Mathematical practice

For this theme, see also Readers.

• “Fermat’s Last Theorem seen as an Exercise in Evolutionary Epistemology”. In: Werner Callebaut & Rik Pinxten (eds.), Evolu­tionary Epistemology, Kluwer, Dordrecht, 1987, pp. 337‑363.
• “Non‑Formal Properties of Real Mathematical Proofs”. In: Arthur Fine & Jarrett Leplin (eds.), PSA 1988. Volume One, PSA, East Lansing, 1988, pp. 249‑254.
• “Foundations of Mathematics or Mathematical Practice: Is One Forced to Choose?” Philo­sophica 43, Gent, 1989, pp. 197‑213. Also in: R. Fischer, S. Restivo & J.P. Van Bende­gem (eds.): Math Worlds: New Directions in the Social Studies and Philosophy of Mathematics. State University New York Press, New York, 1993, pp. 21‑38. → pdf
• “Characteristics of Real Mathematical Proofs” In: A. Diaz, J. Echeverria & A. Ibarra (eds.), Structures in Mathematical Theories, Servicio Editorial Universidad del Pais Vasco, San Sebastian, 1990, pp. 333‑337. → pdf
• “Real‑Life Mathematics versus Ideal Mathematics: The Ugly Truth”. In: Erik C.W. Krabbe, Renée José Dalitz & Pier A. Smit (eds.): Empirical Logic and Public Debate. Essays in Honour of Else M. Barth, Rodopi, Amsterdam, 1993, pp. 263‑272.
• “The Popularization of Mathematics or The Pop-Music of the Spheres”. Communication & Cognition, Vol. 29, 2, 1996, pp. 215-238.
• “Mathematical Experiments and Mathematical Pictures”. In: Igor Douven & Leon Horsten (eds.), Realism in the Sciences. Pro­ceedings of the Ernan McMullin Symposium Leuven 1995. Louvain Philosophical Studies 10. Leuven University Press, Leuven, 1996, pp. 203-216. → pdf
• “Review article: The strange case of the missing body of mathematics. Review of Brain Rotman’s ‘Ad Infini­tum: The Ghost in Tu­ring’s Machine. Taking God out of Mathematics and Putting the Body Back In'”. Semiotica, 112, 3/4, 1996, pp. 403-413.
• “What, if anything, is an experiment in mathe­matics?” In: Dionysios Anapolitanos, Aristi­des Baltas & Stavroula Tsinorema (eds.), Philosophy and the Many Faces of Science, (CPS Pu­blications in the Philosophy of Science), Rowman & Littlefield, Londen, 1998, pp. 172-182. → pdf
• “Analogy and Metaphor as Essentials Tools for the Working Mathemati­cian”. In: Fernand Hallyn (ed.), Metaphor and Analogy in the Sciences, (Origins: Studies in the Sources of Scientific Creativity), Kluwer Academic, Dodrecht, 2000, pp. 105-123.
• “Alternative Mathematics: The Vague Way”. In: Décio Krause, Steven French & Francisco A. Doria (eds.), Festschrift in Honour of Newton C.A. da Costa on the Occasion of his Seventieth Birthday, Synthese, vol. 125, nos. 1-2, 2000, pp 19-31.
• “Die Grenzen der Mathematik sind die Grenzen ihrer Darstellbarkeit”. In: Michael H.G. Hoffmann (Hrsg.), Mathematik verstehen. Semiotische Perspektiven. Hildesheim: Verlag Franzbecker, 2003, pp. 258-270. (German translation of “Review article: The strange case of the missing body of mathematics. Semiotica, 112, 3/4, 1996, pp. 403-413.)
• “The Creative Growth of Mathematics”. In: Dov Gabbay, Shahid Rahman, John Symons en Jean Paul Van Bendegem (eds.), Logic, Epistemology and the Unity of Science (LEUS), Volume 1, Dordrecht: Kluwer Academic, 2004, pp. 229-255.
• “The Unreasonable Richness of Mathematics” (co-author: Bart Van Kerkhove). Journal of Cognition and Culture, vol. 4, no. 3-4, 2004, pp. 525-549.
• “The Collatz Conjecture: A Case Study in Mathematical Problem Solving”. Logic and Logical Philosophy, vol. 14, 2005, pp. 7-23. Special issue “Patterns of Scientific Reasoning”, guest-editor Erik Weber. → pdf
• “Mathematical Practice and Naturalist Epistemology: Structures with Potential for Interaction” (co-author: Bart Van Kerkhove). In: Gerhard Heinzmann & Manuel Rebuschi (eds.): “Aperçus philosophiques en logique et en mathématiques”, Philosophia Scientiae, volume 9, cahier 2, 2005, pp. 61-78.
• “Can There Be an Alternative Mathematics, Really?”. In: Michael H.G. Hoffmann, Johannes Lenhard & Falk Seeger (eds.), Activity and Sign. Grounding Mathematics Education, New York: Springer, 2005, pp. 349-359.
• “Proofs and Arguments: The Special Case of Mathematics”. In: Roberto Festa, Atocha Aliseda & Jeanne Peijnenburg (eds.), Cognitive Structures in Scientific Inquiry. Essays in Debate with Theo Kuipers – Volume 2. (Poznań Studies in the Philosophy of the Sciences and the Humanities 84 – Monographs-in-Debate), Amsterdam/New York: Rodopi, 2005, pp. 157-169.
