Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

Aristotle defines an expression as follows: “An expression is a vocal sound significant by convention, whose parts, when separated, signify something as a word, not as affirmation or negation.” So Aristotle in On Interpretation I¹ and St. Thomas in the same place, lecture 6².

Here expression is defined in general, with respect both to perfect and imperfect expression, whether simple or hypothetical. The first three clauses have been explained in the definition of the term. The clause “whose parts signify when separated” can be explained no better than by saying that an expression is subordinated to a composite concept, as is drawn from St. Thomas, On Interpretation I, lecture 6³, so that within the expression itself there are parts that compose it and correspond to distinct, separate concepts as components of one whole. In virtue of the first point, expressions of a compound figure, such as respublica, signifer, and so on, are not expressions, because they do not correspond to a double concept but to one, even though the vocal sounds separated from the expression signify different things. In virtue of the second point, an expression is distinguished from a complex term, because a complex term also has significant parts and several concepts, but in the manner of a part that further composes, not in the manner of a composite whole.

Aristotle and St. Thomas include the final clause to indicate that the parts of an expression must at least be significant “as a word,” that is, as a term; they need not be affirmation and negation. For even if an expression is hypothetical and has parts consisting of affirmation and negation, nevertheless simple affirmation and negation themselves are also expressions and must be resolved into significant parts, which signify only as a simple term and not as affirmation. Therefore, in defining expression in general, what is common to every expression is included: namely, that it has parts that are simple terms or expressions.

Expression is first divided into perfect and imperfect. According to the Divine Thomas, On Interpretation I, lecture 7⁴, a perfect expression is one “that produces a perfect sense in the mind of the hearer”; an imperfect expression is one “that produces an imperfect sense.”

A sense is called perfect or imperfect not because one involves assent and the other does not, or one involves truth or falsity and the other does not, but precisely because the perfect expression does not leave the intellect suspended, as though awaiting the whole sense of the expression; rather, it completes and expresses the entire thought perfectly, as when I say, “God is the highest good.” An imperfect expression, by contrast, does not explain the entire sense, but seems to suspend the intellect, as when I say “Peter disputing,” “if you should sleep,” “when he was passing by,” and the like. Such expressions are very close to complex terms and differ only in their mode of composing and joining terms: in an expression, they are joined in the manner of a whole, though an imperfect one that leaves the intellect suspended; in a complex term, they are joined in the manner of a composed part.

Before treating the principal perfect expression, which is the proposition, we must treat the method of knowing. For although many things pertaining to the method of knowing are found in the third operation of the intellect, namely argumentation, other such things are found in the second operation, and some pertain even to imperfect expression. Therefore the method of knowing in general is not restricted to perfect or imperfect expression; accordingly, before treating perfect expression specifically, it is fitting to treat the method of knowing in general, which can be found in both perfect and imperfect expression.

Therefore the method of knowing in general is defined as “an expression that makes something unknown manifest.” Note that making manifest is one thing and signifying another. For although a sign seems to make the thing signified manifest to a power, the making manifest of which we now speak is different from signifying absolutely. “Manifest” is taken in two ways: first, as opposed to obscure; second, as opposed to unknown and not presented to a cognitive power. In the first sense, manifestation occurs through something better known and clearer, by which that obscurity is removed. Thus, to make something unknown manifest in our intellect pertains to the method of knowing, provided that this is done by means of an expression. For manifestation by a formal rationale that makes something manifest in a simple way—for example, the authority of a speaker making credible things manifest—is not a method of knowing, because it is not an expression or complex explanation, that is, one ordered to knowledge and having an inferential mode. In the second sense, manifestation occurs through some means or instrument that presents to us an object that was not presented; in this way, making manifest pertains to a sign or representation, speaking generally.

When, then, something unknown or obscure needs to be explained by an expression that explains it and removes that obscurity, such an expression is called a method of knowing, because every manifestation is called knowledge or is ordered to knowledge. Two things can be made manifest to the intellect by an expression: something incomplex or some complex truth. An incomplex thing, such as man, heaven, or earth, is explained by definition with respect to the obscurity of its quiddity, or by division with respect to the confusion of the parts or of the multitude contained in some thing. A complex truth, if obscure or doubtful, is made manifest by proof. Proof is made by reasoning and consequence, and thus is argumentation.

