3. In definitive universal propositions, quality remaining the same and affirmative, when the predicates are the same and the subjects are genus and species, and vice versa, the propositions are subalterns, the subalternation, however, in one case being the reverse of the other ; if negative, they are reciprocals.
4. In definitive universal propositions, quality being different, when the predicates are genus and species, and the subjects the same, the predicate of A being the genus, and of E, the species, the propositions are sub-contraries; but if the predicate of A be the species and that of E the genus, the propositions are contraries; if the predicates are the same and the subjects are genus and species, the propositions are contradictories.
Similar rules can be developed much further under other suppositions, but these are sufficient to show the complications of actual thought, and these complications are very much increased with distributive universals. Here we should be involved in two forms of Opposition according as quantity or quality is considered. But I need not remark further on this point. We see sufficient reasons for very natural errors in thinking in the very complexity of the conditions to be observed, and which are entirely independent of the canons of formal logic. They are, of course, only illustrations of what occurs in other fields as well as in that of thought. For instance, we may have a rule for deducing the sum of the angles of a triangle in pure mathematics, but in actual triangles we may either require a distinct method for this purpose, or observe antecedent precautions for determining the perfection of our triangles. This is only to say that in constructing actual triangles we may be under great incertitude as to their perfection. Also in the construction of bridges or houses, we cannot rely upon the abstract and theoretical strength of materials. We have to take them three or four times as strong as the theory requires. And again, a belt will stretch after use, so that the wheels must either be adjusted to it or some means employed to compensate for the stretching; and so on indefinitely in almost every field of science and art.
