model of the group axioms, which are exemplified (in the Goodmanian sense) by the sensation system. In other words, the shape created in the mind leads to a particular type of platonistic universals, which is a model (in the model theoretical sense) of the mathematical axiom system of the displacement group. The elements of the displacement group are independent and complete entities with respect to the axiom system of the group. But, by analyzing the subgroups of the displacement group (common to geometries with constant curvature) one transforms the variables of the axiom system in "places' whose "objects' lack any ontological commitment except with respect to the specified axioms. In general, a structure R is interpreted as a second order relation, which is exemplified by a system of axioms according to the pragmatic maxim of Peirce." /> Objectivity in mathematics - Heinzmann Gerhard | sdvig press