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Jean Paul Van Bendegem
Vrije Universiteit Brussel
  1. Epistemic injustice in mathematics.Colin Jakob Rittberg, Fenner Stanley Tanswell & Jean Paul Van Bendegem - 2020 - Synthese 197 (9):3875-3904.
    We investigate how epistemic injustice can manifest itself in mathematical practices. We do this as both a social epistemological and virtue-theoretic investigation of mathematical practices. We delineate the concept both positively—we show that a certain type of folk theorem can be a source of epistemic injustice in mathematics—and negatively by exploring cases where the obstacles to participation in a mathematical practice do not amount to epistemic injustice. Having explored what epistemic injustice in mathematics can amount to, we use the concept (...)
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  2.  86
    Frontiers in Paraconsistent Logic.Diderik Batens, Chris Mortensen, Graham Priest & Jean Paul Van Bendegem (eds.) - 2000 - Research Studies Press.
    Paraconsistent logic, logic in which inconsistent information does not deliver arbitrary conclusions, is one of the fastest growing areas of logic, with roots in profound philosophical issues, and applications in information processing and philosophy of science. This book contains selected papers presented at the First World Congress on Paraconsistency, held in Ghent in 1997. It contains papers on various aspects of the subject. As such, it should be of interest to all who want to learn what the subject is, and (...)
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  3. The Impact of the Philosophy of Mathematical Practice on the Philosophy of Mathematics.Jean Paul Van Bendegem - 2014 - In Léna Soler, Sjoerd Zwart, Michael Lynch & Vincent Israel-Jost (eds.), Science After the Practice Turn in the Philosophy, History, and Social Studies of Science. New York, USA: Routledge. pp. 215-226.
     
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  4.  60
    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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  5.  9
    Philosophical Perspectives on Mathematical Practice.Bart Van Kerkhove, Jean Paul Van Bendegem & Jonas De Vuyst (eds.) - 2010 - College Publications.
    It has been observed many times before that, as yet, there are no encompassing, integrated theories of mathematical practice available.To witness, as we currently do, a variety of schools in this field elaborating their philosophical frameworks, and trying to sort out their differences in the course of doing so, is also to be constantly reminded of the fact that a lot of epistemic aspects, extremely relevant to this task, remain dramatically underexamined. This volume wants to contribute to the stock of (...)
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  6. Ross' paradox is an impossible super-task.Jean Paul van Bendegem - 1994 - British Journal for the Philosophy of Science 45 (2):743-748.
  7.  27
    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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  8. 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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  9.  57
    Thought Experiments in Mathematics: Anything but Proof.Jean Paul van Bendegem - 2003 - Philosophica 72 (2):9-33.
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  10.  37
    The Unreasonable Richness of Mathematics.Jean Paul Van Bendegem & Bart Van Kerkhove - 2004 - Journal of Cognition and Culture 4 (3-4):525-549.
    The paper gives an impression of the multi-dimensionality of mathematics as a human activity. This 'phenomenological' exercise is performed within an analytic framework that is both an expansion and a refinement of the one proposed by Kitcher. Such a particular tool enables one to retain an integrated picture while nevertheless welcoming an ample diversity of perspectives on mathematical practices, that is, from different disciplines, with different scopes, and at different levels. Its functioning is clarified by fitting in illustrations based on (...)
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  11. 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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  12.  14
    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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  13. 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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  14.  33
    Non-Formal Properties of Real Mathematical Proofs.Jean Paul van Bendegem - 1988 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:249-254.
    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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  15. Why the largest number imaginable is still a finite number.Jean Paul Van Bendegem - 1999 - Logique Et Analyse 42 (165-166).
  16.  11
    Regulating Academic Pressure: From Fast to Slow.Karen François, Kathleen Coessens, Nigel Vinckier & Jean Paul van Bendegem - 2020 - Journal of Philosophy of Education 54 (5):1419-1442.
    Journal of Philosophy of Education, EarlyView.
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  17.  38
    The Creative Growth of Mathematics.Jean Paul van Bendegem - 1999 - Philosophica 63 (1).
