lty,
If the prisoner is guilty, the witness is not perjured--

do not necessarily hold. If, then, we would guard against fallacy, we
must always make sure before assenting to a disjunctive proposition
that there is really a complete disjunction or mutual incompatibility
between the alternatives.

III.--THE DILEMMA.

A Dilemma is a combination of Hypothetical and Disjunctive
propositions.

The word has passed into common speech, and its ordinary use is a clue
to the logical structure. We are said to be in a dilemma when we
have only two courses open to us and both of them are attended by
unpleasant consequences. In argument we are in this position when we
are shut into a choice between two admissions, and either admission
leads to a conclusion which we do not like. The statement of the
alternatives as the consequences hypothetically of certain conditions
is the major premiss of the dilemma: once we admit that the relations
of Antecedent and Consequent are as stated, we are in a trap, if trap
it is: we are on the horns of the dilemma, ready to be tossed from one
to the other.

For example:--

If A is B, A is C, and if A is not B, A is D. But A either is
or is not B. Therefore, A either is C or is D.

If A acted of his own motive, he is a knave; if A did not act
of his own motive, he is a catspaw. But A either acted of his
own motive or he did not. Thereupon A is either a knave or a
catspaw.

This is an example of the _Constructive_ Dilemma, the form of it
corresponding to the common use of the word as a choice between
equally unpleasant alternatives. The standard example is the dilemma
in which the custodians of the Alexandrian Library are said to have
been put by the Caliph Omar in 640 A.D.

If your books are in conformity with the Koran, they are
superfluous; if they are at variance with it, they are
pernicious. But they must either be in conformity with the
Koran or at variance with it. Therefore they are either
superfluous or pernicious.

Where caution has to be exercised is in accepting the clauses of the
Major. We must make sure that the asserted relations of Reason and
Consequent really hold. It is there that fallacy is apt to creep in
and hide its head. The Alexandrian Librarians were rash in accepting
the first clause of the conqueror's Major: it does not follow that the
books are superfluous unless the doctrines of the Koran are not merely
sound but