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.

THE REASON FOR DOUBT is taken from what has been said: induction is a true species of consequence, since it is a true species of argumentation, and argumentation and consequence are the same. Therefore it must be a good consequence, for a bad consequence does not have the essence of a consequence. But if it is good, it must be formal, because what is not formal can be countered and is consequently not good. Thus, in the account of consequence, a probable consequence is never given: it is either good or bad, and whatever is good is always good, because it is formal. Therefore induction’s being a consequence is the same as its being a formal consequence.

It is confirmed because there are some inductions of which one cannot doubt that they are formal consequences. Therefore one must not deny absolutely that induction is a formal consequence.

The antecedent is proved: A conjunctive descent from a term supposing distributively, and a disjunctive ascent with respect to a term supposing determinately, are formal consequences which admit no counterexample in any matter. This is evident in the following consequences: “This man is white; therefore some man is white”; “Every man is white, and a man exists; therefore this man and that man and that one are white.” Likewise, when an induction itself enumerates all singulars, or at least some of them followed by the phrase “and so on for each,” it is evident that it is a formal consequence, since it proceeds from the collection of all singulars to the universal, which can never be countered.

Finally, it is confirmed because, as the Philosopher says,¹ “universals, about which demonstration is concerned, cannot be known without induction.” If induction were not a good and formal consequence, then every demonstration and science that depends on it would rest on an uncertain and fallible foundation. Therefore induction must be a formal and certain consequence.

Apart from what we said in the text about this difficulty,² I observe here only that induction does not signify merely the account of consequence on the side of the arrangement and form connecting propositions, which is the prior account in a consequence. It also signifies the account of an argument or proof, insofar as it is a topic of arguing and proving a universal proposition by reducing it to its singulars.

IF INDUCTION IS CONSIDERED AS AN ARGUMENT AND A TOPIC OF PROOF, IT DOES NOT ALWAYS PRODUCE EVIDENCE, BUT SOMETIMES ONLY PROBABILITY. From this side one admits that it is a probable consequence, because it rests on the experience of the senses, from which the intellect receives knowledge of universals. Experience, however, is not always infallible, nor can it always survey the whole collection of singulars; consequently it cannot always ground an infallible proof. Some have been mistaken on this point, thinking that the formality of induction requires all singulars to be enumerated in the antecedent, or, if they are not all enumerated, the phrase “and so on for each” to be added. When that phrase is added, they think, induction becomes an effective argument and a formal consequence, since it proceeds from the whole collection of singulars to the universal, which is a passage from an equivalent to an equivalent.

But this does not make induction, precisely as induction, a formal consequence; it adds another topic of argument, namely, from an equivalent to an equivalent, which is always an effective proof. Induction itself, by its own nature and proper force, does not require this. For induction serves to derive knowledge of a universal thing from the experience of the senses itself. If it were necessary to enumerate all singulars contained under the universal, induction would never occur, or only very rarely. Who could experience all singulars? But if, although not all have been experienced, the phrase “and so on for each” is posited for the remaining unexperienced singulars, induction remains nonevident and uncertain with respect to them, since it is not established that the remaining cases are so. Thus the argument is only probable: from the cases experienced (though not all, but many), it infers the universal.

I say the same about certain species of induction in which there is an effective proof and a formal consequence. This is not strictly by the force of induction, but through another added topic of argument. For instance, when from a singular one infers not a universal but a determinate particular, as “Peter runs; therefore some man runs,” the consequence holds not by the force of induction, since only one singular is enumerated, but from a non-broad term to a broad one affirmatively, without distribution of the broad term. Likewise, when from a universally distributed proposition we descend conjunctively to each singular, as “Every man is white; therefore this one is white and that one, and so on,” it holds from a broad term to a non-broad one, with affirmative distribution of the broad term. The same holds from a particular to singulars disjunctively: it follows from an equivalent to an equivalent, or from some similar topic of argument.

Therefore, although induction joined to these or other similar topics of argument is an effective proof and consequence, pure and mere induction does not require this; it can be found when singulars are enumerated sufficiently. I say “sufficiently” to infer a universal probably, if not all singulars are enumerated, or evidently, if both forms belong to induction. Indeed, the former occurs more often, because hardly ever, or never, are all singulars enumerated, and yet induction to a universal simply is given. Indeed, if they are enumerated not only sufficiently but totally, this is not pure induction but a passage from an equivalent to an equivalent, just as when they are enumerated sufficiently not to infer a universally distributed proposition but only a particular one, as we said above. This concerns induction insofar as it is an account of an argument and a topic of proof.

