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

THE VALIDITY OF THE SYLLOGISM. 2O/
(4) The essentials of the dilemma are the plurality
of antecedents or of consequents in the major, and the
disjunctive minor.
Hence there are four possible forms of the dilemma :
(1) Simple Constructive.
If A is B or if C is D, E is F ;
Either A is
. . E is F.
B or C is D ;
(2) Simple Destructive.
If A is B, C is D and E is F ;
Either C is not D or E is not F ;
. . A is not B.
(3) Complex Constructive.
If A is B, C is D ; and if E is F, G is H ;
Either A is B or E is F ;
. . Either C is D or G is H.
(4) Complex Destructive.
If A is B, C is D ; and if E is F, G is H ;
Either C is not D or G is not H ;
. . Either A is not B or E is not F.
We have stated the dilemmas in their longest possible
form. Usually there are less than six terms in the
simple, and less than eight in the complex, dilemmas,
as the following examples will show :
( i ) Simple Constructive.
"
"
If she sinks or if she swims there will be an end to
her ;
But she must either sink or swim ;
Therefore there will be an end to her."
If a science furnishes useful facts, or if the study of
it exercises the reasoning powers, it is worthy of
being cultivated ;
But either a science furnishes useful facts, or its study
exercises the reasoning powers ;
Therefore it is worthy of being cultivated."