 Talking about the “external dimension” of ideas, we made — following Bolzano — intensive usage of a certain relation \(\mathbf{R}\) between ideas and their objects that is basic in Bolzano’s theory of ideas. For ‘\(i \mathbf{R} x\)’ we used phrases such as ‘\(i\) is an idea of \(x\)’ or ‘\(x\) is an object of \(i\)’; other expressions for it are ‘\(i\) represents \(x\)’, ‘\(x\) is subsumed under \(i\)’ or ‘\(x\) falls under \(i\)’ (WL I, 298). The domain of \(\mathbf{R}\) is the set of non-empty ideas, its range being the set of all objects; moreover, \(\mathbf{R}\) has the following properties: it is neither reflexive nor irreflexive (the latter due to counterexamples such as: [idea] \(\mathbf{R}\) [idea]; cf. WL I, 461), it is neither symmetric nor asymmetric, it is neither transitive nor intransitive, and it is neither one-many nor many-one. Since, according to our definition, \(Ext(i) = \{x \mid i \mathbf{R} x\}\), we can express ‘\(i \mathbf{R} x\)’ also in terms of ‘extension’ as ‘\(x \in\) \(Ext(i)\)’.