 The result of applying the operation of variation to a proposition depends essentially on our choice of ideas to be varied in the proposition in question. And it can depend on matters of fact whether or not a proposition is universally valid (or contravalid) with respect to a sequence \(i\) of ideas. Thus, e.g., it is due to the fact that every German is European and no German is American that the proposition [Every German philosopher is European] is universally valid and the proposition [Every German philosopher is American] is universally contravalid with respect to [philosopher]. From a logical point of view, the most interesting results will turn up if all extra-logical parts of a proposition, which are simple (or — as explained before — “relatively” simple), are taken to be variable (WL II, 84). To simplify matters, we will assume for what follows that for any proposition \(s\) there is always fixed a certain alphabetic order of all extra-logical simple ideas contained in it; thereby, for every proposition \(s\), a sequence \(i^{\boldsymbol{s}}\) of all extra-logical simple ideas contained in \(s\) is uniquely determined. It would appear that we now could define the concepts of logico-universal validity and logico-universal contravalidity in the following way: A proposition \(s\) is logico-universally valid, or — put briefly — logically true, iff \(s\) is universally valid with respect to \(i^{\boldsymbol{s}}\); \(s\) is logico-universally contravalid, or — put briefly — logically false, iff \(s\) is universally contravalid with respect to \(i^{\boldsymbol{s}}\); \(s\) is logically analytic iff \(s\) logically true or logically false; and \(s\) is logically synthetic iff\( s\) is not logically analytic.