Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

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.”