (ed.) - 2010 - Springer.
    This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics.
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  18. The Development of Mathematics and the Birth of Phenomenology.Mirja Hartimo - 2010 - In Phenomenology and Mathematics. Springer. pp. 107--121.
  19. Frege's Attack on Husserl and Cantor.Claire Oritz Hill - 1994 - The Monist 77 (3):345-357.
  20. Abstraction and Idealization in Edmund Husserl and Georg Cantor Prior to 1895.Claire Ortiz Hill - 2004 - Poznan Studies in the Philosophy of the Sciences and the Humanities 82 (1):217-244.
    Little is known of Edmund Husserl's direct encounter with Georg Cantor's ideas on Platonic idealism and the abstraction of number concepts during the late 19th century, when Husserl's philosophical orientation changed considerably and definitely. Closely analyzing and comparing the two men's writings during that important time in their intellectual careers, I describe the crucial shift in Husserl's views on psychologism and metaphysical idealism as it relates to Cantor's philosophy of arithmetic. I thus establish connections between their ideas which have been (...)
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  21. Phenomenology and Mathematics. [REVIEW]Carlo Ierna - 2011 - History and Philosophy of Logic 32 (4):399 - 400.
    History and Philosophy of Logic, Volume 32, Issue 4, Page 399-400, November 2011.
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  22. Review of R. Tieszen, Phenomenology, Logic, and the Philosophy of Mathematics[REVIEW]Carlo Ierna - 2007 - History and Philosophy of Logic 28 (2):173-174.
  23. Beauty Is Not Simplicity: An Analysis of Mathematicians' Proof Appraisals.Matthew Inglis & Andrew Aberdein - 2015 - Philosophia Mathematica 23 (1):87-109.
    What do mathematicians mean when they use terms such as ‘deep’, ‘elegant’, and ‘beautiful’? By applying empirical methods developed by social psychologists, we demonstrate that mathematicians' appraisals of proofs vary on four dimensions: aesthetics, intricacy, utility, and precision. We pay particular attention to mathematical beauty and show that, contrary to the classical view, beauty and simplicity are almost entirely unrelated in mathematics.
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  24. 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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  25. Bachelard, Enriques and Weyl: Comparing Some of Their Ideas.Iurato Giuseppe - 2012 - Quaderni di Ricerca in Didattica (Science) 4:40-50.
    Some aspects of Federigo Enriques mathematical philosophy thought are taken as central reference points for a critical historic-epistemological comparison between it and some of the main aspects of the philosophical thought of other his contemporary thinkers like, Gaston Bachelard and Hermann Weyl. From what will be exposed, it will be also possible to make out possible educational implications of the historic-epistemological approach.
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  26. On the Role Played by the Work of Ulisse Dini on Implicit Function Theory in the Modern Differential Geometry Foundations: The Case of the Structure of a Differentiable Manifold, 1.Giuseppe Iurato - manuscript
    In this first paper we outline what possible historic-epistemological role might have played the work of Ulisse Dini on implicit function theory in formulating the structure of differentiable manifold, via the basic work of Hassler Whitney. A detailed historiographical recognition about this Dini's work has been done. Further methodological considerations are then made as regards history of mathematics.
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  27. On the History of Differentiable Manifolds.Giuseppe Iurato - 2012 - International Mathematical Forum 7 (10):477-514.
    We discuss central aspects of history of the concept of an affine differentiable manifold, as a proposal confirming the need for using some quantitative methods (drawn from elementary Model Theory) in Mathematical Historiography. In particular, we prove that this geometric structure is a syntactic rigid designator in the sense of Kripke-Putnam.
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  28. Review of R. Tieszen, Phenomenology, Logic, and the Philosophy of Mathematics[REVIEW]Stephan Käufer - 2006 - Notre Dame Philosophical Reviews 2006 (3).
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  29. The Expressional Limits of Formal Language in the Notion of Quantum Observation.Stathis Livadas - 2012 - Axiomathes 22 (1):147-169.
