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