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  1. Mathematics - an imagined tool for rational cognition.Boris Culina - manuscript
    Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial interpretation of the corresponding language. It follows from the analysis that (i) mathematical objects do not exist in the external world: they are our internally imagined objects, some of which, at least approximately, we can realize or represent; (ii) mathematical truths are not (...)
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  2. The fundamental cognitive approaches of mathematics.Salvador Daniel Escobedo Casillas - manuscript
    We propose a way to explain the diversification of branches of mathematics, distinguishing the different approaches by which mathematical objects can be studied. In our philosophy of mathematics, there is a base object, which is the abstract multiplicity that comes from our empirical experience. However, due to our human condition, the analysis of such multiplicity is covered by other empirical cognitive attitudes (approaches), diversifying the ways in which it can be conceived, and consequently giving rise to different mathematical disciplines. This (...)
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  3. 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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  4. On the Embodiment of Space and Time: Triadic logic, quantum indeterminacy and the metaphysics of relativity.Timothy M. Rogers - manuscript
    Triadic (systemical) logic can provide an interpretive paradigm for understanding how quantum indeterminacy is a consequence of the formal nature of light in relativity theory. This interpretive paradigm is coherent and constitutionally open to ethical and theological interests. -/- In this statement: -/- (1) Triadic logic refers to a formal pattern that describes systemic (collaborative) processes involving signs that mediate between interiority (individuation) and exteriority (generalized worldview or Umwelt). It is also called systemical logic or the logic of relatives. The (...)
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  5. Heidegger, Gendlin and Deleuze on the Logic of Quantitative Repetition.Joshua Soffer - manuscript
    Philosophers such as Nietzsche, Heidegger, Derrida, Deleuze and Gendlin pronounce that difference must be understood as ontologically prior to identity. They teach that identity is a surface effect of difference, that to understand the basis of logico-mathematical idealities we must uncover their genesis in the fecundity of differentiation. In this paper, I contrast Heidegger’s analyses of the present to hand logico-mathematical object, which he discuses over the course of his career in terms of the ‘as’ structure, temporalization and enframing , (...)
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  6. Reducing the Actual: A Phenomenological Bracketing of Deleuze’s Qualities and Extensities.Joshua Soffer - manuscript
    Deleuze is prominent among those philosophers who pronounce that difference must be understood as ontologically prior to identity. He teaches that identity is a surface effect of difference, so to understand the basis of logico-mathematical idealities we must uncover their genesis in the fecundity of differentiation. Deleuze wants to offer a foundation of number and mathematics as a subversive, creative force, an affirmation of Nietzsche’s eternal return as the ‘roll of the dice’. But he begins too late. For Deleuze, virtual (...)
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  7. Phenomenology and Philosophy of Mathematics.Roman Murawski - unknown - Poznan Studies in the Philosophy of the Sciences and the Humanities 98:135-146.
  8. Brouwer's Intuition of Twoity and Constructions in Separable Mathematics.Bruno Bentzen - forthcoming - History and Philosophy of Logic:1-21.
    My first aim in this paper is to use time diagrams in the style of Brentano to analyze constructions in Brouwer's separable mathematics more precisely. I argue that constructions must involve not only pairing and projecting as basic operations guaranteed by the intuition of twoity, as sometimes assumed in the literature, but also a recalling operation. My second aim is to argue that Brouwer's views on the intuition of twoity and arithmetic lead to an ontological explosion. Redeveloping the constructions of (...)
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  9. Intuition, Iteration, Induction.Mark van Atten - 2024 - Philosophia Mathematica 32 (1):34-81.
    Brouwer’s view on induction has relatively recently been characterised as one on which it is not only intuitive (as expected) but functional, by van Dalen. He claims that Brouwer’s ‘Ur-intuition’ also yields the recursor. Appealing to Husserl’s phenomenology, I offer an analysis of Brouwer’s view that supports this characterisation and claim, even if assigning the primary role to the iterator instead. Contrasts are drawn to accounts of induction by Poincaré, Heyting, and Kreisel. On the phenomenological side, the analysis provides an (...)
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  10. Wirkfelder der Phänomenologie: I. Logik und Sprachphilosophie.Emmanuel Alloa & Andris Breitling - 2023 - In Emmanuel Alloa, Thiemo Breyer & Emanuele Caminada (eds.), Handbuch Phänomenologie. Tübingen: Mohr-Siebeck. pp. 254-274.
