-
Mathematical Practice and Naturalist Epistemology: Structures with Potential for InteractionPhilosophia Scientiae 9 (2): 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
-
6Call for Papers First World Congress on Paraconsistency, Gent, Belgium 1997Journal of Applied Non-Classical Logics 6 (2). 1996.
-
Relevant derivability and classical derivability in Fitch-style and axiomatic formulations of relevant logicsLogique Et Analyse 109 (9): 22-31. 1985.
-
7A selection of papers presented at the First World Congress on Paraconsistency 1997Logique Et Analyse 41 161-163. 2001.
-
5Polymath as an Epistemic CommunityIn Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice, Springer. pp. 2727-2756. 2024.The Polymath Project is an online collaborative enterprise that was initiated in 2009, when Timothy Gowers asked whether and how groups could work together to solve mathematical problems that “do not naturally split up into a vast number of subtasks.” Gowers proposed to answer this question himself by actually trying to set up such a collaboration, based on interactions taking place in the comment-threads of a series of posts on a WordPress blog. Hence, the first project officially started in ea…Read more
-
Experiments in Mathematics: Fact, Fiction, or the Future?In Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice, Springer. pp. 2821-2846. 2024.In this chapter, the possibility of experiments in mathematics is examined. A general scheme is proposed as a tool to handle the different forms of experiments that are being used in mathematical practices: computations, “experimental mathematics” as a new research domain in mathematics and computer science, real-world experiments, and thought experiments. In a final section, extensions of the scheme are proposed that further support the conclusion that mathematical experiments are indeed facts …Read more
-
16Felix Lev. Finite Mathematics as the Foundation of Classical Mathematics and Quantum TheoryPhilosophia Mathematica. forthcoming.
-
45Evolutionary Epistemology, Language and Culture: A Non-Adaptationist, Systems Theoretical Approach (edited book)Springer. 2006.For the first time in history, scholars working on language and culture from within an evolutionary epistemological framework, and thereby emphasizing complementary or deviating theories of the Modern Synthesis, were brought together. Of course there have been excellent conferences on Evolutionary Epistemology in the past, as well as numerous conferences on the topics of Language and Culture. However, until now these disciplines had not been brought together into one all-encompassing conference.…Read more
-
17Philosophical 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
-
3Non-Formal Properties of Real Mathematical ProofsPSA Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988 (1): 249-254. 1988.Suppose you attend a seminar where a mathematician presents a proof to some of his colleagues. Suppose further that what he is proving is an important mathematical statement Now the following happens: as the mathematician proceeds, his audience is amazed at first, then becomes angry and finally ends up disturbing the lecture (some walk out, some laugh, …). If in addition, you see that the proof he is presenting is formally speaking (nearly) correct, would you say you are witnessing an extraordin…Read more
-
14Het complexe verhaal van de wiskunde in de TractatusAlgemeen Nederlands Tijdschrift voor Wijsbegeerte 115 (2): 196-208. 2023.The complex story of mathematics in the Tractatus In this paper some thoughts are presented about the treatment of mathematics in the Tractatus Logico-Philosophicus of Ludwig Wittgenstein. After introducing a metaphor for the mathematical ‘building’, we look at the scattered ideas about mathematics in the Tractatus itself. Although the general consensus is that Wittgenstein rejects the entire ‘building’, there are recent insights that suggest that a more coherent view of ‘Tractarian’ mathematics…Read more
-
12Introduction: From Practice to Results in Mathematics and LogicPhilosophia Scientiae 16 (1): 5-11. 2012.1 Mathematical practice: a short overview This volume is a collection of essays that discuss the relationships between the practices deployed by logicians and mathematicians, either as individuals or as members of research communities, and the results from their research. We are interested in exploring the concept of 'practices' in the formal sciences. Though common in the history, philosophy and sociology of science, this concept has surprisingly thus far been little reflected upon in logic...
-
6Introduction to the Special Issue Entitled ‘Mathematics: What Does it All Mean?’Foundations of Science 11 (1-2): 1-3. 2006.
-
40Introduction: From Practice to Results in Mathematics and LogicPhilosophia Scientiae 16 5-11. 2012.1 Mathematical practice: a short overview This volume is a collection of essays that discuss the relationships between the practices deployed by logicians and mathematicians, either as individuals or as members of research communities, and the results from their research. We are interested in exploring the concept of 'practices' in the formal sciences. Though common in the history, philosophy and sociology of science, this concept has surprisingly thus far been little reflected upon in logic...
-
12Introduction: From Practice to Results in Mathematics and LogicPhilosophia Scientiae 16 5-11. 2012.1 Mathematical practice: a short overview This volume is a collection of essays that discuss the relationships between the practices deployed by logicians and mathematicians, either as individuals or as members of research communities, and the results from their research. We are interested in exploring the concept of 'practices' in the formal sciences. Though common in the history, philosophy and sociology of science, this concept has surprisingly thus far been little reflected upon in logic...
