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

2O4
CONDITIONAL ARGUMENTS AND
"
disjunctive proposition,
are at bottom the same.
is P or Q is "
R,
S is either P or O," and "either S
5. The disjunctive syllogism has a disjunctive
major premise and a categorical
The major is,
minor and conclusion.
"
S is either P or and there are four
Q,"
"
"
"
"
possible minors, S is P or S is Q (both A pro
positions), or "S is not P" or "S is not Q" (both E
propositions).
Before we can settle the question, Which of these
lead to valid conclusions ? we must be clear as to
another point. When we say
"
S is either P or do
Q,"
we mean that it cannot be both that the alternatives
are mutually exclusive ? To answer this it is necessary
to distinguish between what we often do mean in
ordinary thinking, speaking, and writing, and what we
ought to mean according to the requirements of Logic.
As a matter of fact, frequently we do mean the alter
natives to be exclusive, but not always. Take the
instances :
following
boat or play cricket
"
All the men in this college either
"
;
" A
good book is valued either
for the usefulness of its contents or the excellence of its
"
style ;
is
"
Either the witness is perjured, or the prisoner
guilty." In all these propositions, the meaning is
merely that if one alternative does not hold, then the
other does hold. In such cases we do not want to deny
that both the alternatives may be true. But for logical
purposes there is no doubt that the alternatives ought
to be mutually exclusive ; this is necessary if such state
ments are to have any scientific value.
We cannot make an exclusive disjunction about any
thing unless we have a considerable amount of know
ledge about it. Even to say such a thing as this,
"You must either pay a fine or go to prison," implies
knowledge of the legal bearings of the circumstances as