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

150
MEDIATE INFERENCE
The first s in thej name indicates that the original minor
premise is to be converted simply ; the m indicates that the
original premises are to be transposed. The C indicates
that from the new pair of premises, thus obtained, we are
and the second
to draw the conclusion in i.
Celarent, fig. ;
s indicates that if we convert this conclusion in Celarent
simply, we shall get our original conclusion.
Convert the original minor, and transpose :
No M is S,
All P is M,
from which in Celarent the conclusion is,
No P is S,
from which again by simple conversion,
No S is P,
which is the original conclusion.
The process of Reduction in the case of the fourth figure
has already been illustrated ( 9).
This operation, of direct application of Immediate
Inference and transposition, is called direct reduction.
By this means we are also said to reduce ostensively
(SetKTt/oo?).
Aristotle did not admit any Immediate
Inference except conversion; and under this limitation
we cannot reduce Baroco and Bocardo directly. Ac
cordingly they are reduced by a distinct process known
as reduction per impossibile (Sia rot) aSvvdrov)
or in
direct reduction : assume the falsity of the conclusion
(i.e., the truth of its contradictory) ; take this contra
dictory with one of the original premises, as the two
premises of a new syllogism in Barbara, the con
clusion of which will be incompatible with the other
premise of the original syllogism. Hence either the
original conclusion is true or one of the original
premises false ; and, since in Deductive Logic the
premises are always assumed to be true, we can only
accept the former alternative.