A compound statement of the form if p then q , also written p implies q , is called a

conditional or an implication, p is called the antecedent or hypothesis and q is called the

consequent or the conclusion.

A conditional is regarded as false only when the antecedent is true and consequent is

false. In all other cases it is considered to be true. Its truth table is, therefore, of the adjoining

form.

Entries in the irst two rows are quite in consonance with

common sense but the entries of the last two rows seem to be

against common sense. According to the third row the conditional

If p then q

is true when p is false and q is true and the compound proposition

is true (according to the fourth row of the table) even when both its

components are false. We attempt to clear the position with the help Table (4)

of an example. Consider the conditional

If a person A lives at Lahore, then he lives in Pakistan.

If the antecedent is false i.e., A does not live in Lahore, all the same he may be living in

Pakistan. We have no reason to say that he does not live in Pakistan.

We cannot, therefore, say that the conditional is false. So we must regard it as true. It must be

remembered that we are discussing a problem of Aristotlian logic in which every proposition

must be either true or false and there is no third possibility. In the case under discussion there

being no reason to regard the proposition as false, it has to be regarded as true. Similarly,

when both the antecedent and consequent of the conditional under consideration are false,

there is no justiication for quarrelling with the proposition. Consider another example.