Hence the method of knowing is adequately divided, on the part of the things that can be made manifest, into definition, division, and argumentation. For this reason, definition and division are sometimes said to pertain to the first operation, or simple apprehension, by reason of their object, which they make manifest: something incomplex.

A definition is “a discourse explaining the nature of a thing or the signification of a term.” For example, when I say, “A human being is a rational animal,” I explain the nature of a human being, which was not explained by that term, “human being.” And when I say, “A white thing is something that has whiteness,” I explain not the nature of a white thing, but the signification of the name, since it is the same as if I said, “A white thing is a word signifying that which has whiteness.” The thing defined corresponds to the definition as its object, and is convertible with it.

Hence three things must be explained: First, which conditions are required for a definition to be good; second, which conditions are required for something to be defined; third, how many kinds of definition there are and in how many ways it is made.

Concerning the first, three conditions are required for a good definition:

The FIRST is that a definition must be given through genus and specific difference. Since this condition includes not only an essential definition, in which genus and specific difference are properly found, but also an accidental and descriptive definition, in which genus and specific difference are not properly present but something standing in their place is, by “genus” we understand something common, and by “specific difference” some particular distinguishing feature. Thus the meaning is that every good definition, in order to explain some nature, ought to explain it through what it has in common with others and through what is proper to it and distinguishes it from the rest; for in this way it encompasses the whole nature of the thing.

The SECOND condition is that a definition must signify more clearly than what is defined, since it makes that evident. From this it follows that what is defined should not enter into the definition, for then it is not rendered clearer but more confused, as in the definition of a human being as a rational animal: it would not be right to add “a rational animal, which is a human being.”

The THIRD condition is that a definition be neither redundant nor incomplete. For if it contains something more or less than what is defined, it does not thereby explain its nature: it either attributes to it something it does not have, or takes away from it something it does have. Thus a definition cannot apply to anything other than what is defined; accordingly, this is the best locus for arguing from the definition to what is defined, and conversely.

Concerning the second, three conditions are likewise required for something to be defined, or to be definable:

The FIRST is that it be one per se, that is, one essence. For if a definition explains several essences, it is not one thing defined but several. Therefore, before something is defined, equivocation and the confusion arising from multiplicity must be removed; then each thing is to be defined individually. But if several things are related as one and concur to constitute a single essence, or if one is related as a thing and the other as its mode, there is no obstacle to their being comprehended in a single definition.

The SECOND condition is that what is defined be universal. For since only quiddity and nature are defined, singular things, which add individual conditions over and above the nature, cannot be defined, just as they cannot fall under a science. Singularity in common can, however, be defined, because it is then taken as a certain quiddity and nature.

The THIRD condition is that everything defined, if it is defined by a rigorous and proper definition, be some species contained under a genus, since every proper definition consists of genus and specific difference. Thus it must be given of something contained under a genus, unless perhaps it is defined through extrinsic causes or relations, which do not convey so rigorous a definition.

There are two kinds of what is defined, namely, remote and proximate. Different authors explain this in different ways, according to how they understand the notion of what is proximate and what is remote. Some say that the proximate thing defined is the very name or term signifying the thing defined, while the remote thing is the thing signified itself. For example, if the definition is that a human being is a rational animal, the term “human being” is the proximate thing defined, whereas the thing signified is remote, since things come near to us by means of terms. Hence in a definition of the meaning of a name there is only one thing defined. Others say that the proximate thing defined is the nature and quiddity itself, which falls immediately under the definition, while the remote things are those in which such a nature is found, namely, individuals. For when I define a human being, human nature is defined immediately, while Peter and its other individuals are defined remotely. Either account may be given.

Concerning the third, definition is of several kinds.

FIRST, it is divided into a definition of the meaning of a name and a definition of the thing. A definition of the meaning of a name explains the signification of the name, and thus comes closest to an etymological account; a definition of the thing explains the nature of the thing signified. For example, if I define “white” as the same as “having whiteness,” that is a definition of the meaning of the name. But if I say that it is “that which scatters vision,” that is a definition of the thing, for it explains what the thing itself is, whereas the former explains what the name signifies. In this distinction between a definition of the meaning of a name and a definition of the thing, we always proceed in the formal and per se sense. For we do not deny that through a definition of the thing we also arrive at knowledge of the proper signification, and that often the signification of a name cannot be explained without declaring the thing itself. Rather, each definition must be judged to be a definition of a name or of a thing according to what it directly and per se explains.

