Geometric diagrams as an effective notation.

In what way does a mathematical proof depend on the notation used in its presentation? This paper examines this question by analysing the computational differences, in the sense of Larkin and Simon's 'Why a diagram is (sometimes) worth 10,000 words', between diagrammatic and sentential notations as...

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Publicado en:Philosophical Investigations Vol. 47; no. 4; pp. 558 - 584
Autor principal: Mumma, John
Formato: Artículo
Publicado: Wiley-Blackwell Oct2024
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Acceso en línea:Ver este registro en EBSCOhost
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        atl: Geometric diagrams as an effective notation.
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        au: Mumma, John
        affil: California State University, San Bernardino California, , USA
      su:
        Mathematical proofs
        Mathematical notation
        Mathematics
        Geometry
        Vocabulary
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          Mathematical proofs
          Mathematical notation
          Mathematics
          Geometry
          Vocabulary
      ab: In what way does a mathematical proof depend on the notation used in its presentation? This paper examines this question by analysing the computational differences, in the sense of Larkin and Simon's 'Why a diagram is (sometimes) worth 10,000 words', between diagrammatic and sentential notations as a means for presenting geometric proofs. Wittgenstein takes up the question of mathematical notation and proof in Section III of Remarks on the Foundations of Mathematics. After discussing his observations on a proof's 'characteristic visual shape' in Section III with respect to arithmetical proofs, the paper shows how the notion of a characteristic visual shape illuminates the special effectiveness of diagrammatic notation in geometry.
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