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Deniz Sarikaya
Vrije Universiteit Brussel
  1. Mathematizing as a Virtuous Practice: Different Narratives and Their Consequences for Mathematics Education and Society.Deborah Kant & Deniz Sarikaya - 2020 - Synthese 199 (1-2):3405-3429.
    There are different narratives on mathematics as part of our world, some of which are more appropriate than others. Such narratives might be of the form ‘Mathematics is useful’, ‘Mathematics is beautiful’, or ‘Mathematicians aim at theorem-credit’. These narratives play a crucial role in mathematics education and in society as they are influencing people’s willingness to engage with the subject or the way they interpret mathematical results in relation to real-world questions; the latter yielding important normative considerations. Our strategy is (...)
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    How to Frame Understanding in Mathematics: A Case Study Using Extremal Proofs.Merlin Carl, Marcos Cramer, Bernhard Fisseni, Deniz Sarikaya & Bernhard Schröder - 2021 - Axiomathes 31 (5):649-676.
    The frame concept from linguistics, cognitive science and artificial intelligence is a theoretical tool to model how explicitly given information is combined with expectations deriving from background knowledge. In this paper, we show how the frame concept can be fruitfully applied to analyze the notion of mathematical understanding. Our analysis additionally integrates insights from the hermeneutic tradition of philosophy as well as Schmid’s ideal genetic model of narrative constitution. We illustrate the practical applicability of our theoretical analysis through a case (...)
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  3. How to Frame a Mathematician.Bernhard Schröder, Martin Schmitt, Deniz Sarikaya & Bernhard Fisseni - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Springer Verlag.
    Frames are a concept in knowledge representation that explains how the receiver, using background information, completes the information conveyed by the sender. This concept is used in different disciplines, most notably in cognitive linguistics and artificial intelligence. This paper argues that frames can serve as the basis for describing mathematical proofs. The usefulness of the concept is illustrated by giving a partial formalisation of proof frames, specifically focusing on induction proofs, and relevant parts of the mathematical theory within which the (...)
     
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    How to Frame a Mathematician.Bernhard Schröder, Martin Schmitt, Deniz Sarikaya & Bernhard Fisseni - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 417-436.
    Frames are a concept in knowledge representation that explains how the receiver, using background information, completes the information conveyed by the sender. This concept is used in different disciplines, most notably in cognitive linguistics and artificial intelligence. This paper argues that frames can serve as the basis for describing mathematical proofs. The usefulness of the concept is illustrated by giving a partial formalisation of proof frames, specifically focusing on induction proofs, and relevant parts of the mathematical theory within which the (...)
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  5.  35
    Lakatos' Undone Work: The Practical Turn and the Division of Philosophy of Mathematics and Philosophy of Science_ - Introduction to the Special Issue on _Lakatos’ Undone Work.Sophie Nagler, Hannah Pillin & Deniz Sarikaya - 2022 - Kriterion - Journal of Philosophy 36:1-10.
    We give an overview of Lakatos’ life, his philosophy of mathematics and science, as well as of this issue. Firstly, we briefly delineate Lakatos’ key contributions to philosophy: his anti-formalist philosophy of mathematics, and his methodology of scientific research programmes in the philosophy of science. Secondly, we outline the themes and structure of the masterclass Lakatos’ Undone Work – The Practical Turn and the Division of Philosophy of Mathematics and Philosophy of Science, which gave rise to this special issue. Lastly, (...)
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    Purifying applied mathematics and applying pure mathematics: how a late Wittgensteinian perspective sheds light onto the dichotomy.José Antonio Pérez-Escobar & Deniz Sarikaya - 2021 - European Journal for Philosophy of Science 12 (1):1-22.
    In this work we argue that there is no strong demarcation between pure and applied mathematics. We show this first by stressing non-deductive components within pure mathematics, like axiomatization and theory-building in general. We also stress the “purer” components of applied mathematics, like the theory of the models that are concerned with practical purposes. We further show that some mathematical theories can be viewed through either a pure or applied lens. These different lenses are tied to different communities, which endorse (...)
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  7.  42
    Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts.Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.) - 2019 - Springer Verlag.
    This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The first two sections focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, (...)
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    Three Roles of Empirical Information in Philosophy: Intuitions on Mathematics Do Not Come for Free.Deniz Sarikaya, José Antonio Pérez-Escobar & Deborah Kant - 2021 - Kriterion – Journal of Philosophy 35 (3):247-278.
    This work gives a new argument for ‘Empirical Philosophy of Mathematical Practice’. It analyses different modalities on how empirical information can influence philosophical endeavours. We evoke the classical dichotomy between “armchair” philosophy and empirical/experimental philosophy, and claim that the latter should in turn be subdivided in three distinct styles: Apostate speculator, Informed analyst, and Freeway explorer. This is a shift of focus from the source of the information towards its use by philosophers. We present several examples from philosophy of mind/science (...)
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  9.  8
    Science Advice: Making Credences Accurate.Simon Blessenohl & Deniz Sarikaya - 2022 - Synthese 200 (2).
    Policy-makers often rely on scientists to inform their decisions. When advising policy-makers, what should scientists say? One view says that scientists ought to say what they have a high credence in. Another view says that scientists ought to say what they expect to lead to good policy outcomes. We explore a third view: scientists ought to say what they expect to make the policy-makers’ credences accurate.
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    Mathesis Universalis, Computability and Proof.Stefania Centrone, Sara Negri, Deniz Sarikaya & Peter M. Schuster (eds.) - 2019 - Cham, Switzerland: Springer Verlag.
    In a fragment entitled Elementa Nova Matheseos Universalis Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is (...)
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