    Die Phänomenologie stellt eine der Hauptströmungen der Gegenwartsphilosophie dar und findet in zahlreichen Wissenschaften sowie in Praxis und Therapeutik starke Resonanz. Nach 120 Jahren Wirkungsgeschichte füllt die Bibliothek phänomenologischer Werke zahllose Bücherregale und selbst für Expert:innen ist die Forschungsliteratur mittlerweile unüberschaubar geworden. An allgemeinen Einführungen sowie spezialisierter Fachliteratur mangelt es dabei keineswegs, wohl aber an einem Handbuch, in dem sowohl der Vielfalt der historischen Entwicklungen als auch dem berechtigten Wunsch nach innerer systematischer Kohärenz Rechnung getragen wird. Das Handbuch Phänomenologie schließt (...)
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  11. Propositions as Intentions.Bruno Bentzen - 2023 - Husserl Studies 39 (2):143-160.
    I argue against the interpretation of propositions as intentions and proof-objects as fulfillments proposed by Heyting and defended by Tieszen and van Atten. The idea is already a frequent target of criticisms regarding the incompatibility of Brouwer’s and Husserl’s positions, mainly by Rosado Haddock and Hill. I raise a stronger objection in this paper. My claim is that even if we grant that the incompatibility can be properly dealt with, as van Atten believes it can, two fundamental issues indicate that (...)
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  12. On Regression Modeling for Students’ Attitude towards Statistics Online Learning in Higher Education.Leomarich Casinillo & Ginna Tavera - 2023 - St. Theresa Journal of Humanities and Social Sciences 9 (2):60-74.
    Students during the distance education were experiencing solitude and depression in their studies due to no social interaction which led to psychological suffering. In this article, college students' attitudes toward statistics learning were investigated, and its predictors by statistical modeling. Secondary data was extracted from a current study from the literature, summarized using descriptive statistics, and presented in tabular form. As for modeling the predictors of students' attitudes in learning statistics, it was done through multiple linear regression via the ordinary (...)
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  13. Role of Imagination and Anticipation in the Acceptance of Computability Proofs: A Challenge to the Standard Account of Rigor.Keith Weber - 2022 - Philosophia Mathematica 30 (3):343-368.
    In a 2022 paper, Hamami claimed that the orthodox view in mathematics is that a proof is rigorous if it can be translated into a derivation. Hamami then developed a descriptive account that explains how mathematicians check proofs for rigor in this sense and how they develop the capacity to do so. By exploring introductory texts in computability theory, we demonstrate that Hamami’s descriptive account does not accord with actual mathematical practice with respect to computability theory. We argue instead for (...)
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  14. Why Did Weyl Think That Emmy Noether Made Algebra the Eldorado of Axiomatics?Iulian D. Toader - 2021 - Hopos: The Journal of the International Society for the History of Philosophy of Science 11 (1):122-142.
    This paper argues that Noether's axiomatic method in algebra cannot be assimilated to Weyl's late view on axiomatics, for his acquiescence to a phenomenological epistemology of correctness led Weyl to resist Noether's principle of detachment.
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  15. Euclid's Error: The Mathematics behind Foucault, Deleuze, and Nietzsche.Ilexa Yardley - 2021 - Intelligent Design Center.
    We have to go all the way back to Euclid, and, actually, before, to figure out the basis for representation, and therefore, interpretation. Which is, pure and simple, the conservation of a circle. As articulated by Foucault, Deleuze, and Nietzsche. 'Pi' (in mathematics) is the background state for everything (a.k.a. 'mind').Providing the explanation for (and the current popularity, and, thus, the 'genius' behind) NFT (non fungible tokens). 'Reality' has, finally, caught up with the 'truth.'.
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  16. How Nature ‘Tokenizes’ Reality.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory/.
    Pi in mathematics is mind in Nature, explaining the tokenization of 'reality.'.
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  17. The Inadequacy of Husserlian Mereology for the Regional Ontology of Quantum Chemical Wholes.Marina P. Banchetti - 2020 - In Essays in Honor of Thomas Seebohm. pp. 135-151.
    In his book, 'History as a Science and the System of the Sciences', Thomas Seebohm articulates the view that history can serve to mediate between the sciences of explanation and the sciences of interpretation, that is, between the natural sciences and the human sciences. Among other things, Seebohm analyzes history from a phenomenological perspective to reveal the material foundations of the historical human sciences in the lifeworld. As a preliminary to his analyses, Seebohm examines the formal and material presuppositions of (...)
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  18. Skolem’s “paradox” as logic of ground: The mutual foundation of both proper and improper interpretations.Vasil Penchev - 2020 - Epistemology eJournal (Elsevier: SSRN) 13 (19):1-16.
