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2006
- handle: 10670/1.my30ch
- 1665-2436
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Revista Latinoamericana de Investigación en Matemática Educativa, RELIME
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Michael Otte, « Proof and Explanation from a Semiotical Point of View », Revista Latinoamericana de Investigación en Matemática Educativa, ID : 10670/1.my30ch
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Résumé
"A distinction between proofs that prove and proofs that explain has over and again playedan important role within recent discussions in epistemology and mathematics education.The distinction goes back to scholars who, like Bolzano or Dedekind, have tried to reestablish pure mathematics as a purely conceptual and analytical science. Theseendeavors did in particular argue in favor of a complete elimination of intuitive or perceptualaspects from mathematical activity, arguing that one has to rigorously distinguish betweena concept and its representations. Using a semiotical approach which negates such aseparation between idea and symbol, we shall argue that mathematics has no explanationsin a foundational sense. To explain amounts to exhibiting the meaning of something.Mathematics has, however, as we shall try to show, no definite meanings, neither in thestructural intra-theoretical sense nor with respect to intuitive objectivity. Signs andmeanings are processes, as we shall argue along with Peirce."