s B, C is D; and if E is F, G is H:
But either C is not D, or G is not H:
.'. Either A is not B, or E is not F.

If poetic justice is observed, virtue is rewarded; and if the
mirror is held up to Nature, the villain triumphs:

But either virtue is not rewarded, or the villain does not
triumph:

.'. Either poetic justice is not observed, or the mirror is
not held up to Nature.

Such are the four Moods of the Dilemma that emerge if we only use
affirmative hypotheticals for the major premise; but, certainly, it is
often quite as natural to employ two negative hypotheticals (indeed,
one might be affirmative and the other negative; but waive that); and
then four more moods emerge, all having negative conclusions. It is
needless to intimidate the reader by drawing up these four moods in
battle array: they always admit of reduction to the foregoing moods by
obverting the hypotheticals. Still, by the same process we may greatly
decrease the number of moods of the Categorical Syllogism; and just as
some Syllogisms are most simply expressed in Celarent or Cesare, so some
Dilemmas are most simply stated with negative major premises--e.g.,
The example of a Simple Constructive Dilemma above given would run more
naturally thus: _If the Tories win, the Government will not innovate;
and if the Whigs, the Lords will not let them_: and similarly
Demosthenes' Dilemma--_If AEschines joined, he is not consistent; and if
he did not, he is not patriotic_. Moreover, the propriety of recognising
Dilemmas with negative major premises, follows from the above analysis
of the Dilemma into a combination of Conditional Syllogisms, even if (as
in Sec. 1 of this chapter) we take account of only four Moods of the
Hypothetical Syllogism.

In the rhetorical use of the Dilemma, it may be observed that the
disjunction in the minor premise ought to be obvious, or (at any rate)
easily acceptable to the audience. Thus, _Either the Tories or the Whigs
will win; Either AEschines joined in the rejoicings, or he did not_; such
propositions are not likely to be disputed. But if the orator must stop
to prove his minor premise, the smacking effect of this figure (if the
expression be allowed) will be lost. Hence the minor premises of other
examples given above are only fit for a select audience. That _Either
ghosts are not spirits, or they do not exert mechanical energy_,
supposes a knowledge of the principle, generally taugh