SECOND, a definition of the thing is divided into essential, descriptive, and causal definitions. An essential, or quidditative, definition is a discourse explaining a thing through its own parts or essential predicates, as in “A human being is a rational animal.” Since in each thing we consider physical parts, such as matter and form, and metaphysical parts, such as genus and specific difference, the quidditative definition is likewise twofold: physical, which is given through matter and form, and metaphysical, which is given through genus and specific difference. Yet in a physical definition matter is also posited in place of genus, and form in place of specific difference, so that it is true that every definition consists of genus and specific difference, or something standing in place of genus and specific difference. A descriptive definition is given through a thing’s accidents, whether proper or common, as when you say, “A human being is an animal capable of laughter,” or “a two-footed animal.” A causal definition is given through extrinsic causes. These extrinsic causes are two: the efficient and the final, as will be said in Book II of the Physics¹, because they do not constitute the nature but are outside it (for matter and form are intrinsic causes). Thus, if you define the human soul as “a form created by God for beatitude,” “by God” is the efficient cause, while “for beatitude” is the end.

Division is “an expression distributing some thing by its members, or a term by its various significations,” as when I say: “Of animal, one is rational and another irrational”; “canis signifies a constellation and signifies an animal.”

Because division is ordered to making manifest, by distribution, the confusion of what is divided, just as definition is ordered to making manifest its quiddity, three conditions are required for a good division. First, each member must be inferior, that is, smaller than what is divided, for every whole is greater than its part. Second, all the dividing members together must exhaust or equal the whole divided, because in a whole there is nothing other than all its parts together. Third, the dividing members must have some opposition between them, at least formal opposition, because if they had no opposition, they would have no distinction but rather identity, and thus would not be different members. All these conditions can be seen in this division: Of animals, one is rational and another irrational; and in this one: Of goods, one is honorable, another useful, another pleasant.

Some add a fourth condition: that division be made into only two dividing members, or at least as few as possible. But although it is true that every division can be reduced to two members if it is stated by contradictories, as in “Of goods, one is honorable and another is not honorable,” this is not always necessary for a good division. Rather, when some genus is distributed into species immediately subordinate to it on an equal footing, it may be divided into those species. But if it is not divided into several species immediately and equally subordinate to it, division should be made into two members, or as few as possible, and then distributed into other subordinate members. Thus substance would not be well divided into man, plant, and angel, but in a certain order into corporeal and spiritual; corporeal into living and nonliving, and so on.

There are many species or modes of division. For just as a whole, which division distributes, is said in many ways, so too is division. There is an essential whole, an integral whole, a universal whole, and a potential whole, and thus the species of division can be multiplied.

To enable you to grasp them all briefly, make two lines or orders. One line consists of divisions per se, the other of divisions per accidens, or accidental divisions. In the division per se, include five species, which are gathered in this way. Whatever is divided is either a vocal sound signifying with respect to its significations, or the thing signified. If the former, it is a division of the name; if the latter, a division of the thing. A thing that is a whole can be compared either with the parts by which it is integrated, the parts by which it is essentially constituted, or the parts subordinated to it. If division is made in the first way, it is partition, by which something is divided into its integral parts, as when you say: “The human body is divided into head, chest, and feet”; “The universe is divided into angels, corruptible bodies, and incorruptible bodies.” If in the second way, it is an essential division into its constituents, as when you say: “Of man, one part is soul, another body”; or, “Of man, one extreme is animal, the other rational.” If in the third way, division is either into parts subordinated to the whole according to predication or according to power. If according to predication, it is division of a genus into species, because the genus is predicated of the species as of its inferiors. Division of a genus by differences also belongs here; indeed, it seems to be the same division, because the genus is not divided into differences, but by differences into species. It is explained better when made by differences, as in: “Of animals, one is rational, another irrational.” This is the most proper and quidditative division, since it concerns those things into which and by which a genus is essentially contracted, and in which the divided item is predicated of the dividing members. If division is made into parts subordinated to the whole that are related as powers, it is division of a potential whole, as when you say: “Of soul, one power is intellective, another appetitive”; “Of prudence, one power is judicative, another deliberative, another imperative.” This division is according to the different functions or powers of a thing.

In the line of divisions per accidens, although divisions can be multiplied infinitely, because no certain rule is given for things that are accidental, nevertheless three are more frequent. First is division of a subject into accidents, as: “Of animals, one is white, another black.” Second, conversely, division of an accident into subjects, as: “Of white things, one is snow, another milk.” Third, division of an accident into accidents, as: “Of white things, one is sweet, another bitter,” and so on.

