cause of B .'. B is the effect of A._

The rule assumes that the reciprocal of a given relation is definitely
known; and so far as this is true it may be extended to more concrete
relations--

_A is a genus of B .'. B is a species of A
A is the father of B .'. B is a child of A._

But not every relational expression has only one definite reciprocal. If
we are told that _A is the brother of B_, we can only infer that _B is
either the brother or the sister of A_. A list of all reciprocal
relations is a desideratum of Logic.

Sec. 5. Obversion (otherwise called Permutation or AEquipollence) is
Immediate Inference by changing the quality of the given proposition and
substituting for its predicate the contradictory term. The given
proposition is called the 'obvertend,' and the inference from it the
'obverse.' Thus the obvertend being--_Some philosophers are consistent
reasoners_, the obverse will be--_Some philosophers are not inconsistent
reasoners_.

The legitimacy of this mode of reasoning follows, in the case of
affirmative propositions, from the principle of Contradiction, that if
any term be affirmed of a subject, the contradictory term may be denied
(chap. vi. Sec. 3). To obvert affirmative propositions, then, the rule
is--Insert the negative sign, and for the predicate substitute its
contradictory term.

A. _All S is P .'. No S is not-P
All men are fallible .'. No men are infallible._

I. _Some S is P .'. some S is not-P
Some philosophers are consistent .'. Some philosophers are not
inconsistent._

In agreement with this mode of inference, we have the rule of modern
English grammar, that 'two negatives make an affirmative.'

Again, by the principle of Excluded Middle, if any term be denied of a
subject, its contradictory may be affirmed: to obvert negative
propositions, then, the rule is--Remove the negative sign, and for the
predicate substitute its contradictory term.

E. _No S is P .'. All S is not-P
No matter is destructible .'. All matter is indestructible._

O. _Some S is not P .'. Some S is not-P
Some ideals are not attainable .'. Some ideals are unattainable._

Thus, by obversion, each of the four propositions retains its quantity
but changes its quality: A. to E., I. to O., E. to A., O. to I. And all
the obverses are infinite propositions, the affirmative infinites having
the sense of negatives, and the negative infinites having the