If both premises are negative, we only know that both the other terms are partly or wholly excluded from the Middle, or are not identical with it in denotation:  where they lie, then, in relation to one another we have no means of knowing.  Similarly, in the mediate comparison of quantities, if we are told that A and C are both of them unequal to B, we can infer nothing as to the relation of C to A. Hence the premises—­

    No electors are sober;
    No electors are independent—­

however suggestive, do not formally justify us in inferring any connection between sobriety and independence.  Formally to draw a conclusion, we must have affirmative grounds, such as in this case we may obtain by obverting both premises: 

      All electors are not-sober;
      All electors are not-independent: 
    .’.  Some who are not-independent are not-sober.

But this conclusion is not in the given terms.

(6) (a) If one premise be negative, the conclusion must be negative:  and (b) to prove a negative conclusion, one premise must be negative.

(a) For we have seen that one premise must be affirmative, and that thus one term must be partly (at least) identified with the Middle.  If, then, the other premise, being negative, predicates the exclusion of the remaining term from the Middle, this remaining term must be excluded from the first term, so far as we know the first to be identical with the Middle:  and this exclusion will be expressed by a negative conclusion.  The analogy of the mediate comparison of quantities may here again be noticed:  if A is equal to B, and B is unequal to C, A is unequal to C.

(b) If both premises be affirmative, the relations to the Middle of both the other terms are more or less inclusive, and therefore furnish no ground for an exclusive inference.  This also follows from the function of the middle term.

For the more convenient application of these canons to the testing of syllogisms, it is usual to derive from them three Corollaries: 

(i) Two particular premises yield no conclusion.

For if both premises be affirmative, all their terms are undistributed, the subjects by predesignation, the predicates by position; and therefore the middle term must be undistributed, and there can be no conclusion.

If one premise be negative, its predicate is distributed by position:  the other terms remaining undistributed.  But, by Canon 6, the conclusion (if any be possible) must be negative; and therefore its predicate, the major term, will be distributed.  In the premises, therefore, both the middle and the major terms should be distributed, which is impossible:  e.g.,

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

Here, indeed, the major term is legitimately distributed (though the negative premise might have been the minor); but M, the middle term, is distributed in neither premise, and therefore there can be no conclusion.