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Deborah Kant
Universität Konstanz
  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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    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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    Interview With a Set Theorist.Deborah Kant & Mirna Džamonja - 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. 3-26.
    The status of independent statements is the main problem in the philosophy of set theory. We address this problem by presenting the perspective of a practising set theorist. We thus give an authentic insight in the current state of thinking in set-theoretic practice, which is to a large extent determined by independence results. During several meetings, the second author asked the first author about the development of forcing, the use of new axioms and set-theoretic intuition on independence. Parts of these (...)
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  5. A General Framework for a Second Philosophy Analysis of Set-Theoretic Methodology.Carolin Antos & Deborah Kant - manuscript
    Penelope Maddy’s Second Philosophy is one of the most well-known ap- proaches in recent philosophy of mathematics. She applies her second-philosophical method to analyze mathematical methodology by reconstructing historical cases in a setting of means-ends relations. However, outside of Maddy’s own work, this kind of methodological analysis has not yet been extensively used and analyzed. In the present work, we will make a first step in this direction. We develop a general framework that allows us to clarify the procedure and (...)
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    Interview With a Set Theorist.Deborah Kant & Mirna Džamonja - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics. Springer Verlag. pp. 3-26.
    The status of independent statements is the main problem in the philosophy of set theory. We address this problem by presenting the perspective of a practising set theorist. We thus give an authentic insight in the current state of thinking in set-theoretic practice, which is to a large extent determined by independence results. During several meetings, the second author asked the first author about the development of forcing, the use of new axioms and set-theoretic intuition on independence. Parts of these (...)
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