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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.  76
    Is Mathematics a Domain for Philosophers of Explanation?Erik Weber & Joachim Frans - 2017 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 48 (1):125-142.
    In this paper we discuss three interrelated questions. First: is explanation in mathematics a topic that philosophers of mathematics can legitimately investigate? Second: are the specific aims that philosophers of mathematical explanation set themselves legitimate? Finally: are the models of explanation developed by philosophers of science useful tools for philosophers of mathematical explanation? We argue that the answer to all these questions is positive. Our views are completely opposite to the views that Mark Zelcer has put forward recently. Throughout this (...)
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  3. Mechanistic Explanation and Explanatory Proofs in Mathematics.Joachim Frans & Erik Weber - 2014 - Philosophia Mathematica 22 (2):231-248.
    Although there is a consensus among philosophers of mathematics and mathematicians that mathematical explanations exist, only a few authors have proposed accounts of explanation in mathematics. These accounts fit into the unificationist or top-down approach to explanation. We argue that these models can be complemented by a bottom-up approach to explanation in mathematics. We introduce the mechanistic model of explanation in science and discuss the possibility of using this model in mathematics, arguing that using it does not presuppose a Platonist (...)
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  4.  21
    Mathematical Proofs in Practice: Revisiting the reliability of published mathematical proofs.Joachim Frans & Laszlo Kosolosky - 2014 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 29 (3):345-360.
    Mathematics seems to have a special status when compared to other areas of human knowledge. This special status is linked with the role of proof. Mathematicians often believe that this type of argumentation leaves no room for errors and unclarity. Philosophers of mathematics have differentiated between absolutist and fallibilist views on mathematical knowledge, and argued that these views are related to whether one looks at mathematics-in-the-making or finished mathematics. In this paper we take a closer look at mathematical practice, more (...)
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  5.  57
    Unificatory Understanding and Explanatory Proofs.Joachim Frans - 2020 - Foundations of Science 26 (4):1105-1127.
    One of the central aims of the philosophical analysis of mathematical explanation is to determine how one can distinguish explanatory proofs from non-explanatory proofs. In this paper, I take a closer look at the current status of the debate, and what the challenges for the philosophical analysis of explanatory proofs are. In order to provide an answer to these challenges, I suggest we start from analysing the concept understanding. More precisely, I will defend four claims: understanding is a condition for (...)
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    Mathematical Explanation: Epistemic Aims and Diverging Assessments.Joachim Frans & Bart Van Kerkhove - 2023 - Global Philosophy 33 (2):1-26.
    Mathematicians suggest that some proofs are valued for their explanatory value. This has led to a philosophical debate about the distinction between explanatory and non-explanatory proofs. In this paper, we explore whether contrasting views about the explanatory value of proof are possible and how to understand these diverging assessments. By considering an epistemic and contextual conception of explanation, we can make sense of disagreements about explanatoriness in mathematics by identifying differences in the background knowledge, skill corpus, or epistemic aims of (...)
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  7. Proof in the History and Philosophy of Mathematical Practice: An Introduction.Joachim Frans & Bart Van Kerkhove - 2024 - In Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice. Cham: Springer. pp. 2037-2043.
    This introductory chapter sets the stage for an engaging exploration of the multifaceted concept of proof in the philosophy of mathematical practice. As a fundamental pillar of mathematics, proof has long been a subject of intense scrutiny for mathematicians and philosophers alike. Traditionally, proofs have been perceived as rigorous and deductive arguments, and this analysis was directed towards the notion of formal proof. However, recent developments have challenged this traditional view, highlighting the dynamic and evolving nature of mathematical proofs. In (...)
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  8. The Game of Fictional Mathematics. Review of “Mathematics and Reality” by Mary Leng.Joachim Frans - 2012 - Constructivist Foundations 8 (1):126-128.
     
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  9.  37
    Revisiting the reliability of published mathematical proofs: where do we go next?Joachim Frans & Laszlo Kosolosky - 2014 - Theoria 29 (3):345-360.
    Mathematics seems to have a special status when compared to other areas of human knowledge. This special status is linked with the role of proof. Mathematicians all too often believe that this type of argumentation leaves no room for errors or unclarity. In this paper we take a closer look at mathematical practice, more precisely at the publication process in mathematics. We argue that the apparent view that mathematical literature is also more reliable is too naive. We will discuss several (...)
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