 Bolzano defines a variety of relations between ideas concerning their extensions, such as the following ones: An idea \(i_1\) is compatible with an idea\( i_2\) iff \(i_1\) and \(i_2\) share a common object, i.e. \(Ext(i_1) \cap\) \(Ext(i_2) \ne \varnothing\); and \(i_1\) is included in \(i_2\) (or: \(i_2\) includes \(i_1)\) iff \(i_1\) is compatible with \(i_2\) and every object of \(i_1\) is also an object of \(i_2\), i.e., \(Ext(i_1) \cap\) \(Ext(i_2) \ne \varnothing\), and \(Ext(i_1) \subseteq\) \(Ext(i_2)\). In Bolzano’s theory of ideas, precise correlates are available of basic concepts of set theory such as the empty set as well as the membership relation and the relation of inclusion between sets. Unfortunately, the clear distinction between membership and inclusion in his theory of ideas vanished in his theory of propositions due to the common form \([A\) has \(b]\) of all propositions whereby \([A]\) can be not only a singular, but also a general (or an empty) idea.