
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

21Introduction to the Special Issue Entitled 'Mathematics: What Does it All Mean?' (review)Foundations of Science 11 (12): 13. 2006.

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

20Classical arithmetic is quite unnaturalLogic and Logical Philosophy 11 (n/a): 231249. 2003.It is a generally accepted idea that strict finitism is a rather marginal view within the community of philosophers of mathematics. If one therefore wants to defend such a position (as the present author does), then it is useful to search for as many different arguments as possible in support of strict finitism. Sometimes, as will be the case in this paper, the argument consists of, what one might call, a “rearrangement” of known materials. The novelty lies precisely in the rearrangement, hence …Read more

19Metadebates on Science: The Blue Book of 'Einstein Meets Magritte' (edited book)Kluwer Academic. 1999.How do scientists approach science? Scientists, sociologists and philosophers were asked to write on this intriguing problem and to display their results at the International Congress `Einstein Meets Magritte'. The outcome of their effort can be found in this rather unique book, presenting all kinds of different views on science. Quantum mechanics is a discipline which deserves and receives special attention in this book, mainly because it is fascinating and, hence, appeals to the general public…Read more

17Argumentation and Pseudoscience The Case for an Ethics ofArgumentationIn Massimo Pigliucci & Maarten Boudry (eds.), Philosophy of Pseudoscience: Reconsidering the Demarcation Problem, University of Chicago Press. 2013.

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.

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

14Why I Am a Constructivist AtheistConstructivist Foundations 11 (1): 138140. 2015.Open peer commentary on the article “Religion: A RadicalConstructivist Perspective” by Andreas Quale. Upshot: An essential feature of Quale’s point of view is the strict distinction between the cognitive and the noncognitive. I argue that this position is untenable and hence that a radical constructivist can discuss religious matters

12Math Worlds: Philosophical and Social Studies of Mathematics and Mathematics Education (edited book)State University of New York Press. 1993.An international group of distinguished scholars brings a variety of resources to bear on the major issues in the study and teaching of mathematics, and on the problem of understanding mathematics as a cultural and social phenomenon. All are guided by the notion that our understanding of mathematical knowledge must be grounded in and reflect the realities of mathematical practice. Chapters on the philosophy of mathematics illustrate the growing influence of a pragmatic view in a field traditiona…Read more

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.

10Do We also Need Secondorder Mathematics?Constructivist Foundations 10 (1): 3435. 2014.Open peer commentary on the article “SecondOrder Science: Logic, Strategies, Methods” by Stuart A. Umpleby. Upshot: The author makes a strong plea for secondorder science but somehow mathematics remains out of focus. The major claim of this commentary is that secondorder science requires secondorder mathematics

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.

10Petite philosophie de l'Art Royal: Analyse de I’alchimie francmaçonne (review)Process Studies 45 (2): 282285. 2016.

9How to tell the continuous from the discreteIn François Beets & Eric Gillet (eds.), Logique En Perspective: Mélanges Offerts à Paul Gochet, Ousia. pp. 501511. 2000.

9Review of T. Koetsier, Lakatos' Philosophy of Mathematics: A Historical Approach (review)Philosophia Mathematica 2 (2). 1994.

8Fading foundations in de wiskunde?Algemeen Nederlands Tijdschrift voor Wijsbegeerte 107 (2): 155159. 2015.

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

5Philosophy 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): 275278. 2000.

3Introduction to the Special Issue Entitled ‘Mathematics: What Does it All Mean?’Foundations of Science 11 (1): 13. 2004.

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.

1Inleiding tot de moderne logica en wetenschapsfilosofie : een terreinverkenningTijdschrift Voor Filosofie 55 (2): 361363. 1993.

Vrije Universiteit BrusselRegular Faculty

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