• “Thought Experiments in Mathematics: Anything But Proof”. Philosophica, vol. 72, special issue on Thought Experiments, Tim De Mey (ed.), 2003 (date of publication 2005), pp. 9-33.
• “Elements for a rhetoric of mathematics: How proofs can be convincing”. In: Cédric Dégremont, Laurent Keiff & Helge Rückert (eds), Dialogues, Logics, and Other Strange Things. Essays in Honour of Shahid Rahman. London: King’s College Publications, 2008, pp. 437-454.
• “Pi on Earth, or Mathematics in the Real World” (co-author: Bart Van Kerkhove). Erkenntnis, vol. 68, nr. 3, 2008, pp. 421-435.
• “Mathematical Arguments in Context” (co-author: Bart Van Kerkhove). Foundations of Science, vol.14, nrs. 1-2, 2009, pp. 45-57. → pdf
• “Arguments and proofs about arguments and proofs”(co-author: Kathleen Coessens). In: Paul Smeyers & Marc Depaepe (eds.), Educational research. Proofs, arguments, and other reasonings: The language of education. Dordrecht: Springer, 2009, pp. 27-42.
• “Revolutions in Mathematics. More than Thirty Years after Crowe’s (1975) ‘Ten ‘Laws’’. A New Interpretation” (co-author: Karen François). In: Benedikt Löwe & Thomas Müller (eds.): PhiMSAMP. Philosophy of Mathematics: Sociological Aspects and Mathematical Practice. London: College Publications, 2010, pp. 107-120 (Texts in Philosophy 11).
• “The good, the beautiful and the literate: making statistics accessible for action” (co-authors: Karen François & Kathleen Coessens). In: Paul Smeyers & Marc Depaepe (eds.), Educational research. The ethics and aesthetics of statistics. Dordrecht: Springer, 2011, pp. 145-160.
• “Introduction: From Practice to Results in Mathematics and Logic” (co-authors: Valeria Giardino, Amirouche Moktefi & Sandra Mols). Philosophia Scientiae, volume 16, cahier 1, 2012, pp. 5-11.
• “The Spaces of Mathematics. Dynamic Encounters between Local and Universal”(co-authors: Karen François & Kathleen Coessens). In: Paul Smeyers & Marc Depaepe (eds.), Educational research. The Importance and Effects of Institutional Space. New York: Springer, 2013, pp. 135-152.
• “Mathematical Arguments and Distributed Knowledge” (co-authors: Bart Van Kerkhove & Patrick Allo). In: Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. New York: Springer, 2013, pp. 339-360.
• “The Impact of the Philosophy of Mathematical Practice on the Philosophy of Mathematics”. In: Léna Soler; Sjoerd Zwart; Michael Lynch & Vincent Israel-Jost (eds.), Science After the Practice Turn in the Philosophy, History, and Social Studies of Science. London: Routledge, 2014, pp. 215-226.
• “Another Look at Mathematical Style, as Inspired by Le Lionnais and the OuLiPo” (co-author: Bart Van Kerkhove). In: Erik Weber, Dietlinde Wouters & Joke Meheus (eds.): Logic, Reasoning and Rationality. New York: Springer, 2014, pp. 233-245.
• “Olympification versus aesthetization: The appeal of mathematics outside the classroom” (co-authors: Karen François & Kathleen Coessens). In: Paul Smeyers & Marc Depaepe (eds.), Educational research. Material culture and the representation of educational research. New York: Springer, 2014, pp. 163-178.
• “The inconsistency of mathematics and the mathematics of inconsistency”. In: Peter Vickers & Otavio Bueno (eds.), Is Science Inconsistent?, special issue of Synthese, vol. 191, nr. 13, 2014, pp. 3063-3078 (doi: 10.1007/s11229-014-0474-6).
• “Mathematics and the New Technologies. Part III: The Cloud and the Web of Proofs”. In: Peter Schroeder-Heister, Gerhard Heinzmann, Wilfrid Hodges & Pierre Edouard Bour (eds.), Logic, Methodology and Philosophy of Science. Proceedings of the 14th International Congress (Nancy). Logic and Science Facing the New Technologies. College Publications, London, 2014, pp. 427-439.
• “The heterogeneity of mathematical research”. In: Can Baskent (ed.), Perspectives on Interrogative Models of Inquiry: Developments in Inquiry and Questions. New York: Springer, 2016, pp. 73-94.
• “On the Plurality of Mathematics Discourses: Between Power and Constraints” (co-authors: Karen François & Kathleen Coessens). In: Paul Smeyers & Marc Depaepe (eds.), Discourses of Change and Changes of Discourse. New York: Springer, 2016, pp. 87-100.
• “The Complementary Faces Of Mathematical Beauty” (co-author: Ronny Desmet). In: Desmet, Ronny (ed.), Intuition in Mathematics and Physics: A Whiteheadian Approach. Anoka, MN: Process Century Press, 2016, pp. 123-145.
• “The Philosophy of Mathematical Practice: What Is It All About?” In: P. Ernest; O. Skovsmose; J.P. van Bendegem; M. Bicudo; R. Miarka; L. Kvasz & R. Moeller, The Philosophy of Mathematics Education. New York: Springer, 2016, pp. 13-18. (ICME-13 Topical Surveys).
• “Contingency in Mathematics: Two Case Studies”. In: Léna Soler, Emiliano Trizio & Andrew Pickering (eds.), Science As It Could Have Been. Discussing the Contigency/Inevitability Problem. Pittsburgh: University of Pittsburgh Press, 2016, pp. 223-239.