 The exemplification of the structure by a large variety of systems (imagined sensations, mathematical and physical facts, objects) having some characters in common is an aesthetic operation, not a logical one. The general group structure is given by intuition rather than by an explicit identity criterion and the determination of its formal properties expressed by the means of sub-groups is the result of a mastery occasioned by concrete systems (samples). The mathematician creates structural harmony as does an artist. In art, the structure can be implicit, while in mathematics it is normally explicit, even if it is qualitative. The number of their exemplifications, i.e., of their applications, is the aesthetic element “uniting” both, mathematical and artistic structures (Poincaré 1905b: 104; 1913b: 280). There is for example nearly no mathematical theory where the notion of group does not intervene by giving the same name to different “things” (Poincaré 1921: 137). Poincaré’s geometric or algebraic conventions form a conceptual construction that is irreducible to a combination of clearly distinguished parts of structural elements and aesthetic exemplifications. In this sense the result of the psycho-physiological genesis of geometry is as a whole a system understood as a pragmatic procedure.