 Due to the domain and the range of \(\mathbf{G}\) being disjunctive sets, the relation \(\mathbf{G}\) has the following formal features: it is irreflexive, asymmetric, and (trivially) transitive; moreover, \(\mathbf{G}\) is many-one, but not one-many. Due to \(\mathbf{G}\)’s being many-one, by each subjective idea and each judgment an idea or a proposition, respectively, is uniquely determined as its material (WL III, 8 f., 108). Most of the important properties, relations and distinctions, which were defined by Bolzano primarily for ideas and propositions, can therefore easily be transferred from the sphere of ideas and propositions to the sphere of subjective ideas and judgments. We therefore will say of a subjective idea that it is simple or complex, empty, singular or general, an intuition, a concept or “mixed” according as the idea grasped by it has the corresponding property; and the same goes for judgments. 