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

IMMEDIATE INFERENCE. 85
by substituting P for P and changing
or
"
"
is to
"
is
not,"
"
"
is not to
"
is," as the case may be. Thus :
A, All S is P, becomes E, No S is P/
E, No S is P, u A,
All S is P.
I, Some S is P, O, Some S is not P.
O, Some S is not P, ,,
I, Some S is P/
In obversion it is desirable, to secure neatness in the
logical form, to substitute a single
term for the contra
dictory P/ if such a term exists. It will, of course, be
one of the negative terms of ordinary language. In the
four examples given above, we may substitute
fallible," "imperfect," "unlearned," "untrustworthy,"
each of which is general enough in meaning to stand
as the pure contradictory of the corresponding positive
term. But the error of using a contrary instead of a
contradictory must be guarded against e.g., if the pre
dicate P were "happy," then "unhappy" would not
be a true contradictory but a contrary, signifying a
definite real quality, which is the opposite of "happy."
"
"
That obversion
produces a really equivalent pro
position is evident from the diagrams, if we remember
that affirmation corresponds to inclusion, and negation
to exclusion. 1
Thus,
if all the circle S is in the circle
P, obviously none of S can be outside P i.e., SaP is
equivalent to StP ;
if no S is in P, all S must be
outside P i.e., SeP and SaP are equivalent ; if some
S is in P, then that part of S is not outside P i.e.,
SiP and SoP are equivalent ;
"
in
if some S is not in
P, that part of S is outside P i.e., SoP is equivalent
to SiP .
1 The logical contradictory of a term P is represented by the
indefinite region outside the circle which stands for P.