Results for 'Jp van Bendegem'

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  1. Sbn 004-232-8 issn 0378-0880 c&c an international interdisciplinary quarterly journal.P. Burghgraeve, W. Callebaut, L. de Ryck-Tasmowski, A. Fache, D. Goyvaerts, F. Hallyn, L. Peferoen, R. Pinxten, M. Spoelders & Jp van Bendegem - 1997 - Communication and Cognition: An Interdisciplinary Quarterly Journal 30.
     
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  2. The Impact of the Philosophy of Mathematical Practice on the Philosophy of Mathematics.Jean Paul Van Bendegem - 2014 - In Lena Soler, Sjoerd Zwart, Michael Lynch & Vincent Israel-Jost, Science After the Practice Turn in the Philosophy, History, and Social Studies of Science. New York: Routledge. pp. 215-226.
     
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  3. In Defence of Discrete Space and Time.Jean Paul van Bendegem - 1995 - Logique Et Analyse 38 (150-1):127-150.
    In this paper several arguments are discussed and evaluated concerning the possibility of discrete space and time.
     
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  4.  44
    Kurt Gödels onvolledigheidsstellingen en de grenzen van de kennis.Jean Paul Van Bendegem - 2021 - Algemeen Nederlands Tijdschrift voor Wijsbegeerte 113 (1):157-182.
    Kurt Gödel’s incompleteness theorems and the limits of knowledge In this paper a presentation is given of Kurt Gödel’s pathbreaking results on the incompleteness of formal arithmetic. Some biographical details are provided but the main focus is on the analysis of the theorems themselves. An intermediate level between informal and formal has been sought that allows the reader to get a sufficient taste of the technicalities involved and not lose sight of the philosophical importance of the results. Connections are established (...)
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  5. Mathematical arguments in context.Jean Paul Van Bendegem & Bart Van Kerkhove - 2009 - Foundations of Science 14 (1-2):45-57.
    Except in very poor mathematical contexts, mathematical arguments do not stand in isolation of other mathematical arguments. Rather, they form trains of formal and informal arguments, adding up to interconnected theorems, theories and eventually entire fields. This paper critically comments on some common views on the relation between formal and informal mathematical arguments, most particularly applications of Toulmin’s argumentation model, and launches a number of alternative ideas of presentation inviting the contextualization of pieces of mathematical reasoning within encompassing bodies of (...)
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  6. Over Newton. Een bedenking en een aanvulling bij Leo Apostel, 'Wat we van Newton hebben geleerd'.Jean Van Bendegem - 1989 - de Uil Van Minerva 6.
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  7.  73
    A Defense of Strict Finitism.J. P. Van Bendegem - 2012 - Constructivist Foundations 7 (2):141-149.
    Context: Strict finitism is usually not taken seriously as a possible view on what mathematics is and how it functions. This is due mainly to unfamiliarity with the topic. Problem: First, it is necessary to present a “decent” history of strict finitism and, secondly, to show that common counterarguments against strict finitism can be properly addressed and refuted. Method: For the historical part, the historical material is situated in a broader context, and for the argumentative part, an evaluation of arguments (...)
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  8.  50
    Finitism in geometry.Jean-Paul Van Bendegem - 2002 - Stanford Encyclopedia of Philosophy.
  9.  28
    Het complexe verhaal van de wiskunde in de Tractatus.Jean Paul Van Bendegem - 2023 - Algemeen Nederlands Tijdschrift voor Wijsbegeerte 115 (2):196-208.
    The complex story of mathematics in the Tractatus In this paper some thoughts are presented about the treatment of mathematics in the Tractatus Logico-Philosophicus of Ludwig Wittgenstein. After introducing a metaphor for the mathematical ‘building’, we look at the scattered ideas about mathematics in the Tractatus itself. Although the general consensus is that Wittgenstein rejects the entire ‘building’, there are recent insights that suggest that a more coherent view of ‘Tractarian’ mathematics can be presented, if we are willing to leave (...)
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  10.  4
    Finite, empirical mathematics, outline of a model.Jean Paul van Bendegem - 1987 - Gent: Rijksuniversiteit te Gent.
  11.  26
    Felix Lev. Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory.Jean Paul Van Bendegem - 2024 - Philosophia Mathematica 32 (2):268-274.
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  12.  17
    (1 other version)Non-Formal Properties of Real Mathematical Proofs.Jean Paul Van Bendegem - 1988 - PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988 (1):249-254.
    Suppose you attend a seminar where a mathematician presents a proof to some of his colleagues. Suppose further that what he is proving is an important mathematical statement Now the following happens: as the mathematician proceeds, his audience is amazed at first, then becomes angry and finally ends up disturbing the lecture (some walk out, some laugh, …). If in addition, you see that the proof he is presenting is formally speaking (nearly) correct, would you say you are witnessing an (...)
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  13.  94
    The Collatz conjecture. A case study in mathematical problem solving.Jean Paul Van Bendegem - 2005 - Logic and Logical Philosophy 14 (1):7-23.
    In previous papers (see Van Bendegem [1993], [1996], [1998], [2000], [2004], [2005], and jointly with Van Kerkhove [2005]) we have proposed the idea that, if we look at what mathematicians do in their daily work, one will find that conceiving and writing down proofs does not fully capture their activity. In other words, it is of course true that mathematicians spend lots of time proving theorems, but at the same time they also spend lots of time preparing the ground, (...)
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  14. Ross' paradox is an impossible super-task.Jean Paul van Bendegem - 1994 - British Journal for the Philosophy of Science 45 (2):743-748.
  15.  20
    Ad-infinitum: The ghost in Turing's machine: Taking God out of mathematics and putting the body back in-Rotman, B.P. Van Bendegem - 1996 - Semiotica 112 (3-4):403-413.
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  16. Why I Am a Constructivist Atheist.J. P. Van Bendegem - 2015 - Constructivist Foundations 11 (1):138-140.
    Open peer commentary on the article “Religion: A Radical-Constructivist Perspective” by Andreas Quale. Upshot: An essential feature of Quale’s point of view is the strict distinction between the cognitive and the non-cognitive. I argue that this position is untenable and hence that a radical constructivist can discuss religious matters.
     
