We may, then, state the following rule for the conversion of propositions in which the whole relation explicitly stated is taken as the copula:  Transpose the terms, and for the given relation substitute its reciprocal.  Thus—­

    A is the 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 sense of affirmatives.