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Profile: Jean Paul van Bendegem (Vrije Universiteit Brussel, University of Ghent)
  1. Jean Paul Van Bendegem (1983). Incommensurability: An Algorithmic Approach. Philosophica 32.
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  2. Bart Van Kerkhove, Jean Paul Van Bendegem & Jonas De Vuyst (eds.) (2010). Philosophical Perspectives on Mathematical Practice. College Publications.
  3.  32
    Jean Paul van Bendegem & Bart van Kerkhove (2009). Mathematical Arguments in Context. 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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  4.  2
    Nigel Vinckier & Jean Paul Van Bendegem (forthcoming). 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] Philosophia Mathematica:nkw005.
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  5. Diderik Batens, Chris Mortensen, Graham Priest & Jean Paul Van Bendegem (eds.) (2000). Frontiers in Paraconsistent Logic. Research Studies Press.
     
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  6.  24
    Bart Van Kerkhove & Jean Paul Van Bendegem (2008). Pi on Earth, or Mathematics in the Real World. 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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  7.  14
    Jean Paul Van Bendegem (1999). The Creative Growth of Mathematics. Philosophica 63.
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  8.  17
    Jean Paul Van Bendegem (1985). Dialogue Logic and Problem-Solving. Philosophica 35.
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  9.  91
    Jean Paul Van Bendegem (1994). Ross' Paradox is an Impossible Super-Task. British Journal for the Philosophy of Science 45 (2):743-748.
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  10.  17
    Jean Paul Van Bendegem (1999). Why the Largest Number Imaginable is Still a Finite Number. Logique Et Analyse 42 (165-166).
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  11.  8
    Jean Paul Van Bendegem (2003). Classical Arithmetic is Quite Unnatural. 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. Jean Paul van Bendegem (1995). In Defence of Discrete Space and Time. 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.  10
    Bart Van Kerkhove & Jean Paul Van Bendegem (2005). Mathematical Practice and Naturalist Epistemology: Structures with Potential for Interaction. 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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  14.  19
    Jean Paul Van Bendegem (1992). Introductory Note. Philosophica 50.
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  15.  9
    Jean Paul Van Bendegem (1989). Introduction. Philosophica 43.
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  16.  7
    Jean Paul Van Bendegem (2005). The Collatz Conjecture. A Case Study in Mathematical Problem Solving. 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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  17.  24
    Jean Paul Van Bendegem (2013). Significs and Mathematics: Creative and Other Subjects. 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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  18.  28
    Jean Paul Van Bendegem (2003). Thought Experiments in Mathematics: Anything but Proof. Philosophica 72:9-33.
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  19.  10
    Diderik Batens, Chris Mortenson, Graham Priest, Jean Paul Van Bendegem, Joke Meheus, Joachim Van Meirvenne & Erik Weber (1996). First World Congress on Paraconsistency. Studia Logica 56 (291).
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  20.  31
    Jean Paul Van Bendegem (1987). Zeno's Paradoxes and the Tile Argument. 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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  21.  7
    Jean Paul Van Bendegem (1982). Pragmatics and Mathematics or How Do Mathematicians Talk? Philosophica 29.
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  22.  19
    Jean Paul Van Bendegem (1992). How Infinities Cause Problems in Classical Physical Theories. Philosophica 50.
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  23.  11
    Jean Paul van Bendegem (2014). Inconsistency in Mathematics and the Mathematics of Inconsistency. 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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  24.  18
    Jean Paul Van Bendegem (1989). Foundations of Mathematics or Mathematical Practice: Is One Forced to Choose? Philosophica 43.
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  25.  39
    Jean Paul Van Bendegem (2005). Proofs and Arguments: The Special Case of Mathematics. 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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  26.  4
    Sal Restivo, Jean Paul Van Bendegem & Roland Fischer (eds.) (1993). Math Worlds: Philosophical and Social Studies of Mathematics and Mathematics Education. 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. Diderik Batens, Jean Paul van Bendegem & International Union of the History and Philosophy of Science (1988). Theory and Experiment Recent Insights and New Perspectives on Their Relation. Monograph Collection (Matt - Pseudo).
     