There are three rules of division, or topics for arguing, which are derived from the conditions of a good division. First: From the divided whole to its division, and conversely, the consequence holds affirmatively or negatively. This is clear because they are mutually convertible. Second: From the divided whole together with the negation of one member, if the division has two members, or of several members, if it is multiple, to the positing of the remaining member, the consequence is good; for example: “A horse is an animal and is not rational; therefore it is irrational.” Third: When the members are really opposed, the consequence from positing one member to denying the other holds good. This is clear because opposites cannot exist together, at least naturally and in themselves.

We must treat this third species of the method of knowing in the third book, to which it directly pertains, since it belongs to the third operation of the intellect. For the present, having distinguished the species of the method of knowing, it is enough to note three things:

FIRST is the definition of argumentation, which is “an expression in which, when one thing is given, another follows,” as when I say: “Peter is an animal; therefore, he is a body.” Hence argumentation must be composed of and consist in three things: the antecedent, as the inferring premise; the consequent, as what is inferred; and the sign of inference, which is the conjunction of antecedent and consequent that indicates inference or following.

SECOND, the species of argumentation are four: syllogism, enthymeme, induction, and example. They can be reduced to two, namely syllogism and induction, for an enthymeme is a kind of imperfect or truncated syllogism, and an example is a kind of part of induction. Argumentation is divided into these species insofar as it makes truth manifest, in which its quiddity consists. There are only two ways of making truth manifest: either by reasoning from principles known by the intellect, or by leading down to sensible things or singulars, since there is the origin of all our cognition. If it proceeds in the first way, it does so by syllogism, which consists of three propositions—the major, the minor, and the consequent—or of two, if it is an enthymeme, namely the antecedent and the consequent. Thus an enthymeme is an imperfect syllogism, because it sets down one proposition as antecedent, whereas a syllogism sets down two; the whole force of inference in a syllogism consists in the union of some things in a third, from which it infers their union with one another. If it proceeds in the second way, it is induction, which infers that something holds universally of all cases, not from connection with a third, but from a sufficient enumeration of several singulars. Example is reduced to this: from one singular it infers not something universal, but another similar thing.

THIRD, there are other divisions of argumentation besides these species. According to the sign of inference, one argumentation is inferential, namely, that made by the particle “therefore,” as: “Man is an animal; therefore, he is living.” Another is conditional, made by the particle “if,” as: “If the sun shines, it is day.” Another is causal, made by the particle “because,” as: “Because man is rational, he is capable of laughter.” These three differ in this: for the truth of a conditional, it is enough that the consequence be good, even if its extremes are false. For example, this conditional is true: “If man flies, he has wings,” although its extremes are false. For the truth of an inferential argument, the antecedent and consequent must be true. I say, for its truth; for as regards the goodness of the consequence, a truth can also follow from a falsehood, as we shall say in book 3¹. For the truth of a causal argument, the extremes must be true and the antecedent must be the cause of the consequent. For it is true that man is an animal and is capable of laughter, but false that he is capable of laughter because he is an animal.

According to quality, consequence is divided into good and bad. A good consequence is one in which the antecedent infers the consequent in such a way that the antecedent cannot be true while the consequent is false. A bad consequence is one in which the antecedent does not infer the consequent, although it seems or is represented as inferring it; because of that signification it is called a consequence, but a bad one, since it does not infer, and the antecedent is true while the consequent is false.

We shall speak of the rules of consequences for distinguishing good ones from bad ones in book 3, where the defects of consequence are to be treated expressly².

The principal species of perfect expression is enunciation or proposition, and it is treated extensively in Logic because it serves above all for the syllogism and reasoning. We take proposition and enunciation to be the same, since this usage has prevailed even among the learned, as is clear in ordinary disputations, in which we use the name proposition more often than enunciation. St. Thomas likewise uses the name proposition for enunciation in Summa Theologiae I, question 13, article 12. Elsewhere, however, with Aristotle, he distinguished the function of a proposition from the simple function of an enunciation, in Posterior Analytics I, lecture 5¹ and Opusculum 48, treatise On the Syllogism Simply, chapter 1²: namely, a proposition adds to an enunciation that it be put forward in order to infer something in argumentation.

