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Profile: Jean Paul van Bendegem (Vrije Universiteit Brussel, University of Ghent)
  1. Philosophical Perspectives on Mathematical Practice.Bart Van Kerkhove, Jean Paul Van Bendegem & Jonas De Vuyst (eds.) - 2010 - College Publications.
  2.  41
    Introductory Note.Jean Paul Van Bendegem - 1988 - Philosophica 42.
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  3. Incommensurability: An Algorithmic Approach.Jean Paul Van Bendegem - 1983 - Philosophica 32.
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  4.  39
    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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  5. Frontiers in Paraconsistent Logic.Diderik Batens, Chris Mortensen, Graham Priest & Jean Paul Van Bendegem (eds.) - 2000 - Research Studies Press.
     
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  6.  4
    Petite Philosophie de l'Art Royal: Analyse de I’Alchimie Franc-Maçonne. [REVIEW]Jean Paul Van Bendegem - 2016 - Process Studies 45 (2):282-285.
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  7.  11
    Non-Formal Properties of Real Mathematical Proofs.van Bendegem Jean Paul - 1988 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:249-254.
    The heuristics and strategies presented in Lakatos' Proofs and Refutations are well-known. However they hardly present the whole story as many authors have shown. In this paper a recent, rather spectacular, event in the history of mathematics is examined to gather evidence for two new strategies. The first heuristic concerns the expectations mathematicians have that a statement will be proved using given methods. The second heuristic tries to make sense of the mathematicians' notion of the quality of a proof.
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  8.  27
    Pi on Earth, or Mathematics in the Real World.Van Kerkhove Bart & Van Bendegem Jean Paul - 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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  9. Ross' Paradox is an Impossible Super-Task.Van Bendegem Jean Paul - 1994 - British Journal for the Philosophy of Science 45 (2):743-748.
  10.  24
    The Creative Growth of Mathematics.Jean Paul Van Bendegem - 1999 - Philosophica 63.
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    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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  12. 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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  13.  23
    Why the Largest Number Imaginable is Still a Finite Number.Jean Paul Van Bendegem - 1999 - Logique Et Analyse 42 (165-166).
  14.  58
    Zeno's Paradoxes and the Tile Argument.Van Bendegem Jean Paul - 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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  15.  10
    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, if (...)
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  16.  21
    Dialogue Logic and Problem-Solving.Jean Paul Van Bendegem - 1985 - Philosophica 35.
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  17.  7
    Feng Ye. Strict Finitism and the Logic of Mathematical Applications.Nigel Vinckier & Jean Paul Van Bendegem - 2016 - Philosophia Mathematica 24 (2):247-256.
  18.  26
    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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  19.  12
    First World Congress on Paraconsistency.Diderik Batens, Chris Mortenson, Graham Priest, Jean Paul Van Bendegem, Joke Meheus, Joachim Van Meirvenne & Erik Weber - 1996 - Studia Logica 56 (291).
  20.  27
    Review of P. Mancosu, K. F. Jørgensen, and S. A. Pedersen (Eds.), Visualization, Explanation and Reasoning Styles in Mathematics[REVIEW]Jean Paul Van Bendegem - 2006 - Philosophia Mathematica 14 (3):378-391.
    What is philosophy of mathematics and what is it about? The most popular answer, I suppose, to this question would be that philosophers should provide a justification for our presently most cherished mathematical theories and for the most important tool to develop such theories, namely logico-mathematical proof. In fact, it does cover a large part of the activity of philosophers that think about mathematics. Discussions about the merits and faults of classical logic versus one or other ‘deviant’ logics as the (...)
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  21.  33
    Thought Experiments in Mathematics: Anything but Proof.Jean Paul Van Bendegem - 2003 - Philosophica 72:9-33.
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  22.  5
    Fading Foundations in de Wiskunde?Jean Paul Van Bendegem - 2015 - Algemeen Nederlands Tijdschrift voor Wijsbegeerte 107 (2):155-159.
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  23.  26
    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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  24.  54
    Alternative Mathematics: The Vague Way.Van Bendegem Jean Paul - 2000 - Synthese 125 (1-2):19-31.
    Is alternative mathematics possible? More specifically, is it possible to imagine that mathematics could have developed in any other than the actual direction? The answer defended in this paper is yes, and the proof consists of a direct demonstration. An alternative mathematics that uses vague concepts and predicatesis outlined, leading up to theorems such as "Small numbers have few prime factors''.
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  25.  24
    How Infinities Cause Problems in Classical Physical Theories.Jean Paul Van Bendegem - 1992 - Philosophica 50.
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  26.  4
    Math Worlds: Philosophical and Social Studies of Mathematics and Mathematics Education.Sal Restivo, Jean Paul Van Bendegem & Roland Fischer (eds.) - 1993 - State University of New York Press.
    An international group of distinguished scholars brings a variety of resources to bear on the major issues in the study and teaching of mathematics, and on the problem of understanding mathematics as a cultural and social phenomenon. All are guided by the notion that our understanding of mathematical knowledge must be grounded in and reflect the realities of mathematical practice. Chapters on the philosophy of mathematics illustrate the growing influence of a pragmatic view in a field traditionally dominated by platonic (...)
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  27. 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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  28.  12
    Introduction.Jean Paul Van Bendegem - 1989 - Philosophica 43.
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  29.  25
    Foundations of Mathematics or Mathematical Practice: Is One Forced to Choose?Jean Paul Van Bendegem - 1989 - Philosophica 43.
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  30.  41
    Paraconsistency and Dialogue Logic Critical Examination and Further Explorations.Van Bendegem Jean Paul - 2001 - Synthese 127 (1-2):35-55.
    The first part of this paper presents asympathetic and critical examination of the approachof Shahid Rahman and Walter Carnielli, as presented intheir paper The Dialogical Approach toParaconsistency. In the second part, possibleextensions are presented and evaluated: (a) top-downanalysis of a dialogue situation versus bottom-up, (b)the specific role of ambiguities and how to deal withthem, and (c) the problem of common knowledge andbackground knowledge in dialogues. In the third part,I claim that dialogue logic is the best-suitedinstrument to analyse paradoxes of the (...)
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  31.  11
    Pragmatics and Mathematics or How Do Mathematicians Talk?Jean Paul Van Bendegem - 1982 - Philosophica 29.
  32. Theory and Experiment Recent Insights and New Perspectives on Their Relation.Diderik Batens, Jean Paul van Bendegem & International Union of the History and Philosophy of Science - 1988
     
