_Middle Term to be distributed._--Essentially the same thing occurs when the middle term is not, at least once, in the premises, used in its most complete and comprehensive sense, or, as the logicians express it, _distributed_. As, for example, when I say, White is a color, the term color is not here distributed, for it properly includes many things besides white. If now I introduce into another proposition the same term in a similar manner, as Black is a color, I evidently include under the term, as now used, some part of the class of things denoted by the general word color, which was not included under the same term as first used. The color which is affirmed to agree with black, is not the same color which is affirmed to agree with white. The term, in fact, denotes one thing in the one proposition, and another in the other. A syllogism thus constructed, is invalid. Hence the rule, that the _middle term must be distributed_, or taken in its completeness, to include the whole class which it properly denotes, _at least once in the premises_. This is done either by making it the _subject of an affirmative_, or the _predicate of a negative proposition_; as, All men are mortal, or, No vice is useful. Here the term man in the one case, and the term useful in the other, are each distributed or taken in their completeness. There is no individual to whom the term man can properly be applied, who is not included in the expression, all men, nor is there any useful thing which is not here denied of vice. _What distributed in the Conclusion._--On the same principle, _no term must be distributed in the conclusion which was not distributed in one of the premises_. This rule is violated in the following syllogism, All birds are bipeds; no man is a bird; therefore, no man is a biped. Here the term biped, in the major premiss, is not taken in its completeness, since many creatures besides birds are bipeds. Birds are only one sort of bipeds. In the conclusion, however, the term biped, being the predicate of a negative proposition, is distributed, the whole class of bipeds is spoken of, and man is excluded from the whole class. The syllogism is, of course, invalid. _Law of negative Premiss._--It is further a law of the syllogism, that _from negative premises nothing can be inferred_. Also, that _if one premiss is negative, the conclusion will be negative_. _Law of particular Premiss._--_From two particular premises nothing follows, but if one premiss is particular, the conclusion will be so._ These rules are too obvious, and too easily verified, to require illustration. IV. DIFFERENT KINDS OF SYLLOGISM. _Syllogisms differ._--We have mentioned as yet only those properties of the syllogism which universally belong to it. There are differences, however, which require to be noticed, and which constitute a distinction of some importance, presenting, in fact, two distinct kinds of syllogism.