@incollection {370857, title = {Learning concepts through the history of mathematics: the case of symbolic algebra.}, booktitle = {Philosophical dimensions in mathematics education}, year = {2007}, pages = {83{\textendash}103}, publisher = {Springer}, isbn = {978-0-387-71571-1}, author = {Heeffer, Albrecht}, editor = {Fran{\c c}ois, Karen and Van Bendegem, Jean Paul} } @incollection {D:eial, title = {The Need for Adaptive Logics in Epistemology}, booktitle = {Logic, Epistemology, and the Unity of Science}, year = {2004}, pages = {459{\textendash}485}, publisher = {Kluwer}, address = {Dordrecht}, abstract = {

After it is argued that philosophers of science have lost their interest in logic because they applied the wrong type of logics, examples are given of the forms of dynamic reasoning that are central for philosophy of science and epistemology. Adaptive logics are presented as a means to understand and explicate those forms of reasoning. All members of a specific (large) set of adaptive logics are proved to have a number of properties that warrant their formal decency and their suitability with respect to understanding and explicating dynamic forms of reasoning. Most of the properties extend to other adaptive logics.

}, author = {Batens, Diderik}, editor = {Rahman, Shahid and Symons, John and Gabbay, Dov M. and Van Bendegem, Jean Paul} } @incollection {152589, title = {Inconsistencies in the history of mathematics: the case of infinitesimals.}, booktitle = {Inconsistency in Science}, series = {Origins}, volume = {2}, year = {2002}, pages = {43{\textendash}57}, publisher = {Kluwer Academic}, address = {Dordrecht}, abstract = {

In this paper I will not confine myself exclusively to historical considerations. Both philosophical and technical matters will be raised, all with the purpose of trying to understand (better) what Newton, Leibniz and the many precursors (might have) meant when they talked about infinitesimals. The technical part will consist of an analysis why apparently infinitesimals have resisted so well to be formally expressed. The philosophical part, actually the most important part of this paper, concerns a discussion that has been going on for some decennia now. After the Kuhnian revolution in philosophy of science, notwithstanding Kuhn’s own suggestion that mathematics is something quite special, the question was nevertheless asked how mathematics develops. Are there revolutions in mathematics? If so, what do we have to think of? If not, why do they not occur? Is mathematics the so often claimed totally free creation of the human spirit? As usual, there is a continuum of positions, but let me sketch briefly the two extremes: the completists (as I call them) on the one hand, and the contingents (as I call them as well) on the other hand.

}, isbn = {1-4020-0630-6}, doi = {10.1007/978-94-017-0085-6_3}, url = {http://dx.doi.org/10.1007/978-94-017-0085-6_3}, author = {Van Bendegem, Jean Paul}, editor = {Meheus, Joke} } @incollection {121607, title = {Alternative mathematics: the vague way.}, booktitle = {Festschrift in honor of {N}ewton {C}.{A}. da {C}osta on the occasion of his seventieth birthday}, volume = {125}, year = {2000}, pages = {19{\textendash}31}, publisher = {Kluwer Academic}, isbn = {N/A}, author = {Van Bendegem, Jean Paul}, editor = {Krause, D{\'e}cio and French, Steven and Doria, Francisco A.} } @incollection {van2000analogy, title = {Analogy and metaphor as essential tools for the working mathematician}, booktitle = {Metaphor and Analogy in the Sciences}, year = {2000}, pages = {105{\textendash}123}, publisher = {Springer}, abstract = {

It may perhaps sound strange if not bizarre to suggest that metaphors and analogies could and should play a role in the practice of mathematics, let alone to claim that they are essential in present-day mathematics. Yet, that will be precisely the claim I will defend in this paper. I do insist that present-day mathematics is the domain of investigation I have in mind. From a historical perspective, and as an example, no one seems to doubt that mathematics one way or another must have arisen out of a specific set of practices, usually referred to as counting and measuring, and that mathematical concepts are metaphorically related to these practices. That view of the matter, however, does not necessarily say anything about the situation today and, indeed, in most cases it does not.

