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Understanding mathematical texts: a hermeneutical approach.

The work done so far on the understanding of mathematical (proof) texts focuses mostly on logical and heuristical aspects; a proof text is considered to be understood when the reader is able to justify inferential steps occurring in it, to defend it against objections, to give an account of the “mai...

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Published in:Synthese Vol. 200; no. 6; pp. 1 - 32
Main Author: Carl, Merlin
Format: Article
Published: Springer Nature Dec2022
Online Access:View this record in EBSCOhost
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        10.1007/s11229-022-03930-5
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        atl: Understanding mathematical texts: a hermeneutical approach.
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        au: Carl, Merlin
        affil: Institut für mathematische, naturwissenschaftliche und technische Bildung, Abteilung für Mathematik und ihre Didaktik, Europa-Universität Flensburg, Auf dem Campus 1b, 24943, Flensburg, Schleswig-Holstein, Germany
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      keyword:
        Gadamer
        Hermeneutics
        Mathematical proof
        Philosophy of mathematics
        Understanding
      ab: The work done so far on the understanding of mathematical (proof) texts focuses mostly on logical and heuristical aspects; a proof text is considered to be understood when the reader is able to justify inferential steps occurring in it, to defend it against objections, to give an account of the “main ideas”, to transfer the proof idea to other contexts etc. (see, e.g., Avigad in The philosophy of mathematical practice, Oxford University Press, Oxford, 2008). In contrast, there is a rich philosophical tradition dealing with the concept of understanding and interpreting texts, namely philosophical hermeneutics, represented, e.g., by Schleiermacher, Dilthey, Heidegger or Gadamer. In this tradition, “understanding” generally refers to the integration in a comprehensive (historical, existential, life-worldly,...) context. In this article, we take some first steps towards exploring the question how the ideas from philosophical hermeneutics presented in Gadamer’s “Truth and Method” apply to mathematical texts and what (if anything) can be learned from these for the didactics and presentation of mathematics.
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    language: English
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