Of the Dilemma regarded as an Immediate Inference.

§ 798. Like the partly conjunctive syllogism, the dilemma can be expressed under the forms of immediate inference. As before, the conclusion in the constructive type resolves itself into the subalternate of the major itself, and in the destructive type into the subalternate of its contrapositive. The simple constructive dilemma, for instance, may be read as follows—

If either A is B or E is F, C is D,
.'. Either A being B or E being F, C is D,

which is equivalent to

Every case of either A being B or E being F is a case of C being D.
.'. Some case of either A being B or E being F is a case of C being D.

The descent here from 'every' to 'some' takes the place of the transition from hypothesis to fact.

§ 799. Again the complex destructive may be read thus—

If A is B, C is D; and if E is F, G is H,
.'. It not being true that C is D and G is H, it is not
true that A is B and E is F,

which may be resolved into two steps of immediate inference, namely, conversion by contraposition followed by subalternation—

All cases of A being B and E being F are cases of C being D and G
being H.
.'. Whatever is not a case of C being D and G being H is not a case
of A being B and E being F.
.'. Some case which is not one of C being D and G being H is not a
case of A being B and E being F.