• 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
  • 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 historical-philosophical 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
  • 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
  •  6
    Perspectives on Mathematical Practices (edited book)
    with Bart van Kerkhove
    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
  •  48
    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 epistemi…Read more
  •  24
    The Unreasonable Richness of Mathematics
    with Bart Van Kerkhove
    Journal of Cognition and Culture 4 (3-4): 525-549. 2004.
  •  10
    Laws 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.
  •  11
    The 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.
  • Mathematical Practice and Naturalist Epistemology: Structures with Potential for Interaction
    with Bart Van Kerkhove
    Philosophia Scientiae 9 (2): 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
  • Mathematical Arguments in Context
    with Bart Kerkhove
    Foundations of Science 14 (1-2): 45-57. 2009.
  •  19
    The Many Faces of Mathematical Constructivism
    with Bart Van Kerkhove
    Constructivist Foundations 7 (2): 97-103. 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 so-called 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
  • Book Review (review)
    Studia Logica 87 (1): 135-138. 2007.
  •  47
    Pi on Earth, or Mathematics in the Real World
    with Bart Van Kerkhove
    Erkenntnis 68 (3): 421-435. 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
  • The logical analysis of time and the problem of indeterminism
    Communication and Cognition. Monographies 26 (2): 209-230. 1993.
  •  21
    The Many Faces of Mathematical Constructivism
    with B. Kerkhove
    Constructivist Foundations 7 (2): 97-103. 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 so-called 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
  •  29
    Non-Formal Properties of Real Mathematical Proofs
    PSA: 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
  •  1
    In Defence of Discrete Space and Time
    Logique 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.
  •  88
    Zeno's paradoxes and the tile argument
    Philosophy 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
  • Een verdediging van het strikt finitisme
    Algemeen Nederlands Tijdschrift voor Wijsbegeerte 102 (3): 164-183. 2010.
  • The possibility of discrete time
    In Craig Callender (ed.), The Oxford Handbook of Philosophy of Time, Oxford University Press. 2011.
  •  25
    Dialogue Logic and Problem-Solving
    Philosophica 35. 1985.
  •  133
    Ross' paradox is an impossible super-task
    British Journal for the Philosophy of Science 45 (2): 743-748. 1994.
  • Beauty in mathematics: Birkhoff revisited
    Tijdschrift Voor Filosofie 60 (1): 106-130. 1998.