The conditional is one of the most common types of logical and mathematical propositions. The generic conditional takes the form: "If p is true, then q is true, too." The first part of the conditional (the "if-clause") is known as the antecedent, the second part as the consequent. The term conditional is used because the antecedent describes a condition for the consequent. Under the condition that p is the case, q is the case, also.

We can distinguish between two types of conditions: necessary and sufficient. The idea is fairly simple: A necessary condition is a condition without which the consequent cannot possibly be true. A sufficient condition guarantees by itself, without the support of any other conditions, that the consequent is true.

The principle can be illustrated with easy examples. Suppose we know an animal, Suzie, and we want to figure out if Suzie is...