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  17.  52
    Classical arithmetic is quite unnatural.Jean Paul Van Bendegem - 2003 - Logic and Logical Philosophy 11:231-249.
    It is a generally accepted idea that strict finitism is a rather marginal view within the community of philosophers of mathematics. If one therefore wants to defend such a position (as the present author does), then it is useful to search for as many different arguments as possible in support of strict finitism. Sometimes, as will be the case in this paper, the argument consists of, what one might call, a “rearrangement” of known materials. The novelty lies precisely in the (...)
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  18. Alternative Mathematics: The Vague Way.Jean Paul Van Bendegem - 2000 - Synthese 125 (1-2):19-31.
    Is alternative mathematics possible? More specifically,is it possible to imagine that mathematics could havedeveloped in any other than the actual direction? Theanswer defended in this paper is yes, and the proofconsists of a direct demonstration. An alternativemathematics that uses vague concepts and predicatesis outlined, leading up to theorems such as ``Smallnumbers have few prime factors''.
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  19.  9
    Experiments in Mathematics: Fact, Fiction, or the Future?Jean Paul Van Bendegem - 2024 - In Bharath Sriraman, Handbook of the History and Philosophy of Mathematical Practice. Cham: Springer. pp. 2821-2846.
    In this chapter, the possibility of experiments in mathematics is examined. A general scheme is proposed as a tool to handle the different forms of experiments that are being used in mathematical practices: computations, “experimental mathematics” as a new research domain in mathematics and computer science, real-world experiments, and thought experiments. In a final section, extensions of the scheme are proposed that further support the conclusion that mathematical experiments are indeed facts and the future.
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  20. Proofs and arguments: The special case of mathematics.Jean Paul Van Bendegem - 2005 - Poznan Studies in the Philosophy of the Sciences and the Humanities 84 (1):157-169.
    Most philosophers still tend to believe that mathematics is basically about producing formal proofs. A consequence of this view is that some aspects of mathematical practice are entirely lost from view. My contention is that it is precisely in those aspects that similarities can be found between practices in the exact sciences and in mathematics. Hence, if we are looking for a (more) unified treatment of science and mathematics it is necessary to incorporate these elements into our view of what (...)
     