  18.  66
    Paraconsistency And Dialogue Logic Critical Examination And Further Explorations.Jean Paul Van Bendegem - 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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  19.  23
    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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  20. 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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  21.  3
    Math and Music: Slow and Not For Profit.Kathleen Coessens, Karen François & Jean Paul Van Bendegem - 2018 - In Paul Smeyers & Marc Depaepe (eds.), Educational Research: Ethics, Social Justice, and Funding Dynamics. Springer Verlag. pp. 73-90.
    This chapter looks at the impact of recent societal approaches of knowledge and science from the perspectives of two rather distant educational domains, mathematics and music. Science’s attempt at ‘self-understanding’ has led to a set of control mechanisms, either generating ‘closure’—the scientists’ non-involvement in society—or ‘economisation’, producing patents and other lucrative benefits. While scientometrics became the tool and the rule for measuring the economic impact of science, counter movements, like the slow science movement, citizen science, empowering music-art initiatives and other (...)
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  22.  12
    We’re Only in It for the Money : The Financial Structure of STEM and STEAM Research.Karen François, Kathleen Coessens & Jean Paul Van Bendegem - 2018 - In Paul Smeyers & Marc Depaepe (eds.), Educational Research: Ethics, Social Justice, and Funding Dynamics. Springer Verlag. pp. 261-274.
    The development of the philosophy of science in the twentieth century has created a framework where issues concerning funding dynamics can be easily accommodated. It combines the historical-philosophical approach of Thomas Kuhn. The University of Chicago Press, Chicago, [1962] ) with the sociological approach of Robert K. Merton The sociology of science. Theoretical and empirical investigations. The University of Chicago Press, Chicago, pp 267–278, [1942] ), linking the ‘exact’ sciences to economy and politics. Out of this came a new domain, (...)
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  23. 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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  24.  27
    Dialogue Logic and Problem-Solving.Jean Paul van Bendegem - 1985 - Philosophica 35.
  25.  27
    Foundations of Mathematics or Mathematical Practice: Is One Forced to Choose?Jean Paul van Bendegem - 1989 - Philosophica 43.
  26.  58
    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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  27.  20
    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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  28. Incommensurability: An algorithmic Approach.Jean Paul van Bendegem - 1983 - Philosophica 32.
  29.  75
    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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  30. 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).
  31. 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.
  32.  24
    Metadebates on science: the blue book of 'Einstein meets Magritte'.Gustaaf C. Cornelis, Sonja Smets & Jean Paul van Bendegem (eds.) - 1999 - Boston: 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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  33.  26
    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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  34.  31
    Evolutionary Epistemology, Language and Culture: A Non-Adaptationist, Systems Theoretical Approach.Nathalie Gontier, Jean Paul van Bendegem & Diederik Aerts (eds.) - 2006 - Springer.
    For the first time in history, scholars working on language and culture from within an evolutionary epistemological framework, and thereby emphasizing complementary or deviating theories of the Modern Synthesis, were brought together. Of course there have been excellent conferences on Evolutionary Epistemology in the past, as well as numerous conferences on the topics of Language and Culture. However, until now these disciplines had not been brought together into one all-encompassing conference. Moreover, previously there never had been such stress on alternative (...)
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  35. 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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  36.  2
    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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  37.  50
    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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  38. Een korte repliek op mijn commentatoren.Jean Paul Van Bendegem - 2010 - Algemeen Nederlands Tijdschrift voor Wijsbegeerte 102 (3):206-211.
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  39.  14
    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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  40. Een verdediging van het strikt finitisme.Jean Paul van Bendegem - 2010 - Algemeen Nederlands Tijdschrift voor Wijsbegeerte 102 (3):164-183.
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  41. Finite, empirical mathematics, outline of a model.Jean Paul van Bendegem - 1987 - Gent: Rijksuniversiteit te Gent.
     
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  42.  4
    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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  43.  37
    How Infinities Cause Problems in Classical Physical Theories.Jean Paul van Bendegem - 1992 - Philosophica 50.
  44.  18
    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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  45.  13
    Introduction.Jean Paul van Bendegem - 1989 - Philosophica 43.
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  46.  47
    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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  47.  45
    Introductory Note.Jean Paul van Bendegem - 1988 - Philosophica 42.
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  48.  2
    Incompleteness, Nonlocality, and Realism. Michael Redhead.Jean Paul van Bendegem - 1989 - Philosophica 44.
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  49.  14
    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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  50.  2
    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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