An enunciation, then, is defined as “an expression signifying the true or the false by asserting,” as when I say, “Man is an animal.” So Aristotle, On Interpretation I³, and St. Thomas, lecture 7⁴. “Expression” is put in place of the genus; “signifying the true or the false” in place of the difference, by which enunciation is distinguished from other expressions, whether imperfect or perfect but not expressing truth. The clause “by asserting” is included not because it is formally found in every proposition, but to indicate how the verb in a simple proposition serves to signify the true or the false, namely, by way of assertion. This is commonly done by a verb in the indicative mood, or must be reduced to it. In a simple enunciation, truth is signified assertively, whether by affirming or denying. In hypothetical propositions, although one does not always proceed assertively, as in conditionals in a non-indicative mood—for example, “If you were to strike Peter, he would kill you”—nevertheless, through some understood sense, the truth of the propositions can be reduced to assertion in the same way that it can be reduced to categorical propositions.

To make clear what signifying the true is, note from St. Thomas, On Interpretation I, lecture 7⁵, that truth is in an enunciation as in a sign of an intellect’s apprehending the true or the false; but the true or the false is in the mind (that is, in the mind’s judgment) as in a subject, as is said in Metaphysics VI⁶; in the object, however, it is as in a cause, because, as is said in the book of the Categories, “from the fact that a thing is or is not, an expression is true or false.”⁷ Here St. Thomas is speaking of a vocal or non-judicative enunciation when he says that truth is in an enunciation as in a sign of an intellect’s apprehending the true or the false; for when speaking of a mental, judicative enunciation, truth is in it as in a subject.

Nevertheless, since a mental, judicative enunciation is also significant and representative of objective truth, we further say that signifying the true or the false in a mental proposition is nothing other than signifying in the manner of composing or dividing, so that something is signified as judgeable. When a predicate is joined to or separated from a subject, the result is that it conforms to and is adequate to the thing itself, or fails to conform to it—not only by conformity or nonconformity of likeness, but by attribution and conjunction of the predicate with the subject. For likeness to an external thing is also found in simple apprehension. Thus St. Thomas teaches in Summa Theologiae I, question 16, article 2, that simple apprehension or sense is true but does not know the true, because it does not know the conformity of truth: it does not apply something to something else or remove it from it. Therefore, to signify the application of one thing to another—or rather, to signify a thing by applying one thing to another in the manner of what is judgeable—is to signify the true or the false. The truth of a proposition itself is not the very signification of the true or the false, but the conformity or adequation to the thing signified that results from such signification. Those who said in a single phrase that to signify the true is to signify that a thing is as it is, and to signify the false is to signify it otherwise than it is, intended to express all of this. But this is not merely signifying in some manner, as a syncategorematic term does, nor merely signifying something simple, as a categorematic term does; it is signifying something composite, or an application of one thing to another, which is an enunciative expression. We shall say below, question 5, how truth or falsity itself is not the essence of a proposition but rather its signification, from which truth or falsity results; and how one truth is formally neither greater nor less than another.

But note that some propositions falsify or destroy their own truth, just as others destroy their own possibility or necessity. This occurs when the very verification of the proposition entails that it is false—that is, from its being as it is signified by that proposition. For example, if I say “Every proposition is false,” or “This proposition is false,” while pointing to that very proposition: from its being as it signifies, it follows that it is false. Such propositions are simply false, because although they have verification, that verification is not simply truth, since falsity follows from it. For evil arises from any defect, and that from which falsity follows is simply not true.

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.

In a proposition, the subject has the character of matter, as it were partial matter, with respect to the predicate, because the predicate is said of the subject and is, as it were, received in it. Again, the subject and predicate are said to be, as it were, the matter of the copula, because according to the relation and agreement of the predicate with the subject, the union itself between predicate and subject is made or not made in the proper way. This relation of the terms, from which the proposition is, as it were, composed as from matter, is called the matter of propositions absolutely.

It is threefold: natural, contingent, and remote. Natural matter is that in which one term belongs to the essence of the other; thus it either grounds an essential relation, as when you say “Man is an animal,” or a necessary relation of a proper attribute, as “Man is capable of laughter.” Contingent matter is that in which the predicate belongs accidentally to the subject and can be present or absent without corruption of the subject, as “Peter is just.” Remote matter is that in which the predicate is incompatible with the subject, as “Man is a stone.” Natural incompatibility is enough: for supernaturally, what was in remote matter—namely, God and man—came to be in natural matter after the Word became man.

