the existence of Opposition. This, of course, is determined by the matter of thought, and the formal elements by which the rules can be stated are the genus and species involved in the subjects or predicates of the propositions.
Thus, formally, no relations of Opposition would be detected between the propositions, "All Americans are men," and "All Americans are Caucasians," but in reality they are subalterns, the species describing the subalternans and the genus the subalternate, questions of quantity being disregarded. When the subjects are genus and species, and the predicates the same, although the propositions are still subalterns, the relation is simply reversed. This, of course, when the propositions are universals. A more practical illustration of the same subalternation would be, "All knowledge is scientific, but whether scientific or not, is true," and "All knowledge is useful and likewise all biological science,"—"knowledge" and "biological science" being genus and species.
In singular propositions a distinct solution must be given. Thus, "Socrates is a man," and " Socrates is a horse," must be regarded as contraries materially, though nothing can be determined formally about them. Then again, "Bismarck is a man" and "Bismarck is a German" are subalterns, the first being the subalternate and the latter the subalternans. And thus the analysis may be carried out with various forms of propositions. Without going through this operation, we may simply formulate a few rules, supplementary to those already mentioned, and dealing with the material import and relations of propositions.
1. In singular propositions, quality remaining the same and affirmative, when the predicates are separate species and the subjects are the same, the propositions are contraries; when the predicates are genus and species, they are subalterns; if negative, they are sub-contraries and subalterns.
2. In singular propositions, quality being different, when the predicates are separate species and the subjects are the same, the propositions are subalterns; when the predicates are genus and species, they are sub-contraries.