-
15We’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
-
34The Interplay of Psychology and Mathematics Education: From the Attraction of Psychology to the Discovery of the SocialJournal of Philosophy of Education 46 (3): 370-385. 2012.It is a rather safe statement to claim that the social dimensions of the scientific process are accepted in a fair share of studies in the philosophy of science. It is a somewhat safe statement to claim that the social dimensions are now seen as an essential element in the understanding of what human cognition is and how it functions. But it would be a rather unsafe statement to claim that the social is fully accepted in the philosophy of mathematics. And we are not quite sure what kind of state…Read more
-
20Regulating Academic Pressure: From Fast to SlowJournal of Philosophy of Education 54 (5): 1419-1442. 2020.Journal of Philosophy of Education, EarlyView.
-
10Math and Music: Slow and Not For ProfitIn Paul Smeyers & Marc Depaepe (eds.), Educational Research: Ethics, Social Justice, and Funding Dynamics, Springer Verlag. pp. 73-90. 2018.This chapter looks at the impact of recent societal approaches of knowledge and science from the perspectives of two rather distant educational domains, mathematics and music. Science’s attempt at ‘self-understanding’ has led to a set of control mechanisms, either generating ‘closure’—the scientists’ non-involvement in society—or ‘economisation’, producing patents and other lucrative benefits. While scientometrics became the tool and the rule for measuring the economic impact of science, counter…Read more
-
4Mathematical Arguments in ContextFoundations of Science 14 (1-2): 45-57. 2009.Except in very poor mathematical contexts, mathematical arguments do not stand in isolation of other mathematical arguments. Rather, they form trains of formal and informal arguments, adding up to interconnected theorems, theories and eventually entire fields. This paper critically comments on some common views on the relation between formal and informal mathematical arguments, most particularly applications of Toulmin’s argumentation model, and launches a number of alternative ideas of presenta…Read more
-
52The Unreasonable Richness of MathematicsJournal of Cognition and Culture 4 (3-4): 525-549. 2004.The paper gives an impression of the multi-dimensionality of mathematics as a human activity. This 'phenomenological' exercise is performed within an analytic framework that is both an expansion and a refinement of the one proposed by Kitcher. Such a particular tool enables one to retain an integrated picture while nevertheless welcoming an ample diversity of perspectives on mathematical practices, that is, from different disciplines, with different scopes, and at different levels. Its functioni…Read more
-
35Pi on Earth, or Mathematics in the Real WorldErkenntnis 68 (3): 421-435. 2008.We explore aspects of an experimental approach to mathematical proof, most notably number crunching, or the verification of subsequent particular cases of universal propositions. Since the rise of the computer age, this technique has indeed conquered practice, although it implies the abandonment of the ideal of absolute certainty. It seems that also in mathematical research, the qualitative criterion of effectiveness, i.e. to reach one’s goals, gets increasingly balanced against the quantitative…Read more
-
40Paraconsistency And Dialogue Logic Critical Examination And Further ExplorationsSynthese 127 (1-2): 35-55. 2001.The first part of this paper presents asympathetic and critical examination of the approachof Shahid Rahman and Walter Carnielli, as presented intheir paper “The Dialogical Approach toParaconsistency”. In the second part, possibleextensions are presented and evaluated: (a) top-downanalysis of a dialogue situation versus bottom-up, (b)the specific role of ambiguities and how to deal withthem, and (c) the problem of common knowledge andbackground knowledge in dialogues. In the third part,I claim t…Read more
-
127Mathematical arguments in contextFoundations of Science 14 (1-2): 45-57. 2009.Except in very poor mathematical contexts, mathematical arguments do not stand in isolation of other mathematical arguments. Rather, they form trains of formal and informal arguments, adding up to interconnected theorems, theories and eventually entire fields. This paper critically comments on some common views on the relation between formal and informal mathematical arguments, most particularly applications of Toulmin’s argumentation model, and launches a number of alternative ideas of presenta…Read more
-
29Introduction to the Special Issue Entitled 'Mathematics: What Does it All Mean?' (review)Foundations of Science 11 (1-2): 1-3. 2006.
-
30Alternative Mathematics: The Vague WaySynthese 125 (1-2): 19-31. 2000.Is alternative mathematics possible? More specifically,is it possible to imagine that mathematics could havedeveloped in any other than the actual direction? Theanswer defended in this paper is yes, and the proofconsists of a direct demonstration. An alternativemathematics that uses vague concepts and predicatesis outlined, leading up to theorems such as ``Smallnumbers have few prime factors''.
-
2What does it all mean? A very short introduction to philosophy. Oxford: Oxford University Press, 1987. Thomas NagelPhilosophica 41 (n/a). 1988.
-
5Bias in Human Reasoning. Causes and Consequences. Essays in Cognitive Psychology, LEA, Hove and London, 1989. Jonathan St.B.T. Evans (review)Philosophica 45 (n/a). 1990.
-
4Choices. An introduction to decision theory. Minneapolis: University of Minnesota Press, 1987. Michael D. ResnikPhilosophica 41 (n/a). 1988.
-
Vrije Universiteit BrusselRegular Faculty
-
Ghent UniversityRegular Faculty
Areas of Specialization
Logic and Philosophy of Logic |
Philosophy of Mathematics |