 We have explained Bolzano’s method of idea-variation in section 3.6 with respect to single propositions. In order to apply it also to arguments, we have now to extend our original definitions to whole sets of propositions. In applying the operation of variation to a set \(\sigma\) of propositions, each member of \(\sigma\) is replaced by its corresponding variant: The j/i-variant of a set \(\sigma\) of propositions is the set of all the \(j/i\)-variants of the members of \(\sigma\). Moreover we will say of a set \(\sigma\) of propositions that it is true iff each of its members is true; and we will say that a sequence \(j\) of ideas verifies a set \(\sigma\) of propositions with respect to \(i\) iff \(j\) verifies each member of \(\sigma\) with respect to \(i\), i.e., iff the \(j/i\)-variant of each member of \(\sigma\) is true. A proposition \(s\) follows from a set \(\sigma\) of propositions (or, in other words, \(s\) is a consequence of \(\sigma)\) with respect to a sequence \(i\) of ideas iff every sequence \(j\) of ideas that verifies \(\sigma\) with respect to \(i\) verifies \(s\) as well with respect to \(i\).