 As far as our first example \(S_1\) is concerned, there are true as well as false variants of it with respect to every single extra-logical part of it and also with respect to every sequence of such parts. But now let us consider the following expamle \(S_2\): [Every German philosopher is European]. It has true as well as false [German]-variants, [European]-variants, ([German], [philosopher])-variants, ([German], [European])-variants, ([philosopher], [European])-variants and also ([German], [philosopher], [European])-variants. But obviously, all [philosopher]-variants of \(S_2\) must be true — provided, says Bolzano, that their subject idea is non-empty. This proviso is a typical feature of Bolzano’s approach and mentioned by him again and again, since — according to his truth condition — a proposition with an empty subject idea is trivially false. Whenever we perform the operation of variation on the subject idea of a proposition (and sometimes also when we perform it only on certain parts of it), however, we will have variants with empty subject ideas; thus, only in exceptional cases all variants of a proposition will turn out to be true. If all \(i\)-variants of a proposition \(s\) with a non-empty subject idea are true, Bolzano will say that \(s\) is universally valid with respect to \(i\). Hereby we have to take into account, that for Bolzano also in his meta-language words such as ‘all’, ‘every’ or ‘each’ have existential import and that therefore his definition must explicitly stated as follows (WL II, 82):