On two immediate inferences by limitation (Q2560798)

When one has the task of determining the truth-value of a categorical proposition \(A\) in relation to a proposition \(B\) whose truth-value is given, one may derive from \(A\) a proposition \(C\) (with subject and predicate as in \(B\)) by the traditional rules of immediate inference, determine the truth-value of \(C\) in relation to \(B\) by the traditional square of opposition, and an the basis of that determination ascertain the truth-value of \(A\). Such an approach requires that we prohibit the inferences by limitation (conversion and contraposition) in those cases where \(B\) is a false universal proposition or where \(B\) is a true particular proposition; otherwise, no satisfactory rules governing this approach can be formulated.