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

2IO CONDITIONAL ARGUMENTS AND
"
fate does not act through doctors," that the calling in of
a doctor is not a link in the "fated" series of events.
In the dilemma with respect to the Alexandrian Library,
Caliph Omar tacitly assumed in the minor premise that the
doctrines of the Koran are not merely sound, but contain
all that is really worth knowing. Or, to put it otherwise, he
ignores the possibility that the books matter on which the Koran does not
may contain useful
touch. Hence the
alternatives given in the minor premise are not exhaustive.
A faulty constructive dilemma may be "rebutted" by a
dilemma which appears equally cogent, and appears to prove
an opposite conclusion. As an example we may take the
Stoic argument with regard to pain :
l
"
If pain is severe, it will be brief; if it lasts long, it will
be slight ;
Pain is either severe or long ;
Therefore it is either brief or slight."
This is faulty, because the alternatives stated in the minor
premise are not exclusive ; pain may be both prolonged and
severe. Accordingly, the argument may be thus rebutted :
"
If pain is brief, it is severe, if it is slight, it is long ;
But pain is either brief or slight ;
Therefore it is either severe or long."
In all such cases the two dilemmas are equally fallacious.
And the is
"rebutting" only apparent, for the two con
clusions are compatible ; they are merely proved by using
the fallacy, so to speak, in two opposite ways.
The usual way of rebutting a complex dilemma will be
seen from the following instances :
If A is B, C is D,and ifE is F, G is H ;
Either A is B or E is F ;
Therefore either C is D or G is H.
Transpose the two consequents in the major premise,
changing each to its negative :
If A is B, G is not H, and if E is F, C is not D ;
Either A is B or E is F ;
Therefore either G is not H or C is not D.
1 Mr Stock quotes the original from Seneca, Epist. xxiv. 14 :
"
Levis est, si ferre possum ; brevis est, si ferre non possum"