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

152
MEDIATE INFERENCE
The new syllogism formed by the contradictory
of this
conclusion, with the same minor, gives a new conclusion in
Celarent:
No S is P.
j
( All M is S.
No M is P.
This conclusion is the contrary of the original major. One
of them must be false, and it can only be this conclusion.
Therefore its assumed premise is false i.e., the original
conclusion is true.
(//) By the employment of obversion, Baroco and Bocardo
may be reduced directly, (i) Baroco may be reduced to
Ferio by contrapositing the major premise and obverting
the minor. (2) Bocardo may be reduced to Darii by con
trapositing the original major, transposing the premises, and
taking the obverted converse of the new conclusion.
It must be borne in mind that the term Reduction
has no meaning except on the Aristotelian view of the
inferiority of the other figures to the first ; and to
"
re
"
duce a mood must always
" mean reduce it to fig. i."
It is possible to transform some of the imperfect moods
into other imperfect moods ; but this is a mere exer
cise in mechanical manipulation, and should not be
called
"
reduction."
11. When one of the premises of a logical syllog
ism is omitted in the verbal expression of it, we have
what in modern text-books is called an enthymeme
(syllogismus decurtatus). This is the form in which syl
logistic arguments are commonly met with. The miss
ing premise is supplied in thought; hence the enthy
meme has the same characteristics as the completely
expressed syllogism. Most commonly the premise
which is omitted but understood is the major, and
then the enthymene is said to be of the first order ;
sometimes, the minor premise is omitted, when it is of