d in neither premise, and therefore there can be no
conclusion.

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 f