Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

In regulating the goodness of any consequence, there is one most universal principle from which the others are derived and to which they are reduced, namely: “In a good consequence, it cannot be that the antecedent is true and the consequent false; rather, if the antecedent is true, so is the consequent.” This principle is immediately reduced to the highest of all principles: “Everything either is or is not,” or “It is impossible for the same thing both to be and not to be at the same time.” For if the antecedent is true, then things are already as it signifies. But if the consequent is false, it draws the antecedent after it by reason of the connection that the truth of the consequent has with the truth of the antecedent. Therefore, to posit a true antecedent and a false consequent is the same as positing a true antecedent and something false on its part, because the consequent is as it were a part of, and something connected with, the antecedent, and the consequence itself is a kind of connection. But what is false in part is not true absolutely. Therefore, if a true antecedent and a false consequent are given, a true antecedent and a non-true one are given, and these are contradictories.

The goodness of consequence is therefore grounded in these principles. Hence the whole effort in assigning defects of consequence consists in producing a true antecedent and a false consequent. Thus, whatever more readily tends to falsify the consequent than the antecedent contributes to a bad consequence; whatever more readily contributes to the truth of the consequent than of the antecedent builds a good consequence. The reason is that the antecedent must contain in itself the truth of the consequent, since the latter is inferred from it. Hence Aristotle said in Posterior Analytics I,¹ “the premises must be more true than the conclusion,” that is, more certain. More, then, must be required for the truth of the antecedent than for the truth of the consequent, since the antecedent is truer than the consequent. Therefore, the antecedent must always be harder to make true than the consequent; for that is harder to obtain which requires more. Since a consequence is nothing other than an inferential connection from one thing to another, and the truth of an antecedent is not well connected with the falsity of what is inferred, the connection itself, or consequence, becomes bad whenever the antecedent is true and the consequent false.

From this principle several rules that dialecticians give concerning the goodness of consequence are made clear. They are usually six, which we reduce to three.

First: If the antecedent is true, so is the consequent; and conversely, if the consequent is false, so is the antecedent. This is the very principle we have stated.

Second: If the antecedent is possible, so is the consequent; and conversely, if the consequent is impossible, so is the antecedent. This follows from the first rule: if the antecedent is possible, then it can be true, and therefore its consequent can also be true. For if it were impossible for the consequent to be true, it could not be true in any case. But since the antecedent is possible, it can be true in some case; then, in some case, the antecedent would be true and the consequent false.

Third: If the antecedent is necessary, so is the consequent; and conversely, if the consequent is contingent, so is the antecedent. This too follows from the same principle: if the antecedent is necessary, it is always true, and therefore the consequent must always be true as well; otherwise there could be a case in which the antecedent is true and the consequent false. Hence, if the consequent is contingent and can be false, the antecedent cannot be necessary, since what is necessary is always true.

Understand, however, that a necessary consequent always follows from a necessary antecedent, but it is not required that the consequent be necessary in every respect. It suffices that it be necessary under the respect and account in which the consequent is contained in the antecedent, and insofar as it is inferred from the antecedent, though not under some other account. For example, in the consequence “God knows that Peter will sin; therefore he will sin,” the consequent is contingent in itself and in its relation to the proximate cause, but it is infallible as something known by God, and consequently as inferred from the antecedent. This is because God knows not only that Peter will sin, but that he will sin freely and contingently. Thus, from that antecedent it is inferred both that he will sin contingently and that it is infallible that he will sin contingently.

Finally, two other rules follow from that principle, and these too serve the goodness of consequence.

First: Whatever follows from the consequent of a good consequence follows from its antecedent. In other words, as is commonly said: “The consequence holds from the first to the last.” This is self-evident.

Second: Whatever is incompatible with the consequent in a good consequence is also incompatible with the antecedent. In other words, if the consequent follows from the antecedent, the opposite of the consequent follows from the opposite of the antecedent. The reason is that if the opposite of the consequent does not entail the opposite of the antecedent, then the opposite of the consequent could stand together with this antecedent, since it does not entail the opposite of the antecedent. But the consequent posited in the consequence is false, given that it was true—that is, inferred from a true antecedent. Therefore, the falsity of the consequent could stand together with the antecedent, and thus a true antecedent and a false consequent would be given. We very often use this rule to establish the goodness of a consequence by proceeding from the contradictory of the consequent to the contradictory of the antecedent. We also use it in reducing syllogisms by impossibility; and counterexamples that serve to show the defect of a consequence also serve in the case where we proceed from the opposite to the opposite.