We have already seen (chap. v. § 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. § 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_ As to Disjunctives, the attempt to put them through these different forms immediately destroys their disjunctive character. Still, given any proposition in the form _A is either B or C_, we can state the propositions that give the sense of obversion, conversion, etc., thus: DATUM.--_A is either B or C;_ OBVERSE.--_A is not both b and c;_ CONVERSE.--_Something, either B or C, is A;_ CONTRAPOSITIVE.--_Nothing that is both b and c is A_. For a Disjunctive in I., of course, there is no Contrapositive. Given a Disjunctive in the form _Either A is B or C is D_, we may write for its Obverse--_In no case is A b, and C at the same time d_. But no Converse or Contrapositive of such a Disjunctive can be obtained, except by first casting it into the hypothetical or categorical form. The reader who wishes to pursue this subject further, will find it elaborately treated in Dr. Keynes' _Formal Logic_, Part II.; to which work the above chapter is indebted. CHAPTER VIII ORDER OF TERMS, EULER'S DIAGRAMS, LOGICAL EQUATIONS, EXISTENTIAL IMPORT OF PROPOSITIONS