Conditional propositions, again, are of two kinds--Hypothetical and Disjunctive. Hypothetical propositions are those that are limited by an explicit conditional sentence, as above, or thus: _If Joe Smith was a prophet, his followers have been unjustly persecuted_. Or in symbols thus: If A is, B is; If A is B, A is C; If A is B, C is D. Disjunctive propositions are those in which the condition under which predication is made is not explicit but only implied under the disguise of an alternative proposition, as _Joe Smith was either a prophet or an impostor_. Here there is no direct predication concerning Joe Smith, but only a predication of one of the alternatives conditionally on the other being denied, as, _If Joe Smith was not a prophet he was an impostor_; or, _If he was not an impostor, he was a prophet_. Symbolically, Disjunctives may be represented thus: A is either B or C, Either A is B or C is D. Formally, every Conditional may be expressed as a Categorical. For our last example shows how a Disjunctive may be reduced to two Hypotheticals (of which one is redundant, being the contrapositive of the other; see chap. vii. § 10). And a Hypothetical is reducible to a Categorical thus: _If the sky is clear, the night is cold_ may be read--_The case of the sky being clear is a case of the night being cold_; and this, though a clumsy plan, is sometimes convenient. It would be better to say _The sky being clear is a sign of the night being cold_, or a condition of it. For, as Mill says, the essence of a Hypothetical is to state that one clause of it (the indicative) may be inferred from the other (the conditional). Similarly, we might write: _Proof of Joe Smith's not being a prophet is a proof of his being an impostor_. This turning of Conditionals into Categoricals is called a Change of Relation; and the process may be reversed: _All the wise are virtuous_ may be written, _If any man is wise he is virtuous_; or, again, _Either a man is not-wise or he is virtuous_. But the categorical form is usually the simplest.