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

90
IMMEDIATE INFERENCE.
"
(3) He jests at scars who never felt a wound."
This is SaP,
"
All who never felt a wound are jesters
at scars."
"
Obverse SeP None ,
wound are other than jesters at scars."
of those who never felt a
Contrapositive, P "
eS, None, other than jesters at
scars, are people who never felt a wound."
EXERCISE VI.
Give, where possible, the contrapositive of each of the
propositions referred to in Ex. III.
12. Inversion is the name given by Mr Keynes to
the process by which from a given proposition we infer
an equivalent one having the same predicate but for
its subject the contradictory of the original subject.
In Conversion we have asked, given a proposition
SP, what information we can derive from it about P ;
in Contraposition we have asked, in the same case,
what information is derivable about not-P ; in Inversion
we now proceed to ask what information is derivable,
from such a proposition, about not-S.
The processes of obversion and conversion are the
only instruments at our command. Starting
with the
given proposition, we apply them alternately till we either
reach the required result (a proposition with not-S in the
subject place), or are brought to a standstill by a proposi
tion which cannot be converted. In doing so, we may
begin either with Obversion or Conversion. It will be
found that an inverse is obtainable only when the original
proposition is universal. From A (All S is P), by apply
ing successively Obversion, Conversion, Obversion, Con
version, Obversion, we obtain O (Some not-S is not P).
From E (No S is P), by applying Conversion, Obver
sion, Conversion, we obtain I (Some not-S is P).
The student should verify these results.