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39Schoonheid 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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69Review of C. Mortensen, Inconsistent Mathematics (review)Philosophia Mathematica 7 (2): 202-212. 1999.
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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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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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1Inleiding tot de moderne logica en wetenschapsfilosofie : een terreinverkenningTijdschrift Voor Filosofie 55 (2): 361-363. 1993.
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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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28Why the largest number imaginable is still a finite numberLogique Et Analyse 42 (165-166). 1999.
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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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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
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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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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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37Feng Ye. Strict Finitism and the Logic of Mathematical ApplicationsPhilosophia Mathematica 24 (2): 247-256. 2016.
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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 |