CHAPTER IL 405 If two particular propositions differ in quality they are sub - contraries; as I Some Vine is a Tree. 22 These may be both true together, O Some Vine is not a Tree.) but they can never be both false. Both particular and universal propositions which agree in quality, but not in quantity, are called subaltern, though these are not properly opposite, as A Every Vine is a Tree. I Some Vine is a Tree. Or thus : E No Vine is a Tree. O Some Vine is not a Tree. The canons of subaltern propositions are usually reckoned these three ; namely, (I.) If an universal proposition be true, the particular will be true also, but not on the contrary. And, (2.) If a particular proposition be false, the universal must be false too, but not on the contrary. (3.) Subaltern propositions, whether universal or particular, may sometimes be both true and sometimes both false. The conversion of propositions, is when the subject and pre- dicate change their places with preservation of the truth. This may be done with constant certainty in all universal negatives and particular affirmatives : as no spirit is an animal, may be converted, no animal is a spirit; and some tree is a vine, may be converted, some vine is a tree,. But there is more of for- mal trifling in this sort of discourse than there is of solid im- provement, because this sort of conversion arises merely from the form of words, as connected in a proposition, rather than from the matter. Yet it may be useful to observe, that there are some propo- sitions, which by reason of the ideas or matter of which they are composed, may be converted with constant truth : such are those propositions whose predicate is a nominal or real definition of the subject, or the difference of it, or a property of the fourth kind, or a superlative degree of any property or quality whatso- ever ; or in short wheresoever the predicate and the subject have exactly the same extension, or the same comprehension; as, " every vine is a tree bearing grapes ; and every tree bearing grapes is a vine : religion is the truest wisdom and, the truest wisdom is religion ; Julius Cæsar was the first Emperor of Rome ; and, the first Emperor of Rome was Julius Cæsar." These are the propositions which are properly convertible, and they Are called reciprocal propositions. SECT. IV. Of pure and modal Propositions. ANOTHER division of propositions among the scholastic writers, is into pure and modal. This may be called (for dis- tinction-sake) a division according to the predicate. c c 3
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