Abstract

Since the beginning of the 19th century, Schleiermacher pointed out the presence of a circle (hermeneutic circle) in the comprehension: A particular element can be considered only taking into account the universe to which it belongs, and vice versa. Heidegger reconsidered the mentioned issue, so the comprehension is not understood according to the model of textual interpretation; it is based on the relationship between human beings and the world. When we consider a “historical” piece of knowledge (both an artistic masterpiece and an ancient mathematical idea) we can try to frame it in its historical period; nevertheless we can read it from our present, actual viewpoint. As regards mathematical knowledge, for instance, it is not really meaningful to look for “general rules” of mathematical evolution. Every culture clearly influenced the development of its own mathematics, for instance, by using artefacts and semiotic representations (Peirce). Both historico-cultural approaches (Radford) and anthropological approaches (D’Amore and Godino) ask us to investigate how cultural contexts determined mathematical experiences. Therefore art and mathematics can be linked by a hermeneutic approach: they are human enterprises and they are not to be considered as paths towards a form of truth “out there” (in Richard Rorty’s words).

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