BUT IF THE ARRANGEMENT AND FORM OF DEDUCING ONE THING FROM ANOTHER IS CONSIDERED, INDUCTION (if taken precisely, without another topic of argument added) DOES NOT SIGNIFY THE PERFECT ARRANGEMENT AND FORM OF A CONSEQUENCE, AS A SYLLOGISM DOES. In a syllogism the arrangement and form itself is grounded in the perfect connection of the terms with one third term as a middle; hence the intellect is compelled to acknowledge the connection of those same terms with one another. Induction, by contrast, does not use the connection of the extremes with one third term as its reason and inferential form. Rather, from the singulars it experiences, as though from the subjective parts of a universal whole, it infers the universal proposition itself, as we said. The connection of the experienced singulars with their universal therefore grounds a consequence that is not formal without qualification, as in a syllogism, but formal inductively. For every consequence is a kind of inference that proves and makes truth evident; and all our truth and knowledge have two processes: first, in their introduction, as they arise from and depend on the senses; second, in their proof from propositions already conceived universally. Consequently, the inference of truth, according to the formal account of consequence and inference, must have two modes of connection and consequence: in inducing or introducing us to knowledge of universals from the singulars themselves, and in proving or reasoning from propositions already made universal to other things. Induction has the arrangement of a consequence only in the first way. Although it can therefore fail and be defective absolutely, it has whatever is required for a formal consequence in the inductive sense, though not for an unqualified and evident proof.

THE REASONS FOR DOUBT STATED AT THE BEGINNING ARE ANSWERED:³ To the first⁴ we reply that induction, according to its precise account as induction, is a true species of consequence, but not as perfect as a syllogism, nor ordered to proving or convincing the intellect. Rather, it is ordered to introducing us to universals through the comparison and enumeration of singulars. In this kind of inducing, it has the formal account of consequence—not as a proof from universals, but as induction from singulars. Its goodness therefore does not consist in fully convincing, but in sufficiently introducing universals from the singulars experienced.

To the first confirmation we reply that those consequences of induction hold not by the precise force of induction, but because they are either reduced to the form of a syllogism or have another topic of argument joined to them, one that has an effective and infallible connection, as we said.

To the second confirmation we reply that all our speculation depends on induction, just as it depends on sense and experience. If the universal propositions of a science are not so abstract and common that their truth can be made evident from any individual, but depend on the enumeration and experience of several cases, as in the natural sciences, they are not as certain as the other, more abstract and common sciences, such as metaphysics and mathematics, whose principles have their full certainty even in one individual—for example, “Everything either is or is not.”

In this question DIFFERENT OPINIONS contend, for the most part, from nearly the same motive.

Because a syllogism proceeds by reasoning, in which the conclusion is inferred and made evident from the connection of the premises, some think that not only the inferring premises but also the inferred conclusion belong to the very essence of a syllogism. For reasoning does not stop at the premises but at the conclusion; and as long as the conclusion is not inferred, the reasoning remains suspended and incomplete. The conclusion, therefore, belongs to the account of a complete and perfect syllogism.

Others, on the contrary, infer from the fact that the conclusion is inferred and made evident through reasoning that it does not belong to the essence of the syllogism but is its effect. For a syllogism is formally a way of knowing and an argument that makes something unknown evident. Its entire account is therefore preserved in its being that which makes evident, not in what is made evident; but the conclusion is what is made evident, not what makes evident.

Finally, others think that a syllogism consists formally only in the very movement or inference, not in the premises or the conclusion, although it includes them as it were materially and obliquely.

The truer view, however, seems to be that the syllogism, in its essential concept, means a discourse composed of antecedent and consequent and the very inference or consequence.

