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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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12Introduction: From Practice to Results in Mathematics and LogicPhilosophia Scientiae 16 (1): 5-11. 2012.1 Mathematical practice: a short overview This volume is a collection of essays that discuss the relationships between the practices deployed by logicians and mathematicians, either as individuals or as members of research communities, and the results from their research. We are interested in exploring the concept of 'practices' in the formal sciences. Though common in the history, philosophy and sociology of science, this concept has surprisingly thus far been little reflected upon in logic...
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12Het complexe verhaal van de wiskunde in de TractatusAlgemeen Nederlands Tijdschrift voor Wijsbegeerte 115 (2): 196-208. 2023.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…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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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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10Introduction: From Practice to Results in Mathematics and LogicPhilosophia Scientiae 16 5-11. 2012.1 Mathematical practice: a short overview This volume is a collection of essays that discuss the relationships between the practices deployed by logicians and mathematicians, either as individuals or as members of research communities, and the results from their research. We are interested in exploring the concept of 'practices' in the formal sciences. Though common in the history, philosophy and sociology of science, this concept has surprisingly thus far been little reflected upon in logic...
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9Math and Music: Slow and Not For ProfitIn Paul Smeyers & Marc Depaepe (eds.), Educational Research: Ethics, Social Justice, and Funding Dynamics, Springer Verlag. pp. 73-90. 2018.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…Read more
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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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5Bias in Human Reasoning. Causes and Consequences. Essays in Cognitive Psychology, LEA, Hove and London, 1989. Jonathan St.B.T. Evans (review)Philosophica 45 (n/a). 1990.
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5Introduction to the Special Issue Entitled ‘Mathematics: What Does it All Mean?’Foundations of Science 11 (1-2): 1-3. 2006.
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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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4Mathematical Arguments in ContextFoundations of Science 14 (1-2): 45-57. 2009.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 presenta…Read more
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4Choices. An introduction to decision theory. Minneapolis: University of Minnesota Press, 1987. Michael D. ResnikPhilosophica 41 (n/a). 1988.
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4Polymath as an Epistemic CommunityIn Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice, Springer. pp. 2727-2756. 2024.The Polymath Project is an online collaborative enterprise that was initiated in 2009, when Timothy Gowers asked whether and how groups could work together to solve mathematical problems that “do not naturally split up into a vast number of subtasks.” Gowers proposed to answer this question himself by actually trying to set up such a collaboration, based on interactions taking place in the comment-threads of a series of posts on a WordPress blog. Hence, the first project officially started in ea…Read more
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4Ascent to Truth. A Critical Examination of Quine’s Philosophy. Munchen: Philosophia Verlag, 1986. Paul GochetPhilosophica 39 (n/a). 1987.
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2Non-Formal Properties of Real Mathematical ProofsPSA Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988 (1): 249-254. 1988.Suppose you attend a seminar where a mathematician presents a proof to some of his colleagues. Suppose further that what he is proving is an important mathematical statement Now the following happens: as the mathematician proceeds, his audience is amazed at first, then becomes angry and finally ends up disturbing the lecture (some walk out, some laugh, …). If in addition, you see that the proof he is presenting is formally speaking (nearly) correct, would you say you are witnessing an extraordin…Read more
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2What does it all mean? A very short introduction to philosophy. Oxford: Oxford University Press, 1987. Thomas NagelPhilosophica 41 (n/a). 1988.
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1Paraconsistent Logic. Essays on the Inconsistent. Munchen: Philosophia Verlag, 1990. Graham Priest, Richard Routley and Jean Norman (eds.) (review)Philosophica 47 (n/a). 1991.
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1Inleiding tot de moderne logica en wetenschapsfilosofie : een terreinverkenningTijdschrift Voor Filosofie 55 (2): 361-363. 1993.
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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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1Wolfgang Pauli. Writings on Physics and Philosophy. Heidelberg, Springer-Verlag, 1994. Charles P. Enz and Karl von Meyenn (eds.) (review)Philosophica 54 (n/a). 1994.
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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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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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Vrije Universiteit BrusselRegular Faculty
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Ghent UniversityRegular Faculty
Areas of Specialization
Logic and Philosophy of Logic |
Philosophy of Mathematics |