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  1. Ferdinando Arzarello, Valeria Andriano, Federica Olivero & Ornella Robutti (1998). Abduction and Conjecturing in Mathematics. 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. John Bell, Hermann Weyl's Later Philosophical Views: His Divergence From Husserl.
    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. Pierre Cassou-Nogues (1999). Towards a Merleau-Pontean Epistemology in Mathematics (Abstract). Chiasmi International 1:300-300.
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  4. Stefania Centrone (2010). Logic and Philosophy of Mathematics in the Early Husserl. 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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  5. Richard Cobb-Stevens (1983). Numbers in Presence and Absence. A Study of Husserl's Philosophy of Mathematics. Review of Metaphysics 37 (1):136-138.
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  6. Helen De Cruz & Johan De Smedt (2013). Mathematical Symbols as Epistemic Actions. 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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  7. John J. Drummond (1985). Review of R. S. Tragesser, Husserl and Realism in Logic and Mathematics. [REVIEW] Review of Metaphysics 38 (4):913-916.
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  8. J. G. Fauvel (1975). Towards a Phenomenological Mathematics. Philosophy and Phenomenological Research 36 (1):16-24.
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  9. Miriam Franchella (2008). Mark Van Atten. Brouwer Meets Husserl: On the Phenomenology of Choice Sequences. Philosophia Mathematica 16 (2):276-281.
  10. D. A. Gillies (1980). Phenomenology and the Infinite in Mathematics. [REVIEW] British Journal for the Philosophy of Science 31 (3):289-298.
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  11. Robert Hanna (2009). Book Review: Logic, Mathematics, and the Mind: A Critical Study of Richard Tieszen's Phenomenology, Logic, and the Philosophy of Mathematics. [REVIEW] Notre Dame Journal of Formal Logic 50 (3):339-361.
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  12. M. Hartimo (2012). Husserl's Pluralistic Phenomenology of Mathematics. 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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  13. Mirja Hartimo (ed.) (2010). Phenomenology and Mathematics. Springer.
    This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics.
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  14. Mirja Hartimo (2010). The Development of Mathematics and the Birth of Phenomenology. In , Phenomenology and Mathematics. Springer. 107--121.
  15. Claire Oritz Hill (1994). Frege's Attack on Husserl and Cantor. The Monist 77 (3):345-357.
  16. Claire Ortiz Hill (2004). Abstraction and Idealization in Edmund Husserl and Georg Cantor Prior to 1895. 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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  17. Carlo Ierna (2011). Phenomenology and Mathematics. [REVIEW] 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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  18. Carlo Ierna (2007). Review of R. Tieszen, Phenomenology, Logic, and the Philosophy of Mathematics. [REVIEW] History and Philosophy of Logic 28 (2):173-174.
  19. Stephan Käufer (2006). Review of R. Tieszen, Phenomenology, Logic, and the Philosophy of Mathematics. [REVIEW] Notre Dame Philosophical Reviews 2006 (3).
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  20. Stathis Livadas (2012). The Expressional Limits of Formal Language in the Notion of Quantum Observation. 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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  21. Gabriele Lolli (2005). Qed: Fenomenologia Della Dimostrazione. Bollati Boringhieri.
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  22. Dietrich Mahnke (1977). From Hilbert to Husserl: First Introduction to Phenomenology, Especially That of Formal Mathematics. Studies in History and Philosophy of Science Part A 8 (1):71-84.
  23. Paolo Mancosu & T. A. Ryckman (2002). Mathematics and Phenomenology: The Correspondence Between O. Becker and H. Weyl. 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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  24. J. Philip Miller (1982). Numbers in Presence and Absence: A Study of Husserl's Philosophy of Mathematics. Distributors for the U.S. And Canada, Kluwer Boston, Inc..
    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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  25. Dermot Moran (1987). Review of R. S. Tragesser, Husserl and Realism in Logic and Mathematics. [REVIEW] Philosophical Studies 31:361-365.
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  26. Gilbert Null (2008). Entities Without Identities Vs. Temporal Modalities of Choice. Husserl Studies 24 (2):119-130.
