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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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16Perspectives 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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14Why I Am a Constructivist AtheistConstructivist Foundations 11 (1): 138-140. 2015.Open peer commentary on the article “Religion: A Radical-Constructivist Perspective” by Andreas Quale. Upshot: An essential feature of Quale’s point of view is the strict distinction between the cognitive and the non-cognitive. I argue that this position is untenable and hence that a radical constructivist can discuss religious matters
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29Foundations of Mathematics or Mathematical Practice: Is One Forced to Choose?Philosophica 43 (n/a). 1989.
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53Dirk Van Dalen, mystic, geometer, and intuitionist. The life of L.e.J. Brouwer, volume 1: The dawning revolutionStudia Logica 74 (3): 469-471. 2003.
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6Philosophy of mathematics today/Evandro Agazzi en György Darvas (eds.).-Dordrecht: Kluwer Academic Publishers, 1997-(Episteme; 22) (review)Studia Logica: An International Journal for Symbolic Logic 65 (2): 275-278. 2000.
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15Review of T. Koetsier, Lakatos' Philosophy of Mathematics: A Historical Approach (review)Philosophia Mathematica 2 (2). 1994.
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39Schoonheid in de wiskunde: Birkhoff revisitedTijdschrift Voor Filosofie 60 (1): 106-130. 1998.Everyone is familiar with the measure of beauty that has been proposed by Birkhoff, the famous formula M = O/C. Although I show that the formula in its original form cannot be maintained, I present a reinterpretation that adapts the formula for measuring the beauty of mathematical proofs. However, this type of measure is not the only aesthetic element in mathematics. There exists a 'romantic' side as well, to use the term introduced by François Le Lionnais. Thus, a more complex proposal of mathe…Read more
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69Review of C. Mortensen, Inconsistent Mathematics (review)Philosophia Mathematica 7 (2): 202-212. 1999.
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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 |