Predication is either identical or formal, and likewise either direct or indirect. Identical predication is that in which the same is predicated of itself, or a synonym of a synonym, as “Man is man.” Formal predication is that in which a form, or something like a form, is predicated of something, as “Man is just,” “Man is an animal.” Direct predication is that in which what has the character of form is predicated of what has the character of subject, whether the form is essential—as a definition or part of a definition predicated of the thing defined, or a superior predicated of an inferior—or an accidental form predicated of a subject. Hence direct predication is either essential or accidental. Indirect predication is that in which, conversely, the subject is said of the form, or the thing defined of the definition, as “The colored thing is a man,” “Rational animal is a man.” Properly speaking, this is neither essential nor accidental predication. We shall treat these matters more fully in Logic, question 5, article 2.

Having explained the nature of propositions, their division, and the diversity of their matter, the order of teaching next requires us to treat the properties of the proposition. Some properties follow the extremes or parts of the proposition themselves; others follow the proposition as a whole. There are five properties of the parts of a proposition that belong to them only insofar as they are within the proposition: supposition, amplification, restriction, alienation, and appellation. The properties that follow the proposition as a whole are three: opposition, conversion, and equipollence.

These properties can be found both in propositions de inesse and in modal propositions. Therefore, we shall treat first the properties of the extremes of a proposition, then the properties of the proposition as a whole; and first in propositions de inesse, then in modal propositions.

Supposition is defined as “the taking of a term for something of which it is verified.” Many modern authors reject this definition, supposing that supposition is only the taking of a name for the thing it signifies; they do not distinguish supposition from signification, or from the exercise of signification by which a word is substituted for a thing in signifying. Hence they reject the old and accepted principle that some propositions have a subject that does not supposit and are therefore false if affirmative, since every name, whether inside or outside a proposition, supposits simply by being substituted for something before the intellect. For Aristotle too said in On Sophistical Refutations I¹ that, because we cannot carry things with us, we use names in place of things.

Moreover, St. Thomas clearly distinguishes the signification of a name from supposition in De Potentia q. 9, a. 4, body and reply to objection 6²; the same is gathered from Summa theologiae I, q. 39, a. 5, reply to objection 5, where he admits the sophists’ rule that “substantive names supposit, while adjectives do not supposit but copulate.” Therefore, for St. Thomas, signification and supposition are not the same.

Finally, St. Thomas gave the reason for this in Sentences III, d. 6, q. 1, a. 3³, where he says: “In every name two things are to be considered: that from which the name is imposed, which is called the quality of the name, and that upon which it is imposed, which is called the substance of the name. Properly speaking, a name is said to signify the form or quality, but to supposit for that upon which it is imposed.” From this he infers in the reply to objection 1 “that a difference of supposition does not produce equivocation, but a difference of signification.” St. Thomas, then, manifestly distinguishes supposition from signification. And from his words we say that, since the signification of a name is a kind of substitution for the thing signified, substitution can be understood in two ways. In one way it is representative substitution, by which words themselves present the things signified to us; this is not supposition but signification. In another way it is applicative substitution: after the intellect has received the representation and signification of a word, it applies the name in different ways in propositions, so that the name stands for that to which it wishes to apply something. For example, when I say, “Man is white,” “man” not only represents human nature to me, but I also substitute it for that to which whiteness is to be applied through the copula “is.” The intellect therefore considers whether, with respect to such a copula, there truly and properly is a subject that is a man; if there is, it truly substitutes that subject in the proposition. If no such subject is found, the substitution is null. Thus, if I were to say, “Antichrist was good” or “Adam is white,” I do not substitute those subjects, and they do not supposit, because with respect to the copula “was,” Antichrist is not given or applied, and with respect to the copula “is,” Adam is not given. Thus these are called propositions with a subject that does not supposit.

The definition is therefore explained as follows: Supposition is “the taking of a term,” that is, a substitutive taking made by the intellect with reference to some copula in a proposition. It is understood as passive taking on the part of the term taken, not active taking on the part of the intellect that takes it. The definition adds “for something of which it is verified.” Understand this to mean: that taking of the term, or substitution, is verified for something, not that the proposition is verified of it. For the truth or verification of the proposition is not required for supposition, since supposition is found even in a false proposition. For example, when I say, “Man is a stone,” “man” supposits because something is truly found to which being a man belongs, in accordance with the demand of the copula “is.” What is required for supposition, however, is verification of the term’s taking and substitution: that what the name belongs to, and for which I substitute it with reference to the proposition’s copula, truly be found and exist in accordance with that copula’s demand.

