-
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
-
53Dirk Van Dalen, mystic, geometer, and intuitionist. The life of L.e.J. Brouwer, volume 1: The dawning revolutionStudia Logica 74 (3): 469-471. 2003.
-
6Philosophy 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): 275-278. 2000.
-
15Review of T. Koetsier, Lakatos' Philosophy of Mathematics: A Historical Approach (review)Philosophia Mathematica 2 (2). 1994.
-
69Review of C. Mortensen, Inconsistent Mathematics (review)Philosophia Mathematica 7 (2): 202-212. 1999.
-
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
-
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
-
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
-
1Inleiding tot de moderne logica en wetenschapsfilosofie : een terreinverkenningTijdschrift Voor Filosofie 55 (2): 361-363. 1993.
-
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
-
28Why the largest number imaginable is still a finite numberLogique Et Analyse 42 (165-166). 1999.
-
Vrije Universiteit BrusselRegular Faculty
-
Ghent UniversityRegular Faculty
Areas of Specialization
Logic and Philosophy of Logic |
Philosophy of Mathematics |