
Upon the Academic Philosopher Caught in the FlyBottleIn 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. 117130. 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 nonexistent possibilities could in principle be realised, the main question thus becomes what prevents us from acting appropriately. In honour of Paul Smeyers,…Read more

We’re Only in It for the Money : The Financial Structure of STEM and STEAM ResearchIn Paul Smeyers & Marc Depaepe (eds.), Educational Research: Ethics, Social Justice, and Funding Dynamics, Springer Verlag. pp. 261274. 2018.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 historicalphilosophical 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 econo…Read more

Math and Music: Slow and Not For ProfitIn Paul Smeyers & Marc Depaepe (eds.), Educational Research: Ethics, Social Justice, and Funding Dynamics, Springer Verlag. pp. 7390. 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 ‘selfunderstanding’ has led to a set of control mechanisms, either generating ‘closure’—the scientists’ noninvolvement 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

8Mystic, Geometer, and Intuitionist. The Life of L. E. J. Brouwer, Volume 1: The Dawning RevolutionStudia Logica 74 (3): 469471. 2003.

6Perspectives 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

The Impact of the Philosophy of Mathematical Practice on the Philosophy of MathematicsIn Léna Soler, S. D. Sjoerd D. Sjoerd Zwart, Michael Lynch & Vincent IsraelJost (eds.), Science After the Practice Turn in the Philosophy, History, and Social Studies of Science, Routledge. pp. 215226. 2014.

48Epistemic Injustice in MathematicsSynthese 130. forthcoming.We investigate how epistemic injustice can manifest itself in mathematical practices. We do this as both a social epistemological and virtuetheoretic 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 epistemi…Read more

24The Unreasonable Richness of MathematicsJournal of Cognition and Culture 4 (34): 525549. 2004.

10Laws of Form and Paraconsistent Logic (review)Constructivist Foundations 13 (1): 2122. 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.

11The Tricky Transition from Discrete to Continuous (review)Constructivist Foundations 12 (3): 253254. 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.

17Moktefi, 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): 101105. 2017.

Mathematical Practice and Naturalist Epistemology: Structures with Potential for InteractionPhilosophia Scientiae 9 (2): 6178. 2005.In current philosophical research, there is a rather onesided 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 largescale to smallscale 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

2Introduction to the Special Issue Entitled ‘Mathematics: What Does it All Mean?’Foundations of Science 11 (1): 13. 2004.

20The Many Faces of Mathematical ConstructivismConstructivist Foundations 7 (2): 97103. 2012.Context: As one of the major approaches within the philosophy of mathematics, constructivism is to be contrasted with realist approaches such as Platonism in that it takes human mental activity as the basis of mathematical content. Problem: Mathematical constructivism is mostly identified as one of the socalled foundationalist accounts internal to mathematics. Other perspectives are possible, however. Results: The notion of “meaning finitism” is exploited to tie together internal and external d…Read more

47Pi on Earth, or Mathematics in the Real WorldErkenntnis 68 (3): 421435. 2008.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…Read more

17Mathematical Practice and Naturalist Epistemology: Structures with Potential for InteractionPhilosophia Scientae 9 6178. 2005.

The logical analysis of time and the problem of indeterminismCommunication and Cognition. Monographies 26 (2): 209230. 1993.

Edereen die niet denkt zoals ik, volge mij. Acta 16e NederlandsVlaamse Filosofiedag (edited book)VUB Press. 1994.

29NonFormal Properties of Real Mathematical ProofsPSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988 249254. 1988.The heuristics and strategies presented in Lakatos' Proofs and Refutations are wellknown. 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

21The Many Faces of Mathematical ConstructivismConstructivist Foundations 7 (2): 97103. 2012.Context: As one of the major approaches within the philosophy of mathematics, constructivism is to be contrasted with realist approaches such as Platonism in that it takes human mental activity as the basis of mathematical content. Problem: Mathematical constructivism is mostly identified as one of the socalled foundationalist accounts internal to mathematics. Other perspectives are possible, however. Results: The notion of “meaning finitism” is exploited to tie together internal and external d…Read more

1In Defence of Discrete Space and TimeLogique Et Analyse 38 (1501): 127150. 1995.In this paper several arguments are discussed and evaluated concerning the possibility of discrete space and time.

88Zeno's paradoxes and the tile argumentPhilosophy of Science 54 (2): 295302. 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 soCalled 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

78The Contributions of Logic to the Foundations of Physics: Foreword (review)Studia Logica 95 (12): 13. 2010.

Een verdediging van het strikt finitismeAlgemeen Nederlands Tijdschrift voor Wijsbegeerte 102 (3): 164183. 2010.

The possibility of discrete timeIn Craig Callender (ed.), The Oxford Handbook of Philosophy of Time, Oxford University Press. 2011.

133Ross' paradox is an impossible supertaskBritish Journal for the Philosophy of Science 45 (2): 743748. 1994.

Vrije Universiteit BrusselRegular Faculty

University of GhentRegular Faculty
Areas of Specialization
Logic and Philosophy of Logic 
Philosophy of Mathematics 