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  28.  7
    Jean Paul van Bendegem (2013). Argumentation and Pseudoscience The Case for an Ethics ofArgumentation. In Massimo Pigliucci & Maarten Boudry (eds.), Philosophy of Pseudoscience: Reconsidering the Demarcation Problem. University of Chicago Press
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  29.  25
    Jean Paul Van Bendegem (2003). Dirk Van Dalen, Mystic, Geometer, and Intuitionist. The Life of L.E.J. Brouwer, Volume 1: The Dawning Revolution. Studia Logica 74 (3):469-471.
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  30.  6
    Jean Paul Van Bendegem (2011). One Hundred Years of Intuitionism (1907-2007). Studia Logica 97 (3):421-425.
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  31.  21
    Jean Paul Van Bendegem (2000). Alternative Mathematics: The Vague Way. 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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  32.  17
    Jean Paul Van Bendegem (2006). Review of P. Mancosu, K. F. Jørgensen, and S. A. Pedersen (Eds.), Visualization, Explanation and Reasoning Styles in Mathematics. [REVIEW] 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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  33.  16
    Jean Paul Van Bendegem (2001). Paraconsistency and Dialogue Logic Critical Examination and Further Explorations. 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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  34.  12
    Jean Paul van Bendegem (1999). Review of C. Mortensen, Inconsistent Mathematics. [REVIEW] Philosophia Mathematica 7 (2):202-212.
  35. Diderik Batens & Jean Paul Van Bendegem (1985). Relevant Derivability and Classical Derivability in Fitch-Style and Axiomatic Formulations of Relevant Logics. Logique Et Analyse 109 (9):22-31.
     
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  36.  2
    Jean Paul van Bendegem (2000). How to Tell the Continuous From the Discrete. In François Beets & Eric Gillet (eds.), Logique En Perspective: Mélanges Offerts à Paul Gochet. Ousia 501--511.
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  37.  4
    Jean Paul Van Bendegem (2006). Review of P. Mancosu, K. F. Jørgensen, and S. A. Pedersen (Eds.), Visualization, Explanation and Reasoning Styles in Mathematics. [REVIEW] Philosophia Mathematica 14 (3):378-391.
  38.  6
    Karen François, Kathleen Coessens & Jean Paul Van Bendegem (2012). The Interplay of Psychology and Mathematics Education: From the Attraction of Psychology to the Discovery of the Social. 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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  39.  11
    Bart Van Kerkhove, Jean Paul Van Bendegem & Sal Restivo (2006). Introduction to the Special Issue Entitled 'Mathematics: What Does It All Mean?'. [REVIEW] Foundations of Science 11 (1-2):1-3.
  40.  10
    Jean Paul Van Bendegem (2007). Book Review. [REVIEW] Studia Logica 87 (1):135-138.
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  41.  3
    Jean Paul van Bendegem (1994). Review of T. Koetsier, Lakatos' Philosophy of Mathematics: A Historical Approach. [REVIEW] Philosophia Mathematica 2 (2).
  42. Diderik Batens, Chris Mortenson, Graham Priest, Jean Paul Van Bendegem, Joke Meheus, Joachim Van Meirvenne & Erik Weber (1996). Call for Papers First World Congress on Paraconsistency, Gent, Belgium 1997. Journal of Applied Non-Classical Logics 6 (2).
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  43.  7
    Gustaaf C. Cornelis, Sonja Smets & Jean Paul van Bendegem (eds.) (1999). Metadebates on Science: The Blue Book of 'Einstein Meets Magritte'. 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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  44. Jean Paul Van Bendegem (2010). Een korte repliek op mijn commentatoren. Algemeen Nederlands Tijdschrift voor Wijsbegeerte 3:206-211.
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  45. Jean Paul van Bendegem (2010). Een verdediging van het strikt finitisme. Algemeen Nederlands Tijdschrift voor Wijsbegeerte 102 (3):164-183.
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  46. Jean Paul van Bendegem (1987). Finite, Empirical Mathematics, Outline of a Model. Rijksuniversiteit Te Gent.
     
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  47. Jean Paul Van Bendegem (1988). Introductory Note. Philosophica 42.
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  48. Jean Paul Van Bendegem (1985). Introductory Note. Philosophica 35.
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  49. Jean Paul Van Bendegem (1993). Inleiding tot de moderne logica en wetenschapsfilosofie : een terreinverkenning. Tijdschrift Voor Filosofie 55 (2):361-363.
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  50. Jean Paul Van Bendegem (2006). Non-Realism, Nominalism and Strict Finitism the Sheer Complexity of It All. Poznan Studies in the Philosophy of the Sciences and the Humanities 90:343-365.
     
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