    A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather a metamathematical axiom about the relation of mathematics and reality. Its investigation needs philosophical (...)
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  19. Sonification Design: From Data to Intelligible Soundfields.David Worrall - 2019 - Springer.
    The contemporary design practice known as data sonification allows us to experience information in data by listening. In doing so, we understand the source of the data in ways that support, and in some cases surpass, our ability to do so visually. -/- In order to assist us in negotiating our environments, our senses have evolved differently. Our hearing affords us unparalleled temporal and locational precision. Biological survival has determined that the ears lead the eyes. For all moving creatures, in (...)
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  20. A case study of misconceptions students in the learning of mathematics; The concept limit function in high school.Widodo Winarso & Toheri Toheri - 2017 - Jurnal Riset Pendidikan Matematika 4 (1): 120-127.
    This study aims to find out how high the level and trends of student misconceptions experienced by high school students in Indonesia. The subject of research that is a class XI student of Natural Science (IPA) SMA Negeri 1 Anjatan with the subject matter limit function. Forms of research used in this study is a qualitative research, with a strategy that is descriptive qualitative research. The data analysis focused on the results of the students' answers on the test essay subject (...)
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  21. Husserl on symbolic technologies and meaning-constitution: A critical inquiry.Peter Woelert - 2017 - Continental Philosophy Review 50 (3):289-310.
    This paper reconstructs and critically analyzes Husserl’s philosophical engagement with symbolic technologies—those material artifacts and cultural devices that serve to aid, structure and guide processes of thinking. Identifying and exploring a range of tensions in Husserl’s conception of symbolic technologies, I argue that this conception is limited in several ways, and particularly with regard to the task of accounting for the more constructive role these technologies play in processes of meaning-constitution. At the same time, this paper shows that a critical (...)
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  22. A Phenomenological Study Of The Lived Experiences Of Nontraditional Students In Higher Level Mathematics At A Midwest University.Brian Bush Wood - 2017 - Dissertation, Keiser University
    The current literature suggests that the use of Husserl’s and Heidegger’s approaches to phenomenology is still practiced. However, a clear gap exists on how these approaches are viewed in the context of constructivism, particularly with non-traditional female students’ study of mathematics. The dissertation attempts to clarify the constructivist role of phenomenology within a transcendental framework from the first-hand meanings associated with the expression of the relevancy as expressed by interviews of six nontraditional female students who have studied undergraduate mathematics. Comparisons (...)
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  23. Reductionism and the Universal Calculus.Gopal Sarma - 2016 - 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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  24. Mathematical models of games of chance: Epistemological taxonomy and potential in problem-gambling research.Catalin Barboianu - 2015 - UNLV Gaming Research and Review Journal 19 (1):17-30.
    Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of (...)
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  25. Les mathématiques et l'expérience: ce qu'en ont dit les philosophes et les mathématiciens.Jean-Pierre Cléro & E. Barbin (eds.) - 2015 - Paris: Hermann.
    Qu{u2019}est-ce que l{u2019}expérience? Que sont les expériences dont peuvent s{u2019}occuper les mathématiques? Quelles sont les caractéristiques des mathématiques qui se soucient de l{u2019}expérience ou des expériences? Comment les discours mathématiques se nouent-ils avec les expériences qu{u2019}ils symbolisent, qu{u2019}ils prétendent parfois refléter ou seulement déterminer sans aucun souci de vérité {OCLCbr#BB}?. Les dix-sept chapitres de cet ouvrage abordent ces questions à partir des discours qu{u2019}ont tenu philosophes et mathématiciens depuis les Sophistes jusqu{u2019}à Thom en passant par Galilée, Hobbes, Locke, Diderot, d{u2019}Alembert, (...)
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  26. 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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  27. 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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  28. Phenomenology of Mathematics.Mark van Atten & Mark Atten - 2015 - In Robert Tragesser, Mark van Atten & Mark Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Cham: Springer Verlag.
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  29. Mathematicians on creativity.Peter Borwein, Peter Liljedahl & Helen Zhai (eds.) - 2014 - [Washington, D.C.]: Mathematical Association of America.
    In their own words, many of the world's foremost mathematicians discuss the art and practice of their work in this book, which shines a light on some of the issues of mathematical creativity. It is neither a philosophical treatise nor the presentation of experimental results, but a compilation of reflections from top-calibre working mathematicians. This approach highlights the creative aspects of the field, illustrates the dramatic variation by individual, and hopes to express the vibrancy of creative minds at work. Organised (...)
