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

a whole ;
THE VALIDITY OF THE SYLLOGISM. 2O$
" A
line must be either straight or curved,"
implies geometrical knowledge of the meaning of straight
and curved, and the relation between the two concepts ;
"
This tree is either an oak or an ash," implies some
knowledge of both these varieties, and a comparison of
that knowledge with the given instance. It is a funda
mental error to suppose that the disjunctive judgment
expresses mere ignorance as to which of two predicates
belongs to a given object. We shall have to return to
this extremely important point.
Let us suppose, however, that the disjunction is not
exclusive, and proceed to ascertain which of the four
possible minor premises give valid conclusions.
(1) S is either P or Q ;
S is P.
No conclusion, because S may be also Q.
(2) S is either P or Q ;
S is Q.
No conclusion, because S may be also P.
(3) S is either P or Q ;
S is not P ;
.-.Sis Q.
(4) S is either P or Q ;
S is not Q ;
.-.Sis P.
Thus when the alternatives are not exclusive, we may
resolve the disjunctive proposition into a pair of hypo-
theticals :
(a) If S is not P it is Q ;
(b) If S is not Q it is P.
This agrees with what we found to be the ordinary
meaning of such judgments.
If the alternatives are mutually exclusive, as for
logical and scientific purposes they ought to be, we