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

86 IMMEDIATE INFERENCE.
In obverting propositions, we must try to make the logical
forms as neat or at least as little removed from the com
mon usages of speech as possible; and to avoid using
terms of the form "not-P" when there is a more familiar
expression with the same meaning. Frequently the phrase
"
"
other than P may be used with advantage. Obversion
may produce exceedingly cumbrous and uncouth forms, but
with a little care this result may be avoided.
(1) "Some of our muscles are without volition."
(a) our muscles ;
(b) things which act without volition ;
(c) affirmed of part of the subject.
"
Hence SiP, Some of our muscles are things which act
without volition." To obvert we substitute "are not" for
"
are," and take the contradictory of the predicate. For
mally, this "
contradictory is, not things which act without
volition"; and this is exactly equivalent to "things which
act with volition." Hence the neatest form of the obverse
is,
" Some of our muscles are not things which act with
volition."
(2) "Every mistake is not a proof of ignorance."
(a) mistakes ;
(b) a proof of ignorance ;
(c) denied of some of the subject.
"
Hence SoP, Some mistakes are not proofs of ignorance.
Obvert by substituting
"
"
are for
"
"
are not and taking the
contradictory of the predicate, which is
"
other than proofs
" some mistakes are other than proofs of
of ignorance,"
ignorance."
The original proposition has a secondary implication,
"some mistakes are proofs of ignorance," with obverse,
"
some mistakes are not other than proofs of ignorance."
(3)
" No one is free who cannot command himself."
(a) those who cannot command themselves ;
(b} free;
(c) denied of the whole of the subject.
"None of those who cannot command them
Hence SeP,
selves are free." Here the most convenient contradictory
of "free" is the negative term "unfree"; and the obverse
is "all who cannot command themselves are unfree," SaP .