A second case in which the hypothetical is a specially appropriate form of statement occurs where a proposition relates to a particular matter and to future time, as If there be a storm to-morrow, we shall miss our picnic. Such cases are of very slight logical interest. It is as exercises in formal thinking that hypotheticals are of most value; inasmuch as many people find them more difficult than categoricals to manipulate.
In discussing Conditional Propositions, the conditional sentence of a Hypothetical, or the first alternative of a Disjunctive, is called the Antecedent; the indicative sentence of a Hypothetical, or the second alternative of a Disjunctive, is called the Consequent.
Hypotheticals, like Categoricals, have been classed according to Quantity and Quality. Premising that the quantity of a Hypothetical depends on the quantity of its Antecedent (which determines its limitation), whilst its quality depends on the quality of its consequent (which makes the predication), we may exhibit four forms:
A. If A is B, C is D;
I. Sometimes when A is B, C is D;
E. If A is B, C is not D;
O. Sometimes when A is B, C is not D.
But I. and O. are rarely used.
As for Disjunctives, it is easy to distinguish the two quantities thus:
A. Either A is B, or C is D;
I. Sometimes either A is B or C is D.
But I. is rarely used. The distinction of quality, however, cannot be made: there are no true negative forms; for if we write—
Neither is A B, nor C D,