An introductory text-book of logic - Mellone, Sydney - Rare Books at ...

198
CONDITIONAL ARGUMENTS AND
2. Conditional arguments 1 consist of
(1) hypothetical syllogisms,
(2) disjunctive syllogisms,
(3) dilemmas, consisting of hypothetical in
combination with disjunctive premises.
Hypothetical syllogisms are said to be either
"
(a) pure, in which both premises are hypothetical,
(b) mixed, in which the major premise is hypo
"
Pure hypothetical
thetical and the minor categorical.
syllogisms are comparatively of
no importance. They are really categoricals expressed
in an intensive form ( 4).
When both premises are hypothetical, the conclusion must
which in form
and moods of
be so ; and, as we may have hypotheticals
correspond to A, E, I, and O, all the figures
the pure hypothetical syllogism correspond to those of the
categorical syllogism.
The following is an example of Cesare:
If A is B, C is never D.
If E is F, C is always D.
. . If E is F, A is never B.
We shall see that hypothetical propositions may be formally
expressed as categoricals, and vice versa; hence also pure
hypothetical syllogisms may be expressed as categorical
syllogisms, and vice versa.
"
3. When a
"
is hypothetical syllogism spoken of, a
mixed hypothetical syllogism is usually meant. It con
sists of a hypothetical major and a categorical minor.
The hypothetical proposition is always taken as the
major premise,
for it asserts that a relation of Reason
and Consequence, between two concepts or judgments,
holds universally as a matter of theory ; and the minor
1 This use of "conditional" as a name for the genus, with
"hypothetical" as species, is not universally accepted, either in the
case of propositions ( i) or arguments ( 2).