Accordingly, it has both an inferential force, which is in the premises, and the inferred thing in the consequent, and the inference itself, which, taken passively, is in the consequent that is inferred, but actively in the premises that infer. Thus it is like an organic instrument consisting of a moving part and a moved part, as in living things one part moves another. For it is clear that the premises themselves are the motive force and reason for knowing the conclusion. Therefore the premises are necessarily and essentially required for the account of a syllogism, which is the instrument by which this cognition of the conclusion is achieved. Similarly, the conclusion itself is the object known; for the syllogism aims at knowing the conclusion through inference. Cognition does not regard its object obliquely and materially, but most formally. Hence a syllogism cannot consist in the movement or inference alone, insofar as inference is taken precisely and passively as that which follows from something else; for in this sense it is found only in the consequent that is inferred. When in some syllogism we admit the premises but deny the consequence, we do not deny the whole syllogism, but only its inference and the passive deduction of what follows. This is a sign that “syllogism” does not stand for inference taken passively, but for the composite of that which infers and that which is inferred, in which the full and adequate inference or consequence is found, taken both actively and passively. For although motion is passive only in what is moved, as action it proceeds from the agent and regards it, and thus regards agent and patient fully and adequately. The example nevertheless fails in this respect: a syllogism is not the motion itself, but a logical instrument by which the intellect is moved from one thing to cognition of another. Hence it must include a moving part, which is the premises, and a moved part, which is the inferred object or conclusion.

We therefore accept the reasoning of the first opinion, which includes the conclusion without excluding the premises. To the second we reply that the conclusion is an effect of the syllogism, not indeed of the whole syllogism but of one part of it. Just as in living things the moved part is an effect of the living thing insofar as it is moved by reason of the moving part, yet adequately and completely includes the whole consisting of moving and moved parts, so the syllogism in its essence adequately and completely includes the illuminating and the illuminated, the thing that makes evident and the thing made evident, as its parts. Thus, although it belongs to the essence of consequence and argumentation to make something unknown evident, the unknown thing itself, which is the conclusion, is essentially included as what is inferred and made evident, and as the object of the thing that makes evident.

Some think that no syllogism needs to be reduced to another, more perfect syllogism; instead, all are regulated just as immediately by the principle: “Whatever things are identical to one third are identical to one another.” Thus, they can be shown immediately by this principle, and not by reduction to another syllogism, because just as in the first four modes of the first figure the extremes are identified with one third, so too in the other syllogisms of the second and third figures, as is clear from any syllogism made in those figures. Therefore, by such a principle one can immediately convince anyone who denies the inference of such syllogisms, and reduction to the first syllogisms of the first figure is not necessary.

Moreover, the Philosopher expressly teaches that all imperfect syllogisms can be reduced to universal syllogisms of the first figure, as is clear in 1 Prior., chapter 7.¹ St. Thomas teaches the same in opusculum 48, On the Syllogism, chapters 6, 7,² and 8.³ And the reason is that although the whole force of syllogism consists in the principle that whatever things are identified with one third are identified with one another, nevertheless, for this identification with one third to be clear, that third must be distributed. For if the middle is held particularly in both premises, nothing follows from pure particulars. If, then, the middle must be identified with the extremes according to distribution, by which it contains and unites the extremes themselves within it, this identification of the middle must be regulated by the principles “Dici de omni” and “Dici de nullo.”

This does not occur with equal evidence in all syllogisms, because it is not equally immediate and self-evident in all that some extreme is contained under the distributed middle itself, as is clear in the first four modes of the first figure. In these, the middle is subject in the major premise and predicate in the minor; consequently, since it is posited universally in the major on the side of the subject, it is then predicated of something in the minor. Hence, precisely by this fact, that of which it is predicated is shown to be contained under the middle itself. This is not made equally clear in the second and third figures, as is evident if we form a syllogism in Barbara: “Every animal is a substance; every man is an animal; therefore every man is a substance.” There the middle term “animal,” in which man and substance are identified, is posited universally on the side of the subject in the major premise. Then, in the minor, since animal is predicated of man, it is clear by this very fact that man is contained under animal, and consequently that substance, which was predicated of animal, will also be predicated by the rule “Dici de omni” of man, who is contained under animal.

This, however, is not made self-evident in the second and third figures. Therefore, for it to be clear that the extremes are thus identified with one third in such a way that “Dici de omni” or “Dici de nullo” is preserved in it, the syllogism must be reduced to the mode of the first figure, and not merely proved immediately by the principle “Whatever things are identical to one third, etc.,” excluding the principles “Dici de omni” and “Dici de nullo.”

As to whether the fourth figure exists, some dispute at greater length. For this difficulty, however, what we taught in the Summulae, book 3, chapter 5, is sufficient. We do not deny this fourth figure; rather, we say that it is reduced to the first and therefore does not constitute a wholly distinct figure, but is contained under the first.