27 found
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  1. Mathematical Explanation: A Contextual Approach.Sven Delarivière, Joachim Frans & Bart Van Kerkhove - 2017 - Journal of Indian Council of Philosophical Research 34 (2):309-329.
    PurposeIn this article, we aim to present and defend a contextual approach to mathematical explanation.MethodTo do this, we introduce an epistemic reading of mathematical explanation.ResultsThe epistemic reading not only clarifies the link between mathematical explanation and mathematical understanding, but also allows us to explicate some contextual factors governing explanation. We then show how several accounts of mathematical explanation can be read in this approach.ConclusionThe contextual approach defended here clears up the notion of explanation and pushes us towards a pluralist vision (...)
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  2. The "Artificial Mathematician" Objection: Exploring the (Im)Possibility of Automating Mathematical Understanding.Sven Delarivière & Bart Van Kerkhove - 2017 - In B. Sriraman (ed.), Humanizing Mathematics and its Philosophy. Cham: Birkhäuser. pp. 173-198.
    Reuben Hersh confided to us that, about forty years ago, the late Paul Cohen predicted to him that at some unspecified point in the future, mathematicians would be replaced by computers. Rather than focus on computers replacing mathematicians, however, our aim is to consider the (im)possibility of human mathematicians being joined by “artificial mathematicians” in the proving practice—not just as a method of inquiry but as a fellow inquirer.
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  3.  29
    New Perspectives on Mathematical Practices: Essays in Philosophy and History of Mathematics. [REVIEW]Bart Van Kerkhove (ed.) - 2009 - World Scientific.
    This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics.
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  4. Philosophical Perspectives on Mathematical Practice.Bart Van Kerkhove, Jean Paul Van Bendegem & Jonas De Vuyst (eds.) - 2010 - College Publications.
  5.  25
    The Unreasonable Richness of Mathematics.Jean Paul Van Bendegem & Bart Van Kerkhove - 2004 - Journal of Cognition and Culture 4 (3-4):525-549.
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  6.  3
    Emily Rolfe*Great Circles: The Transits of Mathematics and Poetry.Jean Paul Van Bendegem & Bart Van Kerkhove - forthcoming - Philosophia Mathematica.
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  7.  48
    Pi on Earth, or Mathematics in the Real World.Bart Van Kerkhove & Jean Paul Van Bendegem - 2008 - Erkenntnis 68 (3):421-435.
    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 one of efficiency, i.e. to minimize one’s means/ends ratio. Our (...)
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  8.  99
    Mathematical Arguments in Context.Jean Paul Van Bendegem & Bart Van Kerkhove - 2009 - Foundations of Science 14 (1-2):45-57.
    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 presentation inviting the contextualization of pieces of mathematical reasoning within encompassing bodies of (...)
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  9.  20
    The Many Faces of Mathematical Constructivism.Bart Van Kerkhove & Jean Van Bendegem - 2012 - Constructivist Foundations 7 (2):97-103.
    Context: As one of the major approaches within the philosophy of mathematics, constructivism is to be contrasted with realist approaches such as Platonism in that it takes human mental activity as the basis of mathematical content. Problem: Mathematical constructivism is mostly identified as one of the so-called foundationalist accounts internal to mathematics. Other perspectives are possible, however. Results: The notion of “meaning finitism” is exploited to tie together internal and external directions within mathematical constructivism. The various contributions to this issue (...)
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  10.  6
    Perspectives on Mathematical Practices.Jean Paul Van Bendegem & Bart van Kerkhove (eds.) - 2007 - Springer.
    Philosophy of mathematics today has transformed into a very complex network of diverse ideas, viewpoints, and theories. Sometimes the emphasis is on the "classical" foundational work (often connected with the use of formal logical methods), sometimes on the sociological dimension of the mathematical research community and the "products" it produces, then again on the education of future mathematicians and the problem of how knowledge is or should be transmitted from one generation to the next. The editors of this book felt (...)
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  11.  28
    Mathematical Naturalism: Origins, Guises, and Prospects. [REVIEW]Bart Van Kerkhove - 2006 - Foundations of Science 11 (1-2):5-39.
    During the first half of the twentieth century, mainstream answers to the foundational crisis, mainly triggered by Russell and Gödel, remained largely perfectibilist in nature. Along with a general naturalist wave in the philosophy of science, during the second half of that century, this idealist picture was finally challenged and traded in for more realist ones. Next to the necessary preliminaries, the present paper proposes a structured view of various philosophical accounts of mathematics indebted to this general idea, laying the (...)