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  21. Zeno's paradoxes and the tile argument.Jean Paul van Bendegem - 1987 - Philosophy of Science 54 (2):295-302.
    A solution of the zeno paradoxes in terms of a discrete space is usually rejected on the basis of an argument formulated by hermann weyl, The so-Called tile argument. This note shows that, Given a set of reasonable assumptions for a discrete geometry, The weyl argument does not apply. The crucial step is to stress the importance of the nonzero width of a line. The pythagorean theorem is shown to hold for arbitrary right triangles.
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  22. Inleiding tot de moderne logica en wetenschapsfilosofie : een terreinverkenning.Jean Paul Van Bendegem - 1993 - Tijdschrift Voor Filosofie 55 (2):361-363.
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  23.  27
    Fading foundations in de wiskunde?Jean Paul Van Bendegem - 2015 - Algemeen Nederlands Tijdschrift voor Wijsbegeerte 107 (2):155-159.
    Amsterdam University Press is a leading publisher of academic books, journals and textbooks in the Humanities and Social Sciences. Our aim is to make current research available to scholars, students, innovators, and the general public. AUP stands for scholarly excellence, global presence, and engagement with the international academic community.
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  24.  10
    First Flemish-Polish Logico-Philosophical Workshop 1999.Jean Van Bendegem, Diderik Batens & J. Perzanowski - 2002 - Logique Et Analyse 42:165-166.
  25.  22
    Pragmatics and Mathematics or how do mathematicians talk?Jean Paul van Bendegem - 1982 - Philosophica 29.
  26.  73
    Thought Experiments in Mathematics: Anything but Proof.Jean Paul van Bendegem - 2003 - Philosophica 72 (2):9-33.
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  27. The possibility of discrete time.J. P. van Bendegem - 2011 - In Craig Callender, The Oxford Handbook of Philosophy of Time. Oxford University Press.
     