    In this article I deal with the notion of observation, from a phenomenologically motivated point of view, and its representation mainly by means of the formal language of quantum mechanics. In doing so, I have taken the notion of observation in two diverse contexts. In one context as a notion related with objects of a logical-mathematical theory taken as registered facts of phenomenological perception ( Wahrnehmung ) inasmuch as this phenomenological idea can also be linked with a process of measurement (...)
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  30. Qed: Fenomenologia Della Dimostrazione.Gabriele Lolli - 2005 - Bollati Boringhieri.
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  31. From Hilbert to Husserl: First Introduction to Phenomenology, Especially That of Formal Mathematics.Dietrich Mahnke - 1977 - Studies in History and Philosophy of Science Part A 8 (1):71-84.
  32. Mathematics and Phenomenology: The Correspondence Between O. Becker and H. Weyl.Paolo Mancosu & T. A. Ryckman - 2002 - Philosophia Mathematica 10 (2):130-202.
    Recently discovered correspondence from Oskar Becker to Hermann Weyl sheds new light on Weyl's engagement with Husserlian transcendental phenomenology in 1918-1927. Here the last two of these letters, dated July and August, 1926, dealing with issues in the philosophy of mathematics are presented, together with background and a detailed commentary. The letters provide an instructive context for re-assessing the connection between intuitionism and phenomenology in Weyl's foundational thought, and for understanding Weyl's term ‘symbolic construction’ as marking his own considered position (...)
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  33. Numbers in Presence and Absence: A Study of Husserl's Philosophy of Mathematics.J. Philip Miller - 1982 - Kluwer Academic Publishers.
    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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  34. Review of R. S. Tragesser, Husserl and Realism in Logic and Mathematics[REVIEW]Dermot Moran - 1987 - Philosophical Studies 31:361-365.
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  35. Phenomenology and Philosophy of Mathematics.Roman Murawski - unknown - Poznan Studies in the Philosophy of the Sciences and the Humanities 98:135-146.
  36. Entities Without Identities Vs. Temporal Modalities of Choice.Gilbert Null - 2008 - Husserl Studies 24 (2):119-130.
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  37. The Eternal Unprovability Filter – Part I.Kiran Pai - 2016 - Dissertation, Thinkstrike
    I prove both the mathematical conjectures P ≠ NP and the Continuum Hypothesis are eternally unprovable using the same fundamental idea. Starting with the Saunders Maclane idea that a proof is eternal or it is not a proof, I use the indeterminacy of human biological capabilities in the eternal future to show that since both conjectures are independent of Axioms and have definitions connected with human biological capabilities, it would be impossible to prove them eternally without the creation and widespread (...)
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  38. Matemática como Ciência mais Geral: Forma da Experiência e Categorias.Cassiano Terra Rodrigues - 2007 - Cognitio-Estudos.
    Este artigo tem como objetivo geral apresentar alguns aspectos básicos da filosofia da matemática de Charles Sanders Peirce, com o intuito de suscitar discussão posterior. Especificamente, são ressaltados: o lugar da matemática na classificação das ciências do autor; a diferença entre matemática e filosofia como cenoscopia; a relação entre as categorias da fenomenologia e matemática; o conceito de experiência e sua formalização possível; a distinção geral entre lógica, como parte da investigação filosófica, e matemática.
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  39. Review of R. Tieszen, Phenomenology, Logic, and the Philosophy of Mathematics[REVIEW]Giuseppina Ronzitti - 2008 - Philosophia Mathematica 16 (2):264-276.
    Richard Tieszen's new book1 is a collection of fifteen articles and reviews, spanning fifteen years, presenting the author's approach to philosophical questions about logic and mathematics from the point of view of phenomenology, as developed by Edmund Husserl in the later phase2 of his philosophical thinking known as transcendental phenomenology, starting in 1907 with the Logical Investigations and characterized by the introduction of the notions of ‘reduction’. Husserlian transcendental phenomenology as philosophy of mathematics is described as one that ‘cuts across’ (...)
