Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

Omitting the division of a proposition into true and false—which is not, strictly speaking, a division, since it can belong to the same proposition; indeed, truth and falsity are not formally in the proposition itself insofar as it is enunciative, but insofar as it is judicative—we note that judgment pertains to assent and dissent, while enunciation pertains to the joining of extremes, upon which the judgment of assent falls as upon its matter, as we shall say in question 5, article 1. Omitting this division, then, and treating the proposition only insofar as it is enunciative, all divisions of the proposition are reduced to four principal divisions, as it were to headings.

The first division is into categorical and hypothetical proposition; this is an essential division, as we shall say in the place mentioned, for it concerns the essential parts of which a proposition consists. A categorical proposition has a subject, a verbal copula, and a predicate as its principal parts. For every proposition must consist of a verb, as Aristotle teaches in On Interpretation I, chapter 5¹, together with St. Thomas in the same place, lecture 1² and lecture 8³. The subject is that of which something is said; the predicate is that which is said of something. Thus, in the proposition “Man is white,” “man” is called the subject, “white” the predicate, and “is” the verbal copula. Because this proposition consists of these as its principal parts, it is called categorical, that is, predicative; others call it simple, because it is composed only of a verb and a name, as St. Thomas says in the cited lecture 8⁴, for there is no simpler composition. A hypothetical proposition, which others call composite or a single conjunction, is one that has two categorical propositions as its principal parts, as “If man runs, man moves.” The hypothetical and categorical proposition thus differ in their copulas and in the extremes joined: a hypothetical proposition does not join by a verb, but by the particle “and,” “if,” or the like; nor does it join terms immediately, but propositions. These copulas and parts differ essentially in their mode of joining.

The second division is according to the quantity of the proposition: universal, particular, indefinite, and singular. Just as in natural things the quantity of a thing follows its matter, so in propositions quantity follows the subject, which is as it were the matter with respect to the predicate and copula. The extension or quantity of a proposition is taken according to the plurality and extension of the subjects to which the predicate belongs. Hence this division is accidental. A universal proposition, therefore, is one in which the subject is affected by some universal sign. Universal signs are every, no, any, neither, and the like, which indicate distribution over several; hence such signs are attached only to a common term, as “Every man disputes.”

But note that sometimes the subject of distribution is distinguished in a proposition from the subject of predication or enunciation, as in “Every man’s horse runs,” where running is predicated of the horse as subject, but distribution belongs not to the subject but to man. Thus the subject of a proposition to which a sign of distribution is attached is called the subject of distribution. This distribution and universality is distribution simply when it does not depend on, or is not restricted by, another preceding term, whose resolution must be made before resolving the distributed term. Distribution is qualified, however, when it depends on a prior resolution, as when I say, “A man’s every horse runs.” Although “horse” is affected by a sign of distribution, it is not universal simply, because it is restricted by “of a man.” We cannot resolve—that is, descend under—the term “horse” before descending under the term “man,” as we shall show clearly in book 3, in the treatise on induction⁵. Thus the universality of propositions is simple when, in its distribution and resolution or descent, it is independent of any prior resolution of another term; when it is dependent, its universality is qualified.

A particular proposition is one in which the subject is affected by a particular sign, as “Some man disputes.” Particular signs are some, someone, another, and the like, which make something belong to several, but not distributively. An indefinite proposition is one in which the subject is a common term and is affected by no sign, as “Man disputes.” A singular proposition is one in which the subject is a singular term, or a common term affected by a sign of singularity, as “Peter disputes,” or “This man disputes.” A singular term is one that can be predicated of only one and not of several.

The third division is into affirmative and negative proposition, which St. Thomas, On Interpretation I, lecture 8⁶, calls a division of a genus into species. An affirmative proposition is one in which the predicate is affirmed of the subject, as “Man is white”; a negative proposition is one in which the predicate is denied of the subject. Thus affirmation makes a composition, while negation makes a division.

Because affirmation and negation are considered according to the copula, we must note that the copula is twofold: one is principal, which joins the predicate to the subject; the other is less principal (also called implication), which is part of an extreme. For example, when I say, “Peter, who is learned, is just,” “who is” belongs on the side of the subject and constitutes one extreme, upon which falls the copula that joins the predicate; this latter is principal. The principal copula is either simple or complex: simple, when I posit only one, for example, “Peter is just”; complex, when a double copula is posited, for example, “Peter is or was just.” In complex copulas, if both are negated or both affirmed, it is clear that the whole proposition is affirmative or negative: “Peter neither is nor was white” is simply negative; “Peter is and was white” is simply affirmative. But if one is affirmed and the other negated, as in “Peter is or was not white,” it is formally of mixed quality. It is virtually affirmative if it itself entails an affirmative proposition, and virtually negative if it is entailed by a negative proposition. The reason is that if a proposition entails an affirmative one, the proposition entailed cannot be verified unless the extremes supposit; therefore, the extremes must also supposit in its antecedent, since in a good consequence the antecedent cannot be true and the consequent false. Hence a proposition that entails an affirmative by a good consequence must be virtually affirmative: that is, its verification requires what an affirmative proposition requires, namely, the supposition of the extremes. For example, “Peter is and was not white” is virtually affirmative, because it entails “Peter is white,” which is absolutely affirmative.

On the contrary, if a proposition is entailed by a negative one, it is called virtually negative, although it is mixed in quality, because its verification requires only what a negative proposition requires: namely, that it be verified⁷ without supposition of the extremes. For it is entailed by a negative proposition, which is verified without supposition of the extremes; consequently, the proposition it entails is verified in the same way, since in a good consequence, if the antecedent is true, the consequent cannot be false. Thus, “Peter is or was not white” is entailed by “Peter was not white,” and so the first is virtually negative.⁸

A negative proposition consists of a negated copula; and negation is of a malign nature, destroying whatever it finds after it. Consequently, doubled negation produces affirmation, because the first negation destroys the second. Likewise, since negation has the power to distribute, if it encounters a distributed subject, it removes that subject’s distribution, which dialecticians call “immobilizing.” Thus negation mobilizes—that is, distributes—what has been immobilized and immobilizes what has been mobilized, that is, what is distributed, as when you say, “Not every man disputes”: “not every” is the same as “some,” a particular proposition, as discussed in the chapter on Equipollence.⁹

The fourth division is into the de inesse proposition and the modal proposition. A modal proposition is one in which the verb or copula is qualified by one of four modes: necessarily, contingently, possibly, or impossibly, because these modes affect the verb itself with respect to the rationale and qualification of composing and copulating the proposition. A de inesse proposition, however, joins and composes one extreme with another without such modes, even if it contains other adverbs modifying the verb or predicate. Thus “Peter is white” and “Peter lives justly” are de inesse propositions, whereas “Peter disputes contingently” and “he sees necessarily” are modal propositions. We shall discuss these modes more fully when treating oppositions.¹⁰

All these divisions are made and taken on the side of the copula, except the division into universal and particular, etc., which is taken according to quantity on the side of the subject. For the categorical and hypothetical are distinguished by the copula: the categorical has a verbal copula, the hypothetical a conjunction of propositions. Likewise, the affirmative has an affirmed copula, the negative a negated copula. The modal has a copula qualified by a qualification affecting the composition itself; the de inesse proposition has a simple and absolute copula.