Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

In the preceding book, chapter 5, on argumentation, we said that all the species of argumentation could be reduced to two: induction and syllogism. For an enthymeme is a truncated syllogism, and an example is an imperfect induction, as St. Thomas says at the end of 1 Poster., lect. 1.¹ Hence, finally, in lecture 30 of the same book,² St. Thomas lists only two ways of acquiring knowledge: demonstration and induction. Demonstration is a syllogism that proceeds from universals, while induction proceeds from singulars, since all our cognition originates from singulars, which are perceived through the senses.

Induction is therefore defined as “a progression from singulars sufficiently enumerated to the universal”; for example, if you say, “This fire heats, and that one, and that one, etc.; therefore every fire heats.” And since opposites have the same account, under this definition of induction by ascent is understood its opposite, descent, that is, a progression from the universal to singulars. Induction, insofar as it proceeds by ascent, is ordered to discovering and proving universal truths as universal—that is, insofar as they consist of the singulars contained under them. For something cannot be proved to be such universally except because its singulars are such. Descent, however, is ordered chiefly to showing the falsity of a universal as universal: the falsity of a universal is best shown by descending under it and showing that some singular is not such. Still, once the truth of the universal has been established and discovered through ascent, descent also serves to show the universal’s correspondence to the singulars contained under it. The principal function of induction, however, is to bring proof of a universal to the senses by ascending from singulars.

It is therefore clear that Aristotle rightly set out the difference between syllogism and induction in the second book of the Prior Analytics, chapter 23.³ A syllogism uses a middle term to show that the extremes are united with one another; induction, by contrast, proves the extreme of the middle by means of a third. That is to say, a syllogism uses premises in which the middle is assumed to be united with the extremes, so that through it the union of the extremes with one another may be proved. Induction, however, does not assume a middle uniting the extremes in order to prove that the extremes are united with one another. Rather, it proves that an extreme, or some predicate, belongs to a common subject because it belongs to the singulars, or that it belongs to the singulars because it belongs to the common subject.

You may ask how many kinds of ascent and descent there are and what they are. I answer that there are four: conjunctive, disjunctive, compounded, and disjoined. Conjunctive ascent and descent occurs when singulars are enumerated through conjunctive propositions, as in “Every man is an animal; therefore this man is an animal, and that man is an animal,” etc. Disjunctive occurs when they are enumerated through disjunctive propositions, as in “Some man is white; therefore either this man is white, or that man is white,” etc. Compounded ascent and descent occurs when a term is resolved by singulars enumerated together in a complex proposition. For example, “All the apostles of God are twelve” is resolved as “This one and that one, etc., are twelve,” enumerating them all in one proposition. Disjoined occurs when a term is resolved through its singulars, enumerated separately in a single proposition. Thus, if you say, “Every man is an animal,” the predicate “animal” is resolved disjointly as “Every man is this animal or that animal or that other animal,” so that the whole disjunction is the predicate. Whether induction, by its formal account and its own proper force, is a formal consequence, we shall say below in question 8, article 2.