 Bolzano’s system of extensional relations between propositions with variable ideas is motivated by similar thoughts, though it is cast in terms of the extensions of ideas, propositions, and variable ideas within them. The key notion is that of a collection of ideas \(i’, j’, k’, \ldots\) which, when substituted for the variable ideas \(i, j, k, \ldots\) in propositions \(A, B, C, \ldots\), results in a collection of propositions all of which are true. (More loosely, Bolzano speaks of “collections of ideas whose substitution for \(i, j, k, \ldots\), makes all of \(A, B, C, \ldots\) true” (TS II: §155, 114, 122, and §156, 133).) We will call such collections of ideas \(i’, j’, k’, \ldots\) verifying ideas for \(A, B, C, \ldots\) relative to the variable ideas \(i, j, k, \ldots.\)