Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

A good consequence is one in which the consequent is inferred from the antecedent. A bad one is one in which the consequent is not inferred from the antecedent, although it is represented as being inferred. The consequent is not inferred from an antecedent when a true antecedent and a false consequent can be given. Whenever, however, the consequent follows by a true and proper inference, whether it is true from a false or a true antecedent, the consequence is good.

Two matters therefore come very briefly under discussion here. First: Is this difference between a good and a bad consequence essential or accidental? Second: How is it true that the true follows from the false, when the false never follows from the true?

To the first, the answer is affirmative: this division is essential, and therefore analogical, speaking of formal consequence simply, which is what we are treating here.

THE REASON IS that the essential and intrinsic form of consequence is the inferential connection of antecedent with consequent. But a bad consequence lacks this inferential force; therefore, it lacks the essential form of consequence. A good and a bad consequence thus differ as a living human being and one lacking life, which agree analogically in the account of “human being.” Nor can one grant that a formal consequence has some connection and yet can sometimes fail, and so be called bad. A form that is once liable to fail and can at least sometimes admit a counterexample is formally not good for that very reason; it entirely lacks a formal connection, that is, the arrangement required for inference. Thus the consequent can sometimes follow from the antecedent only accidentally, never by the force of the form, but by reason of the matter.

YOU WILL OBJECT, FIRST: A connection in reality between antecedent and consequent is not required for the account of consequence. Therefore, consequence does not lack its essential account because no connection is present, provided that a connection is represented as present. The antecedent is proved: A probable consequence is a true consequence, for it is a true topical syllogism; nevertheless, in reality it may lack connection, because many false things are more probable than true ones. Therefore, an actual connection is not required for the essential account of consequence; apparent connection and signification suffice.

SECOND OBJECTION: To be true or false is an accidental division; therefore to be a good or bad consequence is also accidental. For good and bad in consequence are related as true and false in a proposition, since a good consequence is one in which one thing truly follows from another, while a bad one is one in which it does not truly follow.

TO THE FIRST OBJECTION, the answer is that, speaking of formal consequence, that is, one which infers by the force of its form and arrangement, there is no probable or topical consequence: it is either good or bad.¹ A consequence that is once good on the side of form cannot fail; consequently, on the side of form it cannot be topical. For if it can fail, it can admit a counterexample and be vitiated; consequently, a true antecedent and false consequent can be given. A form of consequence that can admit a counterexample is therefore for that very reason bad on the side of form; if it is sometimes good, it is good only materially and by reason of the matter, not the form. In this respect, however, we are mistaken and equivocate if we think consequence and argument are the same, though they differ greatly: argument pertains to proof, but consequence to the very inference and form of following one thing from another. Proof can be evident or probable. Hence a syllogism, considered on the side of matter and in the manner of posterior analytics, that is, on the side of proof, is divided into demonstrative and topical; but it is not so divided prioristically, on the side of form. Here, however, we speak only of consequence on the side of form and prioristically.

TO THE SECOND OBJECTION, the answer is that truth or falsity does not change the enunciative signification that constitutes a proposition; rather, with its signification unchanged, its truth can change depending on whether the thing exists or not. But the goodness or badness of a consequence changes the very form of its connection and inference and, consequently, the essential account of consequence itself, which does not consist in signifying truths but in connecting them in a suitable way for inference.

Concerning the second difficulty, the question is how only the true can follow from the true, whereas the true can follow from the false. For it is not apparent how the true can be contained in the false so as to be inferred from it, while the false cannot be contained in the true, since true and false are equally opposed to one another.

The answer, omitting the solution of some who say that every falsehood contains something true, by reason of which it can infer the true, while the true must contain nothing false and therefore cannot infer the false—omitting this solution, I say, because sometimes both premises can be false and yet infer a true consequent, as when you say: “Every stone is living, and every human being is a stone; therefore every human being is living.” Here nothing is inferred by virtue of anything true on the part of the premises.

I ANSWER, THEREFORE, SECONDLY, that the true is said to follow from the false, not because it can be caused or made evident by the false, but because assent to a true conclusion can well stand together with false premises.

Hence it is one thing for the true to follow from the false, another for the true to be proved by the false. The latter can never hold, as St. Thomas very well observes in Metaphysics I, lecture 2.² Consequently, the true cannot be made evident by the false or caused by it, since if it were caused by it, it would be proved through it. The true is therefore said to follow from the false only insofar as, even when a false premise is admitted, the connection with a true conclusion can still stand, because the falsity of the premises does not always destroy every consequent truth; nor does evil destroy every good. But if true premises are granted, then by this very fact the false consequent cannot be granted but must be denied. Once the consequent is denied, the antecedent with which it is connected must also be denied, since to deny that consequent is the same as admitting its opposite. The opposite of the consequent, however, entails the opposite of the antecedent; therefore the opposite of the antecedent must be admitted and the antecedent itself denied. Thus, from first to last: if the false followed from the granting of the true, the same antecedent would be both granted and denied.

An argument could also be made here about a contingent consequent following from necessary propositions, as in “God knows that Peter will sin; therefore Peter will sin.” The antecedent is necessarily true, while the consequent is contingent and consequently can be false; thus a true antecedent and false consequent would be given. See the solution above in Summulae, book 3, chapter 11, and among the theologians in 1. p. q. 14. art. 13.