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93Frontiers in Paraconsistent Logic (edited book)Research Studies Press. 2000.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…Read more
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23Kurt Gödels onvolledigheidsstellingen en de grenzen van de kennisAlgemeen Nederlands Tijdschrift voor Wijsbegeerte 113 (1): 157-182. 2021.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…Read more
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17Emily Rolfe* Great Circles: The Transits of Mathematics and PoetryPhilosophia Mathematica 28 (3): 431-441. 2020.
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4Upon the Academic Philosopher Caught in the Fly-BottleIn Stefan Ramaekers & Naomi Hodgson (eds.), Past, Present, and Future Possibilities for Philosophy and History of Education: Finding Space and Time for Research, Springer Verlag. pp. 117-130. 2018.Philosophy as an academic discipline has grown into something highly specific. This raises the question whether alternatives are available within the academic world itself – what I call the Lutheran view – and outside of academia – what I call the Calvinist view. Since I defend the thesis that such alternatives partially exist and as yet non-existent possibilities could in principle be realised, the main question thus becomes what prevents us from acting appropriately. In honour of Paul Smeyers,…Read more
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13Dirk Van Dalen, Mystic, Geometer, and Intuitionist. The life of L.E.J. Brouwer, Volume 1: The Dawning Revolution (review)Studia Logica 74 (3): 469-471. 2003.
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17Perspectives on Mathematical Practices (edited book)Springer. 2007.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. T…Read more
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The Impact of the Philosophy of Mathematical Practice on the Philosophy of MathematicsIn Léna Soler, S. D. Sjoerd D. Sjoerd Zwart, Michael Lynch & Vincent Israel-Jost (eds.), Science After the Practice Turn in the Philosophy, History, and Social Studies of Science, Routledge. pp. 215-226. 2014.
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149Epistemic injustice in mathematicsSynthese 197 (9): 3875-3904. 2020.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 in…Read more
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11Laws of Form and Paraconsistent Logic (review)Constructivist Foundations 13 (1): 21-22. 2017.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.
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13The Tricky Transition from Discrete to Continuous (review)Constructivist Foundations 12 (3): 253-254. 2017.I show that the author underestimates the tricky matter of how to make a transition from the discrete, countable to the continuous, uncountable case.
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27Moktefi, 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)Acta Baltica Historiae Et Philosophiae Scientiarum 5 (1): 101-105. 2017.
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22Mathematical Practice and Naturalist Epistemology: Structures with Potential for InteractionPhilosophia Scientiae 9 61-78. 2005.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 …Read more
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The logical analysis of time and the problem of indeterminismCommunication and Cognition. Monographies 26 (2): 209-230. 1993.
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Edereen die niet denkt zoals ik, volge mij. Acta 16e Nederlands-Vlaamse Filosofiedag (edited book)VUB Press. 1994.
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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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Een verdediging van het strikt finitismeAlgemeen Nederlands Tijdschrift voor Wijsbegeerte 102 (3): 164-183. 2010.
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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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119Zeno'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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The possibility of discrete timeIn Craig Callender (ed.), The Oxford Handbook of Philosophy of Time, Oxford University Press. 2011.
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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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157Ross' paradox is an impossible super-taskBritish Journal for the Philosophy of Science 45 (2): 743-748. 1994.
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193Review of C. Mortensen, Inconsistent Geometry (review)Philosophia Mathematica 20 (3): 365-372. 2012.
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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 |