 Poincaré’s often quoted structuralist Credo that in mathematics an entity “exists” means “that its defintion does not imply a contradiction” (1902: 70; 2017: 38–39; 1905c: 819), must be seen in a non-Hilbertian light. Poincaré’s geometric propositions (conventions), which are neither true nor false, are not propositional schemata that can be satisfied by a model. For reasons concerning in particular the involvement of a vicious circle with respect to the principle of complete induction, Poincaré rejects the idea of ensuring mathematical reliability with a Hilbert-style consistency proof (Poincaré 1906: 301; cf. Detlefsen 1986: 59 ff. for a critical assessment). Even with respect to geometry, he takes a structural position without, however, disengaging meaning and knowledge completely from ostension. Nevertheless, Poincaré begins his alternative reliability construction only apparently with sensations as ostensive contacts with the given, since he is not an empiricist. Instead, in a move similar to Helmholtz’s conception of intuition as imagined sensible impressions, Poincaré introduces a representation of a two-place sensation relation, based on the imagination of single sensations. The representation of an object in sensible space means nothing other than the deliberate and conscious representation of muscular sensations thought necessary to reach the object (Poincaré 1902: 82; 2017: 48–49). The sensation relations are then the place-holder of the categories (forms) of sensible space and of groups. Poincaré’s conventions in geometry are first of all the tool that he uses to close (by decision) the gap between the exactness of a structure and the objectivity of sensation-relations based on an imagined ostensive contact (reflecting on sensations). If this interpretation is right, then Poincaré’s concept of structure is not the new Hilbertian one that derives from the axiomatization of Euclidean geometry, but rather constitutes a development of the traditional algebraic concept of structure and concerns continuous groups on the one hand and the type of iteration and complete induction on the other hand. His epistemological stance has a strong affinity with Schlick’s General Theory of Knowledge. Given, on the one hand, that “pure quality is impenetrable” and, on the other hand, that knowledge is public—“no discourse, no objectivity” (Poincaré 1905b: 179; 1913b: 347–48)—how is it possible that although we cannot be sure that our experience is the same, we can intersubjectively know the same thing? The answer is found in the thesis that “science is a system of relations” (Poincaré 1905b: 181; 1913b: 349).