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  33.  5
    Feng Ye. Strict Finitism and the Logic of Mathematical Applications. Synthese Library; 355. Springer, 2011. ISBN: 978-94-007-1346-8 ; 978-94-007-1347-5 . Pp. Xii + 272. [REVIEW]Nigel Vinckier & Jean Paul Van Bendegem - forthcoming - Philosophia Mathematica:nkw005.
  34.  40
    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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  35.  29
    Dirk Van Dalen, Mystic, Geometer, and Intuitionist. The Life of L.E.J. Brouwer, Volume 1: The Dawning Revolution.Jean Paul Van Bendegem - 2003 - Studia Logica 74 (3):469-471.
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  36.  9
    Argumentation and Pseudoscience The Case for an Ethics ofArgumentation.Jean Paul van Bendegem - 2013 - In Massimo Pigliucci & Maarten Boudry (eds.), Philosophy of Pseudoscience: Reconsidering the Demarcation Problem. University of Chicago Press.
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  37.  6
    How to Tell the Continuous From the Discrete.Jean Paul van Bendegem - 2000 - In François Beets & Eric Gillet (eds.), Logique En Perspective: Mélanges Offerts à Paul Gochet. Ousia. pp. 501--511.
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  38. Relevant Derivability and Classical Derivability in Fitch-Style and Axiomatic Formulations of Relevant Logics.Diderik Batens & Jean Paul Van Bendegem - 1985 - Logique Et Analyse 109 (9):22-31.
  39.  7
    One Hundred Years of Intuitionism (1907-2007).Jean Paul Van Bendegem - 2011 - Studia Logica 97 (3):421-425.
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  40.  10
    The Interplay of Psychology and Mathematics Education: From the Attraction of Psychology to the Discovery of the Social.Karen François, Kathleen Coessens & Jean Paul Van Bendegem - 2012 - Journal of Philosophy of Education 46 (3):370-385.
    It is a rather safe statement to claim that the social dimensions of the scientific process are accepted in a fair share of studies in the philosophy of science. It is a somewhat safe statement to claim that the social dimensions are now seen as an essential element in the understanding of what human cognition is and how it functions. But it would be a rather unsafe statement to claim that the social is fully accepted in the philosophy of mathematics. (...)
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  41.  12
    Review of C. Mortensen, Inconsistent Mathematics[REVIEW]Jean Paul van Bendegem - 1999 - Philosophia Mathematica 7 (2):202-212.
  42.  13
    Introduction to the Special Issue Entitled 'Mathematics: What Does It All Mean?'. [REVIEW]Bart Van Kerkhove, Jean Paul Van Bendegem & Sal Restivo - 2006 - Foundations of Science 11 (1-2):1-3.
  43.  4
    Review of T. Koetsier, Lakatos' Philosophy of Mathematics: A Historical Approach[REVIEW]Jean Paul van Bendegem - 1994 - Philosophia Mathematica 2 (2).
  44.  1
    Call for Papers First World Congress on Paraconsistency, Gent, Belgium 1997.Diderik Batens, Chris Mortenson, Graham Priest, Jean Paul Van Bendegem, Joke Meheus, Joachim Van Meirvenne & Erik Weber - 1996 - Journal of Applied Non-Classical Logics 6 (2).
  45.  10
    Metadebates on Science: The Blue Book of 'Einstein Meets Magritte'.Gustaaf C. Cornelis, Sonja Smets & Jean Paul van Bendegem (eds.) - 1999 - Kluwer Academic.
    How do scientists approach science? Scientists, sociologists and philosophers were asked to write on this intriguing problem and to display their results at the International Congress `Einstein Meets Magritte'. The outcome of their effort can be found in this rather unique book, presenting all kinds of different views on science. Quantum mechanics is a discipline which deserves and receives special attention in this book, mainly because it is fascinating and, hence, appeals to the general public. This book not only contains (...)
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  46. Een korte repliek op mijn commentatoren.Jean Paul Van Bendegem - 2010 - Algemeen Nederlands Tijdschrift voor Wijsbegeerte 3:206-211.
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  47. Een verdediging van het strikt finitisme.Jean Paul van Bendegem - 2010 - Algemeen Nederlands Tijdschrift voor Wijsbegeerte 102 (3):164-183.
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  48. Finite, Empirical Mathematics, Outline of a Model.Jean Paul van Bendegem - 1987 - Rijksuniversiteit Te Gent.
     
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  49. Non-Realism, Nominalism and Strict Finitism the Sheer Complexity of It All.Jean Paul Van Bendegem - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 90:343-365.
  50. 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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