}, doi = {10.1007/978-94-015-9442-4_7}, author = {Van Bendegem, Jean Paul}, editor = {Hallyn, Fernand} } @incollection {J:ana, title = {An Extremely Rich Paraconsistent Logic and the Adaptive Logic Based on It}, booktitle = {Frontiers of Paraconsistent Logic}, year = {2000}, pages = {189{\textendash}201}, publisher = {Research Studies Press}, address = {Baldock, UK}, author = {Meheus, Joke}, editor = {Batens, Diderik and Mortensen, Chris and Priest, Graham and Van Bendegem, Jean Paul} } @book {D\&CMGPJpVB, title = {Frontiers of Paraconsistent Logic}, series = {Frontiers of Paraconsistent Logic}, year = {2000}, publisher = {Research Studies Press}, organization = {Research Studies Press}, address = {Baldock, UK}, editor = {Batens, Diderik and Mortensen, Chris and Priest, Graham and Van Bendegem, Jean Paul} } @incollection {121604, title = {Human(istisch)e wiskunde of de mogelijkheid van een alternatieve wiskunde.}, booktitle = {De toekomst van het heden : zijn we op weg naar een menselijker samenleving?}, year = {2000}, pages = {127{\textendash}140}, publisher = {Humanistisch Vrijzinnige Dienst}, isbn = {9074174051}, author = {Van Bendegem, Jean Paul} } @incollection {D:surv-ial, title = {A Survey of Inconsistency-Adaptive Logics}, booktitle = {Frontiers of Paraconsistent Logic}, year = {2000}, pages = {49{\textendash}73}, publisher = {Research Studies Press}, address = {Baldock, UK}, abstract = {

This paper offers a systematic review of some central philosophical and technical results on adaptive logics. Quite a few of the results are still in print or forthcoming.

}, author = {Batens, Diderik}, editor = {Batens, Diderik and Mortensen, Chris and Priest, Graham and Van Bendegem, Jean Paul} } @article {135002, title = {The creative growth of mathematics}, journal = {Philosophica}, volume = {63}, year = {1999}, pages = {119{\textendash}152}, issn = {0379-8402}, author = {Van Bendegem, Jean Paul} } @incollection {VanBendegem1999, title = {Oorlog en vrede in wetenschapsland}, booktitle = {Denken als Openheid. {L}iber Amicorum {H}ubert {D}ethier}, year = {1999}, pages = {153-160}, publisher = {VUB}, author = {Van Bendegem, Jean Paul}, editor = {Walraves, Else and Stuy, Johan} } @article {van1998schoonheid, title = {Schoonheid in de wiskunde: Birkhoff Revisited}, journal = {Tijdschrift voor Filosofie}, volume = {60}, year = {1998}, pages = {106{\textendash}130}, abstract = {

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 {\textquoteright}romantic{\textquoteright} side as well, to use the term introduced by Fran{\c c}ois Le Lionnais. Thus, a more complex proposal of mathematical beauty is presented. Finally and as a consequence, I argue against the dichotomy that associates science, including mathematics, with the beauty of simplicity and that associates the arts with the beauty of complexity. As an example, the work of Oulipo, Raymond Queneau in particular, is briefly presented.

}, author = {Van Bendegem, Jean Paul} } @incollection {von1998if, title = {What, if anything, is an experiment in mathematics?}, booktitle = {Philosophy and the Many Faces of Science}, year = {1998}, pages = {172{\textendash}182}, publisher = {Rowman \& Littlefield}, author = {Van Bendegem, Jean Paul}, editor = {Anapolitanos, Dionysios and Baltas, Aristides and Tsinorema, Stavroula} } @article {VanBendegem1998, title = {Zeker lezen: logica.}, journal = {Wijsgerig Perspectief op Maatschappij en Wetenschap}, volume = {38}, year = {1998}, pages = {68-69}, author = {Van Bendegem, Jean Paul} } @article {VanBendegem1997, title = {L.E.J. Brouwer.}, journal = {Kritisch Denkerslexicon}, volume = {23}, year = {1997}, pages = {1-14}, author = {Van Bendegem, Jean Paul} } @incollection {VanBendegem1997c, title = {Twee grote verhalen over wetenschap (voor allen en voor niemand).}, booktitle = {Ik \& het verhaal}, year = {1997}, pages = {107-130}, publisher = {Uitgaven Woord en Argument}, address = {Hasselt}, author = {Van Bendegem, Jean Paul}, editor = {Vandormael, Jan} } @incollection {VanBendegem1997b, title = {Vrijzinnig (?) humanisme (?) in een moderne (?) wereld.}, booktitle = {Grondslagen Vrijzinnig Humanisme}, year = {1997}, pages = {149-169}, publisher = {Humanistisch Vrijzinnige Dienst}, address = {Antwerpen}, author = {Van Bendegem, Jean Paul}, editor = {Van Kerckhove, Christian} } @article {VanBendegem1997a, title = {Wetenschap en religie: zo verzoenbaar als men maar wil.}, journal = {Mores}, volume = {42}, year = {1997}, pages = {381-388}, author = {Van Bendegem, Jean Paul} } @incollection {257816, title = {Mathematical Experiments and Mathematical Pictures}, booktitle = {Realism in the Sciences}, year = {1996}, pages = {203{\textendash}216}, publisher = {Universitaire Pers}, address = {Leuven}, author = {Van Bendegem, Jean Paul}, editor = {Douven, Igor and Horsten, Leon} } @incollection {257818, title = {Ook het oneindige is ons werk}, booktitle = {Leo Apostel. Tien filosofen getuigen}, year = {1996}, pages = {119{\textendash}134}, publisher = {Hadewijch}, address = {Antwerpen/Baarn}, author = {Van Bendegem, Jean Paul}, editor = {Batens, Diderik} } @article {van1996strange, title = {The strange case of the missing body of mathematics}, journal = {Semiotica}, volume = {112}, number = {3-4}, year = {1996}, pages = {403{\textendash}413}, abstract = {