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  27. Cassiano Terra Rodrigues (2007). Matemática como Ciência mais Geral: Forma da Experiência e Categorias. 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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  28. Giuseppina Ronzitti (2008). Review of R. Tieszen, Phenomenology, Logic, and the Philosophy of Mathematics. [REVIEW] Philosophia Mathematica 16 (2):264-276.
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  29. Giuseppina Ronzitti (2008). Review of R. Tieszen, Phenomenology, Logic, and the Philosophy of Mathematics. [REVIEW] Philosophia Mathematica 16 (2):264-276.
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  30. David Woodruff Smith (2002). Mathematical Form in the World. 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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  31. R. Tieszen (2006). 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] Philosophia Mathematica 14 (1):112-130.
  32. Richard Tieszen (2010). Mathematical Realism and Transcendental Phenomenological Realism. In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer. 1--22.
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  33. Richard Tieszen (2010). Review of E. Husserl, Introduction to Logic and Theory of Knowledge: Lectures 1906/07 Collected Works, Vol. 13. Translated by Claire Ortiz Hill. [REVIEW] Philosophia Mathematica 18 (2):247-252.
    (No abstract is available for this citation).
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  34. Richard Tieszen (2002). Phenomenology and Mathematics: Dedicated to the Memory of Gian-Carlo Rota (1932 4 27-1999 4 19). Philosophia Mathematica 10 (2):97-101.
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  35. Richard L. Tieszen (2005). Phenomenology, Logic, and the Philosophy of Mathematics. 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 book is divided into three parts. Part I, Reason, Science, and Mathematics 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, (...)
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  36. Iulian D. Toader (2011). Objectivity Sans Intelligibility. Hermann Weyl's Symbolic Constructivism. Dissertation, University of Notre Dame
  37. Robert S. Tragesser (1984). Husserl and Realism in Logic and Mathematics. 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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  38. M. van Atten (2013). 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] Philosophia Mathematica 21 (1):115-123.
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  39. M. van Atten (2006). Two Draft Letters From Godel on Self-Knowledge of Reason. Philosophia Mathematica 14 (2):255-261.
    In his text ‘The modern development of the foundations of mathematics in the light of philosophy’ from around 1961, Gödel announces a turn to Husserl's phenomenology to find the foundations of mathematics. In Gödel's archive there are two draft letters that shed some further light on the exact strategy that he formulated for himself in the early 1960s. Transcriptions of these letters are presented, together with some comments.
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  40. M. van Atten (2002). Why Husserl Should Have Been a Strong Revisionist in Mathematics. Husserl Studies 18 (1):1-18.
    Husserl repeatedly has claimed that (1) mathematics without a philosophical foundation is not a science but a mere technique; (2) philosophical considerations may lead to the rejection of parts of mathematical practice; but (3) they cannot lead to mathematical innovations. My thesis is that Husserl's third claim is wrong, by his own standards.
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  41. Mark van Atten, Dirk van Dalen & And Richard Tieszen (2002). Brouwer and Weyl: The Phenomenology and Mathematics of the Intuitive Continuumt. Philosophia Mathematica 10 (2):203-226.
    Brouwer and Weyl recognized that the intuitive continuum requires a mathematical analysis of a kind that set theory is not able to provide. As an alternative, Brouwer introduced choice sequences. We first describe the features of the intuitive continuum that prompted this development, focusing in particular on the flow of internal time as described in Husserl's phenomenology. Then we look at choice sequences and their logic. Finally, we investigate the differences between Brouwer and Weyl, and argue that Weyl's conception of (...)
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  42. Markus Sebastiaan Paul Rogier van Atten (2007). Brouwer Meets Husserl: On the Phenomenology of Choice Sequences. Springer.
    Can the straight line be analysed mathematically such that it does not fall apart into a set of discrete points, as is usually done but through which its fundamental continuity is lost? And are there objects of pure mathematics that can change through time? Mathematician and philosopher L.E.J. Brouwer argued that the two questions are closely related and that the answer to both is "yes''. To this end he introduced a new kind of object into mathematics, the choice sequence. But (...)
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  43. D. van Dalen (1993). Richard L. Tieszen. 'Mathematical Intuition: Phenomenology and Mathematical Knowledge'. [REVIEW] Husserl Studies 10 (3):249-252.
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  44. Olav K. Wiegand (2010). On Referring to Gestalts. In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer. 183--211.
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