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  28.  51
    The Creative Growth of Mathematics.Jean Paul van Bendegem - 1999 - Philosophica 63 (1).
  29.  14
    Ascent to Truth. A Critical Examination of Quine’s Philosophy. Munchen: Philosophia Verlag, 1986. Paul Gochet.Jean Paul van Bendegem - 1987 - Philosophica 39.
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  30.  17
    Choices. An introduction to decision theory. Minneapolis: University of Minnesota Press, 1987. Michael D. Resnik.Jean Paul van Bendegem - 1988 - Philosophica 41.
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  31.  13
    Music and Schema Theory. Cognitive Foundations of Systematic Musicology. Heidelberg: Springer-Verlag, 1995. Marc Leman.Jean Paul van Bendegem - 1997 - Philosophica 59 (1).
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  32.  9
    What does it all mean? A very short introduction to philosophy. Oxford: Oxford University Press, 1987. Thomas Nagel.Jean Paul van Bendegem - 1988 - Philosophica 41.
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  33.  25
    Perspectives on Mathematical Practices.Jean Paul Van Bendegem & Bart van Kerkhove (eds.) - 2007 - Springer.
    Philosophy of mathematics today has transformed into a very complex network of diverse ideas, viewpoints, and theories. Sometimes the emphasis is on the "classical" foundational work (often connected with the use of formal logical methods), sometimes on the sociological dimension of the mathematical research community and the "products" it produces, then again on the education of future mathematicians and the problem of how knowledge is or should be transmitted from one generation to the next. The editors of this book felt (...)
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  34.  70
    Inconsistency in mathematics and the mathematics of inconsistency.Jean Paul van Bendegem - 2014 - Synthese 191 (13):3063-3078.
    No one will dispute, looking at the history of mathematics, that there are plenty of moments where mathematics is “in trouble”, when paradoxes and inconsistencies crop up and anomalies multiply. This need not lead, however, to the view that mathematics is intrinsically inconsistent, as it is compatible with the view that these are just transient moments. Once the problems are resolved, consistency (in some sense or other) is restored. Even when one accepts this view, what remains is the question what (...)
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  35. Why the largest number imaginable is still a finite number.Jean Paul Van Bendegem - 1999 - Logique Et Analyse 42 (165-166).
  36. Ontwerp voor een analytische filosofie van de eindigheid.Jean Paul van Bendegem - 2003 - Algemeen Nederlands Tijdschrift voor Wijsbegeerte 95 (1):61-72.
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  37.  49
    Dialogue Logic and Problem-Solving.Jean Paul van Bendegem - 1985 - Philosophica 35.
  38.  33
    Foundations of Mathematics or Mathematical Practice: Is One Forced to Choose?Jean Paul van Bendegem - 1989 - Philosophica 43.
  39.  81
    Pi on Earth, or Mathematics in the Real World.Bart Van Kerkhove & Jean Paul Van Bendegem - 2008 - Erkenntnis 68 (3):421-435.
    We explore aspects of an experimental approach to mathematical proof, most notably number crunching, or the verification of subsequent particular cases of universal propositions. Since the rise of the computer age, this technique has indeed conquered practice, although it implies the abandonment of the ideal of absolute certainty. It seems that also in mathematical research, the qualitative criterion of effectiveness, i.e. to reach one’s goals, gets increasingly balanced against the quantitative one of efficiency, i.e. to minimize one’s means/ends ratio. Our (...)
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  40.  31
    Strict finitism as a viable alternative in the foundations of mathematics.P. Van Bendegem - 1996 - Logique Et Analyse 37 (145):23-40.
  41. Incommensurability: An algorithmic Approach.Jean Paul van Bendegem - 1983 - Philosophica 32.
  42.  59
    How Infinities Cause Problems in Classical Physical Theories.Jean Paul van Bendegem - 1992 - Philosophica 50.
  43.  43
    Introduction.Jean Paul van Bendegem - 1989 - Philosophica 43.
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  44.  33
    Significs and mathematics: Creative and other subjects.Jean Paul Van Bendegem - 2013 - Semiotica 2013 (196):307-323.
    Journal Name: Semiotica - Journal of the International Association for Semiotic Studies / Revue de l'Association Internationale de Sémiotique Volume: 2013 Issue: 196 Pages: 307-323.
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  45.  17
    Polymath as an Epistemic Community.Patrick Allo, Jean Paul Van Bendegem & Bart Van Kerkhove - 2024 - In Bharath Sriraman, Handbook of the History and Philosophy of Mathematical Practice. Cham: Springer. pp. 2727-2756.
    The Polymath Project is an online collaborative enterprise that was initiated in 2009, when Timothy Gowers asked whether and how groups could work together to solve mathematical problems that “do not naturally split up into a vast number of subtasks.” Gowers proposed to answer this question himself by actually trying to set up such a collaboration, based on interactions taking place in the comment-threads of a series of posts on a WordPress blog. Hence, the first project officially started in early (...)
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  46.  36
    Emily Rolfe* Great Circles: The Transits of Mathematics and Poetry.Jean Paul Van Bendegem & Bart Van Kerkhove - 2020 - Philosophia Mathematica 28 (3):431-441.
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  47.  23
    Dirk De Bock& Geert Vanpaemel. Rods, sets and arrows: The rise and fall of modern mathematics in Belgium. New York, NY: Springer, 2019, xxii +293 pp. ISBN : 9783030205980; 9783030205997. [REVIEW]Jean Paul Van Bendegem - 2021 - Centaurus 63 (3):603-604.
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  48.  33
    Moktefi, Amirouche & Abeles, Francine F., eds. , ‘What the Tortoise Said to Achilles’. Lewis Carroll’s Paradox of Inference, special double issue of The Carrollian, The Lewis Carroll Journal, no. 28 , 136pp, ISSN 1462 6519, also ISBN 978 0 904117 39 4. [REVIEW]Jean Paul Van Bendegem - 2017 - Acta Baltica Historiae Et Philosophiae Scientiarum 5 (1):101-105.
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  49. The Tricky Transition from Discrete to Continuous. [REVIEW]Jean Paul Van Bendegem - 2017 - Constructivist Foundations 12 (3):253-254.
    I show that the author underestimates the tricky matter of how to make a transition from the discrete, countable to the continuous, uncountable case.
     
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  50. Mathematical Practice and Naturalist Epistemology: Structures with Potential for Interaction.Bart Van Kerkhove & Jean Van Bendegem - 2005 - Philosophia Scientiae 9 (2):61-78.
    In current philosophical research, there is a rather one-sided focus on the foundations of proof. A full picture of mathematical practice should however additionally involve considerations about various methodological aspects. A number of these is identified, from large-scale to small-scale ones. After that, naturalism, a philosophical school concerned with scientific practice, is looked at, as far as the translations of its epistemic principles to mathematics is concerned. Finally, we call for intensifying the interaction between both dimensions of practice and epistemology.
     
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