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

AND THE ARISTOTELIAN SYLLOGISM. !$!
Examples : (a) Reduce Baroco per impossibile :
All P is M.
Some S is not M.
Some S is not P.
If this conclusion is false, its contradictory must be true ;
that is :
All S is P.
Make this the minor of a new syllogism with the original
major :
( All P is M,
\ All S is P,
from which the conclusion in Barbara is,
All S is M,
which contradicts the original minor. Therefore All S is M
is false, and therefore since the process, being Barbara, is
valid, one of its premises must be false. This can only be
the assumed premise All S is P ; and if this is false, Some S
is not P, the original conclusion, is true.
(b) Reduce Bocardo per impossibile :
Some M is not P.
All M is S.
Some S is not P.
Take the contradictory of this conclusion with the original
minor and draw a conclusion from them in Barbara :
All S is P.
j
\ All M is S.
All M is P.
This new conclusion must be false, for it contradicts the
original major; hence its assumed premise All S is P is
false immt the original conclusion Some S is not P is true.
(c) The process of indirect reduction may be applied to
any of the imperfect moods. Aristotle when mentioning
the it process applies to Darapti :
f All M is P.
IA11 M is S.
Some S is P.