Ecole Normale Supérieure Toward a Hermeneutic Categorical Mathematics or

why Category theory does not support mathematical structuralism 1. Mathematical Interpretation a) Hermeneutics of the Pythagorean theorem In his (1883) and a number of later writings W. Dilthey urges the autonomy of humanities (Geisteswissenschaften)1 from natural sciences (Naturswissenschaften). Dilthey’s principle argument is methodological: objecting against attempts of Compte and Mill to extend scientific methods to moral, political and other humanities issues Dilthey purports to constitute the autonomy of humanities by providing them with a proper methodology independent from that of natural sciences. An important role in the Dilthey’s methodology of humanities plays his notion of hermeneutic understanding, viz. an understanding achieved through an interpretation, which Dilthey distinguishes from understanding achieved through a scientific explanation. As it has been noticed already by Husserl (1954) and recently stressed by Brown (1991), Crease (1997) and Salanskis (1991) hermeneutic issues are in fact not less important in natural sciences and mathematics than in humanities. A straightforward evidence of the relevance of understanding through interpretation in mathematics comes from the usua