73 found
Order:
See also
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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  2.  77
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   20 citations  
  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.
     
    Export citation  
     
    Bookmark   6 citations  
  4.  58
    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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  5.  3
    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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark   5 citations  
  6.  24
    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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark   7 citations  
  7. 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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  8.  35
    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 (...)
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  9.  10
    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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark   5 citations  
  10. 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.
     
    Export citation  
     
    Bookmark   9 citations  
  11. Ross' paradox is an impossible super-task.Jean Paul van Bendegem - 1994 - British Journal for the Philosophy of Science 45 (2):743-748.
  12.  99
    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.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  13.  52
    Thought Experiments in Mathematics: Anything but Proof.Jean Paul van Bendegem - 2003 - Philosophica 72 (2):9-33.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  14.  8
    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.
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  15.  31
    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.
    Direct download  
     
    Export citation  
     
    Bookmark   6 citations  
  16. Why the largest number imaginable is still a finite number.Jean Paul Van Bendegem - 1999 - Logique Et Analyse 42 (165-166).
  17.  36
    The Creative Growth of Mathematics.Jean Paul van Bendegem - 1999 - Philosophica 63 (1).
  18.  62
    Paraconsistency And Dialogue Logic Critical Examination And Further Explorations.Jean Paul Van Bendegem - 2001 - Synthese 127 (1):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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  19. 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 (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  20. Inleiding tot de moderne logica en wetenschapsfilosofie : een terreinverkenning.Jean Paul Van Bendegem - 1993 - Tijdschrift Voor Filosofie 55 (2):361-363.
    No categories
     
    Export citation  
     
    Bookmark   4 citations  
  21.  22
    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 (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  22. 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 (...)
     
    Export citation  
     
    Bookmark   3 citations  
  23.  5
    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, (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  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.  51
    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 (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  27. Incommensurability: An algorithmic Approach.Jean Paul van Bendegem - 1983 - Philosophica 32.
  28.  68
    Alternative Mathematics: The Vague Way.Jean Paul Van Bendegem - 2000 - Synthese 125 (1):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''.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  29.  45
    Introductory Note.Jean Paul van Bendegem - 1988 - Philosophica 42.
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  30. Een verdediging van het strikt finitisme.Jean Paul van Bendegem - 2010 - Algemeen Nederlands Tijdschrift voor Wijsbegeerte 102 (3):164-183.
    No categories
     
    Export citation  
     
    Bookmark   1 citation  
  31.  12
    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 knowledgeIn 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 with (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  32.  59
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  33.  66
    Review of C. Mortensen, Inconsistent Mathematics[REVIEW]Jean Paul van Bendegem - 1999 - Philosophia Mathematica 7 (2):202-212.
  34.  12
    Emily Rolfe* Great Circles: The Transits of Mathematics and Poetry.Jean Paul Van Bendegem & Bart Van Kerkhove - 2020 - Philosophia Mathematica 28 (3):431-441.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  35.  44
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  36.  21
    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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  37. Een korte repliek op mijn commentatoren.Jean Paul Van Bendegem - 2010 - Algemeen Nederlands Tijdschrift voor Wijsbegeerte 102 (3):206-211.
    No categories
     
    Export citation  
     
    Bookmark  
  38. Finite, Empirical Mathematics, Outline of a Model.Jean Paul van Bendegem - 1987 - Rijksuniversiteit Te Gent.
     
    Export citation  
     
    Bookmark  
  39. 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.
  40. Ontwerp voor een analytische filosofie van de eindigheid.Jean Paul van Bendegem - 2003 - Algemeen Nederlands Tijdschrift voor Wijsbegeerte 95 (1):61-72.
    No categories
     
    Export citation  
     
    Bookmark  
  41. Tot in der Eindigheid.Jean Paul Van Bendegem - 1998 - Tijdschrift Voor Filosofie 60 (2):405-407.
    No categories
     
    Export citation  
     
    Bookmark  
  42.  8
    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.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  43.  21
    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.
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  44.  26
    Feng Ye. Strict Finitism and the Logic of Mathematical Applications.Nigel Vinckier & Jean Paul Van Bendegem - 2016 - Philosophia Mathematica 24 (2):247-256.
  45.  31
    How Infinities Cause Problems in Classical Physical Theories.Jean Paul van Bendegem - 1992 - Philosophica 50.
  46.  45
    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.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  47. 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.
     
    Export citation  
     
    Bookmark  
  48.  27
    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.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  49. Laws of Form and Paraconsistent Logic. [REVIEW]Jean Paul Van Bendegem - 2017 - Constructivist Foundations 13 (1):21-22.
    The aim of this commentary is to show that a new development in formal logic, namely paraconsistent logic, should be connected with the laws of form. This note also includes some personal history to serve as background.
     
    Export citation  
     
    Bookmark  
  50.  24
    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. (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
1 — 50 / 73