 In proceeding this way, however, we would have to face serious problems concerning purely logical propositions, i.e., propositions all of whose parts are purely logical ideas. Due to our requirement (v) above concerning Bolzano’s replacement operation, neither an \(i\)-variant in general nor an \(i^s\)-variant in particular is defined for a purely logical proposition, since it does not contain any extra-logical idea. In consequence the preceding definitions of logical truth, logical falsity and logical analyticity are not applicable to purely logical propositions, since they do not contain any extra-logical idea. Consider, however, the following three purely logical propositions: [There is something, or it is not the case that there is something], [There is something, and it is not the case that there is something], and [There is something]. The first of these three propositions is obviously logically true, the second one logically false, and the third one is neither logically true nor logically false. Giving up requirement (v), as some would like to have it, results in a purely logical proposition being its only own \(i^{\boldsymbol{s}}\)-variant. That, however, would turn every purely logical proposition either into a logical truth or into a logical falsity according to our definition, in contrast to the fact that the proposition [There is something], i.e. [[something] has non-emptiness], is not logically analytic; it is a truth of logic, but nevertheless not logically true (WL II, 375).