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29Schoonheid in de wiskunde: Birkhoff revisitedTijdschrift Voor Filosofie 60 (1): 106-130. 1998.Everyone is familiar with the measure of beauty that has been proposed by Birkhoff, the famous formula M = O/C. Although I show that the formula in its original form cannot be maintained, I present a reinterpretation that adapts the formula for measuring the beauty of mathematical proofs. However, this type of measure is not the only aesthetic element in mathematics. There exists a 'romantic' side as well, to use the term introduced by François Le Lionnais. Thus, a more complex proposal of mathe…Read more
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68A Defense of Strict FinitismConstructivist Foundations 7 (2): 141-149. 2012.Context: Strict finitism is usually not taken seriously as a possible view on what mathematics is and how it functions. This is due mainly to unfamiliarity with the topic. Problem: First, it is necessary to present a “decent” history of strict finitism and, secondly, to show that common counterarguments against strict finitism can be properly addressed and refuted. Method: For the historical part, the historical material is situated in a broader context, and for the argumentative part, an evalua…Read more
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40Proofs and arguments: The special case of mathematicsPoznan Studies in the Philosophy of the Sciences and the Humanities 84 (1): 157-169. 2005.Most philosophers still tend to believe that mathematics is basically about producing formal proofs. A consequence of this view is that some aspects of mathematical practice are entirely lost from view. My contention is that it is precisely in those aspects that similarities can be found between practices in the exact sciences and in mathematics. Hence, if we are looking for a (more) unified treatment of science and mathematics it is necessary to incorporate these elements into our view of what …Read more
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81A Defense of Strict FinitismConstructivist Foundations 7 (2): 141-149. 2012.Context: Strict finitism is usually not taken seriously as a possible view on what mathematics is and how it functions. This is due mainly to unfamiliarity with the topic. Problem: First, it is necessary to present a “decent” history of strict finitism (which is now lacking) and, secondly, to show that common counterarguments against strict finitism can be properly addressed and refuted. Method: For the historical part, the historical material is situated in a broader context, and for the argume…Read more
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1Inleiding tot de moderne logica en wetenschapsfilosofie : een terreinverkenningTijdschrift Voor Filosofie 55 (2): 361-363. 1993.
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28Why the largest number imaginable is still a finite numberLogique Et Analyse 42 (165-166). 1999.
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29Classical 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
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14Petite philosophie de l'Art Royal: Analyse de I’alchimie franc-maçonne (review)Process Studies 45 (2): 282-285. 2016.
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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
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39Feng Ye. Strict Finitism and the Logic of Mathematical ApplicationsPhilosophia Mathematica 24 (2): 247-256. 2016.
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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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Van gebroken orde naar herstelde fragmenten. Enkele bedenkingen bij Leo Apostels recente publicatiesde Uil Van Minerva 10. 1994.
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Een verdediging van het strikt finitismeAlgemeen Nederlands Tijdschrift voor Wijsbegeerte 102 (3): 164-183. 2010.
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77The Collatz conjecture. A case study in mathematical problem solvingLogic and Logical Philosophy 14 (1): 7-23. 2005.In previous papers (see Van Bendegem [1993], [1996], [1998], [2000], [2004], [2005], and jointly with Van Kerkhove [2005]) we have proposed the idea that, if we look at what mathematicians do in their daily work, one will find that conceiving and writing down proofs does not fully capture their activity. In other words, it is of course true that mathematicians spend lots of time proving theorems, but at the same time they also spend lots of time preparing the ground, if you like, to construct a …Read more
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Non-Realism, Nominalism and Strict Finitism the Sheer Complexity of It AllPoznan Studies in the Philosophy of the Sciences and the Humanities 90 343-365. 2006.
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98Zeno's paradoxes and the tile argumentPhilosophy 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
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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.
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The possibility of discrete timeIn Craig Callender (ed.), The Oxford Handbook of Philosophy of Time, Oxford University Press. 2011.
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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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73Review of C. Mortensen, Inconsistent Geometry (review)Philosophia Mathematica 20 (3): 365-372. 2012.
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152Ross' paradox is an impossible super-taskBritish Journal for the Philosophy of Science 45 (2): 743-748. 1994.
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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
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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 |