55. Range of the Rules of the Syllogism. Logic and Truth. -- The rules just given relate only to logical deduction. But logical connection between antecedent and consequent is one thing; the truth of the consequent is another. The necessary connection between the things laid down and the thing which springs from them does not affect the truth or falsity of the premises containing the former.

Two general laws govern the truth and the falsity of conclusions:

(1) If the premises are true, so will be the conclusion: Ex vera non sequitur nisi verum. The conclusion, indeed, confines itself to affirming relations seen in the premises; if they have been recognized in the premises, there can be no error in expressing them in the conclusion.

Corollary: As true premises cannot lead to a false conclusion, we may fairly refute a doctrine or a theory by arguing from the falsity of its consequences. Atheism, for example, is refuted by its consequences.

(2) If the premises are false, or if one of them is false, the conclusion will generally be false; but it may be true. Ex falso sequitur quidlibet.

Examples given by Aristotle: "Every man is a mineral. Every mineral is an animal. Therefore every man is an animal." -- "Every mineral is an animal. No horse is an animal. Therefore no horse is a mineral." -- "Every horse is an animal. No man is an animal. Therefore no man is a horse."

From a false principle one may arrive at an exact result, either because the principle is a mixture of true and false, and it has been used only in so far as it is true; or because the errors proceeding from the principle have ended by compensating one another.

Corollary: Since a false antecedent may have a true consequent, a doctrine or theory cannot be rigorously established by showing that this or that one of its consequences is true. Newton, for example, had deduced from his theory of emissions many consequences in respect to the nature of light which were afterwards verified by experiment; nevertheless, the theory itself was disproved. For an argument drawn from the consequences of a Theory to be conclusive, it must be demonstrable that the theory leads to none but true consequences.