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  40. Husserl's Epistemology of Mathematics and the Foundation of Platonism in Mathematics.E. Rosado Handdock Guillermo - 1987 - Husserl Studies 4 (2):81-102.
  41. Reductionism and the Universal Calculus.Gopal P. Sarma - forthcoming - Arxiv Preprint Arxiv:1607.06725.
    In the seminal essay, "On the unreasonable effectiveness of mathematics in the physical sciences," physicist Eugene Wigner poses a fundamental philosophical question concerning the relationship between a physical system and our capacity to model its behavior with the symbolic language of mathematics. In this essay, I examine an ambitious 16th and 17th-century intellectual agenda from the perspective of Wigner's question, namely, what historian Paolo Rossi calls "the quest to create a universal language." While many elite thinkers pursued related ideas, the (...)
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  42. Mathematical Form in the World.David Woodruff Smith - 2002 - Philosophia Mathematica 10 (2):102-129.
    This essay explores an ideal notion of form (mathematical structure) that embraces logical, phenomenological, and ontological form. Husserl envisioned a correlation among forms of expression, thought, meaning, and object—positing ideal forms on all these levels. The most puzzling formal entities Husserl discussed were those he called ‘manifolds’. These manifolds, I propose, are forms of complex states of affairs or partial possible worlds representable by forms of theories (compare structuralism). Accordingly, I sketch an intentionality-based semantics correlating these four Husserlian levels of (...)
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  43. 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]R. Tieszen - 2006 - Philosophia Mathematica 14 (1):112-130.
  44. Review of E. Husserl, Introduction to Logic and Theory of Knowledge: Lectures 1906/07 Collected Works, Vol. 13. Translated by Claire Ortiz Hill[REVIEW]Richard Tieszen - 2010 - Philosophia Mathematica 18 (2):247-252.
    (No abstract is available for this citation).
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  45. Mathematical Realism and Transcendental Phenomenological Realism.Richard Tieszen - 2010 - In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer. pp. 1--22.
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  46. Phenomenology, Logic, and the Philosophy of Mathematics.Richard Tieszen - 2005 - Cambridge University Press.
    Offering a collection of fifteen essays that deal with issues at the intersection of phenomenology, logic, and the philosophy of mathematics, this 2005 book is divided into three parts. Part I contains a general essay on Husserl's conception of science and logic, an essay of mathematics and transcendental phenomenology, and an essay on phenomenology and modern pure geometry. Part II is focused on Kurt Godel's interest in phenomenology. It explores Godel's ideas and also some work of Quine, Penelope Maddy and (...)
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  47. Phenomenology and Mathematics: Dedicated to the Memory of Gian-Carlo Rota (1932 4 27-1999 4 19).Richard Tieszen - 2002 - Philosophia Mathematica 10 (2):97-101.
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  48. Objectivity Sans Intelligibility. Hermann Weyl's Symbolic Constructivism.Iulian D. Toader - 2011 - Dissertation, University of Notre Dame
  49. Husserl and Realism in Logic and Mathematics.Robert S. Tragesser - 1984 - Cambridge University Press.
    In this book Robert Tragesser sets out to determine the conditions under which a realist ontology of mathematics and logic might be justified, taking as his starting point Husserl's treatment of these metaphysical problems. He does not aim primarily at an exposition of Husserl's phenomenology, although many of the central claims of phenomenology are clarified here. Rather he exploits its ideas and methods to show how they can contribute to answering Michael Dummet's question 'Realism or Anti-Realism?'. In doing so he (...)
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  50. Fabrizio Palombi, the Star & the Whole: Gian-Carlo Rota on Mathematics and Phenomenology. Boca Raton: Crc Press, 2011. Isbn 978-1-56881-583-1 (Pbk). Pp. XIV + 124. English Translation of la Stella E L'Intero: La Ricerca di Gian-Carlo Rota Tra Matematica E Fenomenologia. 2nd Rev. Ed. Torino: Bollati Boringhieri, 2003. [REVIEW]M. van Atten - 2013 - Philosophia Mathematica 21 (1):115-123.
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