59. Nature and Rules of the Conditional Syllogism. -- The conditional syllogism is that which has a conditional proposition for its major. E. g.: If the soul is simple, it is imperishable; but the human soul is simple; therefore it is imperishable.

In the major there is only the assertion of a necessary connection between the condition (simplicity of the soul) and the conditioned (incorruptibility).

As soon as this connection is accepted as necessary, the rest reduces to an ordinary reasoning the antecedent of which forms the minor and the consequent conclusion.

The whole interest of the conditional syllogism, then, is in the major, which is equivalent to an absolute affirmative proposition. The proposition, "If the soul is simple, it is imperishable," is equivalent to, "Every simple thing is imperishable." Now a universal affirmative is not convertible (42).

From this observation we deduce the rules of the conditional syllogism:

(1) Affirm the condition, or antecedent, and you must affirm the conditioned proposition, or consequent. E. g.: If you are from Brussels, you are a Belgian. But you are from Brussels. Therefore you are a Belgian.

(2) Deny the conditioned proposition, or consequent, and you must deny the condition, or antecedent. E. g.: If you are from Brussels, you are a Belgian. But you are not a Belgian. Therefore you are not from Brussels.

But the inverse is not true.

Remarks: (1) Nevertheless, the matter of the conditional proposition may possibly be such that the truth of the consequent carries with it the truth of the antecedent. E. g.: If a figure is a circle, it has equal radii.

(2) The conjunction if does not always mean, in the thought of one who uses it, a connection of necessary dependence between the antecedent and the consequent; it frequently indicates only a partial or a contingent connection, and in that case expresses a presumption rather than a rigorous inference. E. g.: If this man were sorely tried by migfortune, he would return to a better state of mind.