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  12.  7
    Vagueness Unlimited: In Defence of a Pragmatical Approach to Sorites Paradoxes.Bart Van Kerkhove - 2003 - Logic and Logical Philosophy 11:251-276.
    As far as ‘modern’ logical theories of vagueness are concerned, a main distinction can be drawn between ‘semantical’ ones and ‘pragmatical’ ones. The latter are defended here, because they tend to retake into account important contextual dimensions of the problem abandoned by the former. Their inchoate condition seems not alarming, since they are of surprisingly recent date. This, however, could very well be an accidental explanation. That is, the true reason for it might sooner or later turn out to be (...)
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  13.  94
    Vagueness-Adaptive Logic: A Pragmatical Approach to Sorites Paradoxes.Bart Van Kerkhove & Guido Vanackere - 2003 - Studia Logica 75 (3):383-411.
    This paper defends a pragmatical approach to vagueness. The vagueness-adaptive logic VAL is a good reconstruction of and an excellent, instrument for human reasoning processes in which vague predicates are involved. Apart from its proof-theory and semantics, a Sorites-treating model based on it is presented, disarming the paradox. The paper opens perspectives with respect to the construction of theories by means of vague predicates.
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  14.  64
    Review of B. Heintz, Die Innenwelt der Matheznatik. Zur Kultur Und Praxis Einer Beweisenden Disziplin. [The Inner World of Mathematics. On the Culture and Practice of a Proof-Based Discipline.][REVIEW]Bart Van Kerkhove - 2004 - Philosophia Mathematica 12 (1):75-78.
  15. Methodological Triangulation in Empirical Philosophy.Benedikt Löwe & Bart Van Kerkhove - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. Bloomsbury Academic. pp. 15-37.
  16. Direct Perception in Mathematics: A Case for Episemological Priority.Bart Van Kerkhove & Erik Myin - 2002 - Logique Et Analyse 45 (179-180):357-72.
  17.  23
    Danielle Macbeth. Realizing Reason: A Narrative of Truth and Knowing. Oxford: Oxford University Press, 2014. ISBN: 978-0-19-870479-1. Pp. Xii + 494. [REVIEW]Bart Van Kerkhove - 2015 - Philosophia Mathematica 23 (1):140-144.
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  18.  15
    The Importance of Being Externalist About Mathematics - One More Turn?Bart Van Kerkhove & Hans Comijn - 2004 - Philosophica 74.
  19.  17
    Whitehead Ou Le Cosmos Torrentiel [Whitehead or the Torrential Cosmos].Bart Van Kerkhove - 2010 - Process Studies 39 (2):356-358.
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  20.  15
    Editorial Introduction.Bart Van Kerkhove - 2004 - Philosophica 74.
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  21.  23
    The Philosophy of Mathematical Practice.Bart Van Kerkhove - 2010 - International Studies in the Philosophy of Science 24 (1):118 – 122.
    This title offers philosophical analyses of important characteristics of contemporary mathematics and of many aspects of mathematical activity which escape purely formal logical treatment.
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  22.  21
    Introduction to the Special Issue Entitled 'Mathematics: What Does It All Mean?'. [REVIEW]Bart Van Kerkhove, Jean Paul Van Bendegem & Sal Restivo - 2006 - Foundations of Science 11 (1-2):1-3.
  23.  5
    Whitehead Ou Le Cosmos Torrentiel [Whitehead or the Torrential Cosmos]: Introductions À Procès Et Réalité [Introductions to Process and Reality]. [REVIEW]Bart Van Kerkhove - 2010 - Process Studies 39 (2):356-358.
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  24. Foundations of the Formal Sciences VII, Studies in Logic.Karen François, Benedikt Löwe, Thomas Müller & Bart van Kerkhove (eds.) - forthcoming - College Publications.
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  25. Boekbesprekingen/Comptes Rendus.Bart Van Kerkhove - 2009 - Studium : Revue D’Histoire des Sciences Et des Universités 2 (4):223-243.
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  26. Laat Ons Niet Ernstig Blijven, Huldeboek Voor Jean Paul Van Bendegem.Bart Van Kerkhove, Karen François, Steffen Ducheyne & Patrick Allo (eds.) - 2018 - Academia Press.
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  27. Mathematical Practice and Naturalist Epistemology: Structures with Potential for Interaction.Bart Van Kerkhove & Jean Van Bendegem - 2005 - Philosophia Scientiae 9 (2):61-78.
    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 intensifying the interaction between both dimensions of practice and epistemology.
     
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