The Inverse form has been objected to on the ground that the inference All A is B .’.  Some not-A is not B, distributes B (as predicate of a negative proposition), though it was given as undistributed (as predicate of an affirmative proposition).  But Dr. Keynes defends it on the ground that (1) it is obtained by obversions and conversions which are all legitimate and (2) that although All A is B does not distribute B in relation to A, it does distribute B in relation to some not-A (namely, in relation to whatever not-A is not-B).  This is one reason why, in stating the rule in chap. vi.  Sec. 6, I have written:  “an immediate inference ought to contain nothing that is not contained, or formally implied, in the proposition from which it is inferred”; and have maintained that every term formally implies its contradictory within the suppositio.

Sec. 11.  Immediate Inferences from Conditionals are those which consist—­(1) in changing a Disjunctive into a Hypothetical, or a Hypothetical into a Disjunctive, or either into a Categorical; and (2) in the relations of Opposition and the equivalences of Obversion, Conversion, and secondary or compound processes, which we have already examined in respect of Categoricals.  As no new principles are involved, it may suffice to exhibit some of the results.

We have already seen (chap. v.  Sec. 4) how Disjunctives may be read as Hypotheticals and Hypotheticals as Categoricals.  And, as to Opposition, if we recognise four forms of Hypothetical A. I. E. O., these plainly stand to one another in a Square of Opposition, just as Categoricals do.  Thus A. and E. (If A is B, C is D, and If A is B, C is not D) are contraries, but not contradictories; since both may be false (C may sometimes be D, and sometimes not), though they cannot both be true.  And if they are both false, their subalternates are both true, being respectively the contradictories of the universals of opposite quality, namely, I. of E., and O. of A. But in the case of Disjunctives, we cannot set out a satisfactory Square of Opposition; because, as we saw (chap. v.  Sec. 4), the forms required for E. and O. are not true Disjunctives, but Exponibles.

The Obverse, Converse, and Contrapositive, of Hypotheticals (admitting the distinction of quality) may be exhibited thus: 

      DATUM.  OBVERSE.

A. If A is B, C is D If A is B, C is not d I. Sometimes when A is B, C is D Sometimes when A is B, C is not d E. If A is B, C is not D If A is B, C is d O. Sometimes when A is B, C is not D Sometimes when A is B, C is d

    CONVERSE.  CONTRAPOSITIVE.

Sometimes when C is D, A is B If C is d, A is not B
Sometimes when C is D, A is B (none)
If C is D, A is not B Sometimes when C is d, A is B
          (none) Sometimes when C is d, A is B