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  30. Review of M. Hartimo (ed.), Phenomenology and Mathematics[REVIEW]Stefania Centrone - 2014 - Philosophia Mathematica 22 (1):126-129.
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  31. Weyl on Fregean Implicit Definitions: Between Phenomenology and Symbolic Construction.Demetra Christopoulou - 2014 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 45 (1):35-47.
    This paper aims to investigate certain aspects of Weyl’s account of implicit definitions. The paper takes under consideration Weyl’s approach to a certain kind of implicit definitions i.e. abstraction principles introduced by Frege.ion principles are bi-conditionals that transform certain equivalence relations into identity statements, defining thereby mathematical terms in an implicit way. The paper compares the analytic reading of implicit definitions offered by the Neo-Fregean program with Weyl’s account which has phenomenological leanings. The paper suggests that Weyl’s account should be (...)
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  32. Mathematician's call for interdisciplinary research effort.Catalin Barboianu - 2013 - International Gambling Studies 13 (3):430-433.
    The article addresses the necessity of increasing the role of mathematics in the psychological intervention in problem gambling, including cognitive therapies. It also calls for interdisciplinary research with the direct contribution of mathematics. The current contributions and limitations of the role of mathematics are analysed with an eye toward the professional profiles of the researchers. An enhanced collaboration between these two disciplines is suggested and predicted.
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  33. Mathematical symbols as epistemic actions.Johan De Smedt & Helen De Cruz - 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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  34. Experiencing mathematics: what do we do, when we do mathematics?Reuben Hersh - 2013 - Providence, Rhode Island: American Mathematical Society.
    The question ``What am I doing?'' haunts many creative people, researchers, and teachers. Mathematics, poetry, and philosophy can look from the outside sometimes as ballet en pointe, and at other times as the flight of the bumblebee. Reuben Hersh looks at mathematics from the inside; he collects his papers written over several decades, their edited versions, and new chapters in his book Experiencing Mathematics, which is practical, philosophical, and in some places as intensely personal as Swann's madeleine. --Yuri Manin, Max (...)
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  35. Elements of Logical Reasoning.Jan von Plato - 2013 - Cambridge and New York: Cambridge University Press.
    Some of our earliest experiences of the conclusive force of an argument come from school mathematics: faced with a mathematical proof, we cannot deny the conclusion once the premises have been accepted. Behind such arguments lies a more general pattern of 'demonstrative arguments' that is studied in the science of logic. Logical reasoning is applied at all levels, from everyday life to advanced sciences, and a remarkable level of complexity is achieved in everyday logical reasoning, even if the principles behind (...)
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  36. 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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  37. 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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  38. 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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  39. Bachelard, Enriques and Weyl: comparing some of their ideas.Giuseppe Iurato - 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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  40. 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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  41. Sensing objectivity: A comment on Mary Leng's "Creation and Discovery in Mathematics".Michael Detlefsen - 2011 - In John Polkinghorne (ed.), Mathematics and its Significance. Oxford University Press. pp. 70-71.
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  42. 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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  43. Objectivity Sans Intelligibility. Hermann Weyl's Symbolic Constructivism.Iulian D. Toader - 2011 - Dissertation, University of Notre Dame
    A new form of skepticism is described, which holds that objectivity and understanding are incompossible ideals of modern science. This is attributed to Weyl, hence its name: Weylean skepticism. Two general defeat strategies are then proposed, one of which is rejected.
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  44. Phenomenology and mathematics.Mirja Hartimo (ed.) - 2010 - London: Springer.
    This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics.
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  45. The development of mathematics and the birth of phenomenology.Mirja Hartimo - 2010 - In Phenomenology and Mathematics. Springer. pp. 107--121.
  46. Edmund Husserl. Introduction to Logic and Theory of Knowledge: Lectures 1906\textfractionsolidus{}07 Collected Works, vol. 13. Translated by Claire Ortiz Hill: Critical Studies/Book Reviews. [REVIEW]Richard Tieszen - 2010 - Philosophia Mathematica 18 (2):247-252.
    (No abstract is available for this citation).
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  47. Mathematical realism and transcendental phenomenological realism.Richard Tieszen - 2010 - In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer. pp. 1--22.
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  48. On referring to Gestalts.Olav K. Wiegand - 2010 - In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer. pp. 183--211.
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  49. Logic and philosophy of mathematics in the early Husserl.Stefania Centrone - 2009 - New York: 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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  50. 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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