La notion d{\textquoteright}infini est analys{\'e}e en comparant les math{\'e}matiques et la th{\'e}ologie car les math{\'e}maticiens ont pendant longtemps per{\c c}u une relation entre la notion infinie math{\'e}matique et la notion d{\textquoteright}infinit{\'e} de Dieu

}, author = {Van Bendegem, Jean Paul} } @article {257814, title = {Strict finitism as a viable alternative in the foundations of mathematics}, journal = {Logique et Analyse}, volume = {37}, number = {145}, year = {1996}, pages = {23{\textendash}40}, issn = {0024-5836}, author = {Van Bendegem, Jean Paul} } @article {van1995defence, title = {In defence of discrete space and time}, journal = {Logique et Analyse}, volume = {38}, number = {150-151-152}, year = {1995}, pages = {127-150}, abstract = {

In this paper several arguments are discussed and evaluated concerning the possibility of discrete space and time.

}, author = {Van Bendegem, Jean Paul} } @incollection {D:alaoetb, title = {Adaptieve logica{\textquoteright}s: een aanzet om elkaar te begrijpen}, booktitle = {Iedereen die niet denkt zoals ik, volge mij. {A}cta 16de {N}ederlands-{V}laamse Filosofiedag}, year = {1994}, pages = {13{\textendash}19}, publisher = {VUB-Pers}, author = {Batens, Diderik}, editor = {Van Bendegem, Jean Paul and Kornelis, Gustaaf} } @incollection {J:nvfb, title = {Elk wetenschapper zijn onderzoeksprogramma?}, booktitle = {Iedereen die niet denkt zoals ik, volge mij. {A}cta 16de {N}ederlands-{V}laamse Filosofiedag}, year = {1994}, pages = {61{\textendash}67}, publisher = {VUB-Pers}, author = {Meheus, Joke}, editor = {Van Bendegem, Jean Paul and Kornelis, Gustaaf} } @incollection {241638, title = {Waarom {W}esley {S}almons causaal-mechanische model van verklaring niet volstaat}, booktitle = {Iedereen die niet denkt zoals ik, volge mij. {A}cta 16de {N}ederlands-{V}laamse Filosofiedag}, year = {1994}, pages = {81-86}, publisher = {VUB Press}, isbn = {9789054870845}, author = {Weber, Erik}, editor = {Van Bendegem, Jean Paul and Cornelis, Gustaaf C} } @book {DJp:t\&e, title = {Theory and Experiment. {R}ecent Insights and New Perspectives on Their Relation}, year = {1988}, publisher = {Reidel}, organization = {Reidel}, address = {Dordrecht}, editor = {Batens, Diderik and Van Bendegem, Jean Paul} } @article {DJp:rd\&cl, title = {Relevant derivability and classical derivability in {F}itch-style and axiomatic formulations of relevant logics}, journal = {Logique et Analyse}, volume = {28}, number = {109}, year = {1985}, pages = {21{\textendash}31}, author = {Batens, Diderik and Van Bendegem, Jean Paul} } @incollection {LA\&D\&a, title = {An empirical investigation on scientific observation}, booktitle = {Theory of Knowledge and Science Policy}, year = {1979}, pages = {3{\textendash}36}, publisher = {Communication \& Cognition}, author = {Apostel, Leo and Batens, Diderik and Breusegem, Erwin and De Coninck, Jan and De Waele, Danny and Pinxten, Rik and Swings, Jean and Van Bendegem, Jean Paul and Vandamme, Fernand}, editor = {Callebaut, Werner and De Mey, Marc and Pinxten, Rik and Vandamme, Fernand} }