Still, an exception may be made by admitting a bi-designate conclusion: 

      Some P is M;
      Some S is not M: 
    .’.  Some S is not some P.

(ii) If one premise be particular, so is the conclusion.

For, again, if both premises be affirmative, they only distribute one term, the subject of the universal premise, and this must be the middle term.  The minor term, therefore, is undistributed, and the conclusion must be particular.

If one premise be negative, the two premises together can distribute only two terms, the subject of the universal and the predicate of the negative (which may be the same premise).  One of these terms must be the middle; the other (since the conclusion is negative) must be the major.  The minor term, therefore, is undistributed, and the conclusion must be particular.

(iii) From a particular major and a negative minor premise nothing can be inferred.

For the minor premise being negative, the major premise must be affirmative (5th Canon); and therefore, being particular, distributes the major term neither in its subject nor in its predicate.  But since the conclusion must be negative (6th Canon), a distributed major term is demanded, e.g.,

      Some M is P;
      No S is M: 
    .’. ------

Here the minor and the middle terms are both distributed, but not the major (P); and, therefore, a negative conclusion is impossible.

Sec. 3.  First Principle or Axiom of the Syllogism.—­Hitherto in this chapter we have been analysing the conditions of valid mediate inference.  We have seen that a single step of such inference, a Syllogism, contains, when fully expressed in language, three propositions and three terms, and that these terms must stand to one another in the relations required by the fourth, fifth, and sixth Canons.  We now come to a principle which conveniently sums up these conditions; it is called the Dictum de omni et nullo, and may be stated thus: 

    Whatever is predicated (affirmatively or negatively) of a
    term distributed,

    With which term another term can be (partly or wholly)
    identified,

    May be predicated in like manner (affirmatively or
    negatively) of the latter term (or part of it).

Thus stated (nearly as by Whately in the introduction to his Logic) the Dictum follows line by line the course of a Syllogism in the First Figure (see chap.  X. Sec. 2).  To return to our former example:  All authors are vain is the same as—­Vanity is predicated of all authors; Cicero is an author is the same as—­Cicero is identified as an author; therefore Cicero is vain, or—­Vanity may be predicated of Cicero.  The Dictum then requires:  (1) three propositions; (2) three terms; (3) that the middle term be distributed; (4) that one premise be affirmative, since only by an affirmative proposition can one term be identified with another; (5) that if one premise be negative the conclusion shall be so too, since whatever is predicated of the middle term is predicated in like manner of the minor.