us still
with a hypothetical conclusion. This circumstance seems to ally them
more closely with Categorical Syllogisms than with those that are
discussed in the present chapter. That they are Categoricals in disguise
may be seen by considering that the above syllogism is not materially
significant, unless in each proposition the word 'If' is equivalent to
'Whenever.' Accordingly, the name 'Hypothetical Syllogism,' is here
employed in the older usage.

Sec. 2. A Disjunctive Syllogism consists of a Disjunctive Major Premise, a
Categorical Minor Premise, and a Categorical Conclusion.

How many Moods are to be recognised in this kind of argument depends on
whether the alternatives of the Disjunctive Premise are regarded as
mutually exclusive or possibly coincident. In saying '_Either_ A is B,
_or_ C is D,' do we mean 'either, but not both,' or 'either, it may be
both'? (See chap. v. Sec. 4.)

When the alternatives of the Disjunctive are not exclusive, we have only
the

_Modus tollendo ponens._

Either A is B, or C is D;
A is not B (or C is not D):
.'. C is D (or A is B).

Either wages fall, or the weaker hands are dismissed;

Wages do not fall:
.'. The weaker hands are dismissed.

But we cannot argue--

Wages fall:
.'. The weaker hands are not dismissed;

since in 'hard times' both events may happen together.

Rule of the _Modus tollendo ponens_: If one alternative be denied, the
other is affirmed.

When, however, the alternatives of the Disjunctive are mutually
exclusive, we have also the

_Modus ponendo tollens._

Either A is B, or C is D;
A is B (or C is D):
.'. C is not D (or A is not B).

Either the Tories or the Whigs win the election;

The Tories win:
.'. The Whigs do not win.

We may also, of course, argue as above in the _Modus tollendo ponens_--

The Tories do not win:
.'. The Whigs do.

But in this example, to make the _Modus tollendo ponens_ materially
valid, it must be impossible that the election should result in a tie.
The danger of the Disjunctive Proposition is that the alternatives may
not, between them, exhaust the possible cases. Only contradictory
alternatives are sure to cover the whole ground.

Rule of the _Modus ponendo tollens:_ If one alternative be affirmed, the
other is denied.

Since a disjunctive proposition may be turned into a hypothetical
proposition (chap. v.