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25Metadebates on science: the blue book of 'Einstein meets Magritte' (edited book)Kluwer Academic. 1999.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…Read more
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1In Defence of Discrete Space and TimeLogique Et Analyse 38 (150-1): 127-150. 1995.In this paper several arguments are discussed and evaluated concerning the possibility of discrete space and time.
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37Feng Ye. Strict Finitism and the Logic of Mathematical ApplicationsPhilosophia Mathematica 24 (2): 247-256. 2016.
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Een verdediging van het strikt finitismeAlgemeen Nederlands Tijdschrift voor Wijsbegeerte 102 (3): 164-183. 2010.
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Van gebroken orde naar herstelde fragmenten. Enkele bedenkingen bij Leo Apostels recente publicatiesde Uil Van Minerva 10. 1994.
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74The Collatz conjecture. A case study in mathematical problem solvingLogic and Logical Philosophy 14 (1): 7-23. 2005.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 you like, to construct a …Read more
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Non-Realism, Nominalism and Strict Finitism the Sheer Complexity of It AllPoznan Studies in the Philosophy of the Sciences and the Humanities 90 343-365. 2006.
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23How to tell the continuous from the discreteIn François Beets & Eric Gillet (eds.), Logique En Perspective: Mélanges Offerts à Paul Gochet, Ousia. pp. 501--511. 2000.
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118Zeno's paradoxes and the tile argumentPhilosophy of Science 54 (2): 295-302. 1987.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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11Do We also Need Second-order Mathematics?Constructivist Foundations 10 (1): 34-35. 2014.Open peer commentary on the article “Second-Order Science: Logic, Strategies, Methods” by Stuart A. Umpleby. Upshot: The author makes a strong plea for second-order science but somehow mathematics remains out of focus. The major claim of this commentary is that second-order science requires second-order mathematics
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The possibility of discrete timeIn Craig Callender (ed.), The Oxford Handbook of Philosophy of Time, Oxford University Press. 2011.
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193Review of C. Mortensen, Inconsistent Geometry (review)Philosophia Mathematica 20 (3): 365-372. 2012.
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156Ross' paradox is an impossible super-taskBritish Journal for the Philosophy of Science 45 (2): 743-748. 1994.
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32Math Worlds: Philosophical and Social Studies of Mathematics and Mathematics Education (edited book)State University of New York Press. 1993.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 traditiona…Read more
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Over Newton. Een bedenking en een aanvulling bij Leo Apostel, 'Wat we van Newton hebben geleerd'de Uil Van Minerva 6. 1989.
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55Inconsistency in mathematics and the mathematics of inconsistencySynthese 191 (13): 3063-3078. 2014.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…Read more
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Vergauwen, R., A Metalogical Theory of Reference (review)Tijdschrift Voor Filosofie 56 (2): 350. 1994.
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De Pater, W., Vergauwen, R., Logica: formeel en informeel (review)Tijdschrift Voor Filosofie 55 (3): 570. 1993.
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64Review 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. 2006.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’…Read more
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36Non-Formal Properties of Real Mathematical ProofsPSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988 249-254. 1988.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 quali…Read more
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Vrije Universiteit BrusselRegular Faculty
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Ghent UniversityRegular Faculty
Areas of Specialization
Logic and Philosophy of Logic |
Philosophy of Mathematics |