-
32Math 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
-
29Foundations of Mathematics or Mathematical Practice: Is One Forced to Choose?Philosophica 43 (n/a). 1989.
-
28Significs and mathematics: Creative and other subjectsSemiotica 2013 (196): 307-323. 2013.Journal Name: Semiotica - Journal of the International Association for Semiotic Studies / Revue de l'Association Internationale de Sémiotique Volume: 2013 Issue: 196 Pages: 307-323
-
28Why the largest number imaginable is still a finite numberLogique Et Analyse 42 (165-166). 1999.
-
28Classical arithmetic is quite unnaturalLogic and Logical Philosophy 11 (n/a): 231-249. 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
-
28Introduction to the Special Issue Entitled 'Mathematics: What Does it All Mean?' (review)Foundations of Science 11 (1-2): 1-3. 2006.
-
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.
-
26Metadebates 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
-
23Argumentation 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.
-
23How to tell the continuous from the discreteIn François Beets & Eric Gillet (eds.), Logique En Perspective: Mélanges Offerts à Paul Gochet, Ousia. pp. 501--511. 2000.
-
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
-
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
-
17Emily Rolfe* Great Circles: The Transits of Mathematics and PoetryPhilosophia Mathematica 28 (3): 431-441. 2020.
-
17Perspectives 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
-
17Regulating Academic Pressure: From Fast to SlowJournal of Philosophy of Education 54 (5): 1419-1442. 2020.Journal of Philosophy of Education, EarlyView.
-
16Fading foundations in de wiskunde?Algemeen Nederlands Tijdschrift voor Wijsbegeerte 107 (2): 155-159. 2015.Amsterdam University Press is a leading publisher of academic books, journals and textbooks in the Humanities and Social Sciences. Our aim is to make current research available to scholars, students, innovators, and the general public. AUP stands for scholarly excellence, global presence, and engagement with the international academic community.
-
16Philosophical Perspectives on Mathematical Practice (edited book)College Publications. 2010.It has been observed many times before that, as yet, there are no encompassing, integrated theories of mathematical practice available.To witness, as we currently do, a variety of schools in this field elaborating their philosophical frameworks, and trying to sort out their differences in the course of doing so, is also to be constantly reminded of the fact that a lot of epistemic aspects, extremely relevant to this task, remain dramatically underexamined. This volume wants to contribute to the …Read more
-
15Review of T. Koetsier, Lakatos' Philosophy of Mathematics: A Historical Approach (review)Philosophia Mathematica 2 (2). 1994.
-
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
-
14We’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. 261-274. 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 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
-
14Petite philosophie de l'Art Royal: Analyse de I’alchimie franc-maçonne (review)Process Studies 45 (2): 282-285. 2016.
-
14Felix Lev. Finite Mathematics as the Foundation of Classical Mathematics and Quantum TheoryPhilosophia Mathematica. forthcoming.
-
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.
-
Vrije Universiteit BrusselRegular Faculty
-
Ghent UniversityRegular Faculty
Areas of Specialization
Logic and Philosophy of Logic |
Philosophy of Mathematics |