Therefore, to confirm and show a term’s supposition, we use a proposition that demonstrates it with reference to the copula. Thus, if I say, “Man is white,” I show that “man” supposits because, with a man demonstrated in relation to the copula “is,” it is true to say, “This is a man.” In the proposition “Adam was,” “Adam” supposits because this individual, demonstrated as Adam, was at some time. And if I say, “Man is a name,” the subject’s supposition is verified by saying, “Man”—with the spoken word demonstrated—is the word “man,” or “is the word ‘man’”; and so with the rest. This demonstration, when I say “This is,” etc., need not be made to the senses; it suffices to demonstrate it to the intellect, because past and future things are not demonstrated to the senses, and the same is true of hidden things. For example, if I say, “Gold is not demonstrated,” meaning gold that is in the earth, “gold” supposits because it is verified by saying, “This (with the gold demonstrated by the intellect) is gold,” though not when demonstrated by the senses. For then the proposition would be false, as it would also be false if “not demonstrated” were not demonstrated even to the intellect. Therefore, the proposition that demonstrates supposition does not give it verification, but designates and shows it. Thus, when supposition is said to be the taking of a term for something of which it is verified, this means that it is verified of that thing in the proposition where the term is used, not in the proposition where it is demonstrated in a signified act, as one that manifests or proves supposition.

From what has been said, it follows that a term does not supposit outside a proposition. For although a term and any significant word outside a proposition signify as a term, I do not apply and substitute it for something, verifying it according to the demand of a copula, except in a proposition, where alone a copula is found and one thing is applied to another as predicate and subject. Thus applicative substitution for something, verified according to the demand of a copula—which is supposition—does not occur outside a proposition. Significative substitution, however, ordered to composing a proposition, does occur there.

It follows secondly that supposition, as explained in the definition, is defined so generally that it can also apply to adjectives when they are used adjectivally. For example, if I say, “Peter is white,” “white” is also taken for something of which it is verified and to which the notion of white belongs according to the demand of the copula. If, however, supposition is taken more narrowly to mean not only being taken for something but also supplying a subject to a verb—which is supposing in the stricter sense—then adjectives do not supposit, but copulate their formal signification to another supposit, as the ancients said.

Since supposition is the taking of a term for that of which it is verified, it involves a relation and order to three things, and its divisions are taken accordingly: it relates to what is signified, for which it supposits; to the verb, with respect to which it supposits; and to a modifying sign, by which it is modified in order to supposit.

FIRST, then, on the side of what is signified, supposition is divided into proper and improper. Proper supposition is taking a term for what it properly signifies or represents. For example, when I say “The lion roars,” “lion” is taken for the animal it properly signifies. Improper supposition is taking it for what it signifies improperly and, as it were, metaphorically. Thus, when I say, “The lion of the tribe of Judah conquered,” “lion” is taken for Christ, whom it does not properly signify. So in “Christ conquered” and “The lion of the tribe of Judah conquered,” the subject is taken for the same thing, namely Christ, but with a different concept and representation. In the first, Christ is represented absolutely and simply, because properly; in the second, Christ is represented with a connotation of the real lion. Thus the name “lion” improperly represents and supposits for Christ by reason of its connotation, not by representing him through its simple and direct signification. These metaphorical modes of speech are therefore elegant and pleasing, since they signify things not simply, but as it were by a circuit and connotation.

Proper supposition is divided into three species: material, simple, and personal.

Material supposition is taking a term for itself, that is, for the word itself. That is why in defining proper supposition we said it is taking a term for what it properly signifies or represents. For when it supposits materially, it represents itself, not signifies, as when I say, “Man is a noun,” or “blitiri is a vocal sound,” unless perhaps “the word man” or “the word blitiri” is understood. Material supposition is recognized in three ways. First, when a non-signifying term is used, such as blitiri or scindapsus, since these can supposit only for themselves. Second, when signs of mention are used, such as “this word,” “this term,” and so forth; these make the thing they indicate stand materially. Third, when the predicate signifies not the thing but the term, as in “Man is a vocal sound” or “man is a noun.”

Simple supposition is taking a term for what it signifies first and immediately, not mediately. Thus, if I say “Man is a species,” “man” supposits simply. Note that names signify two things: first, what is primary and formal, and second, that in which this primary item is found. The latter is as it were the name’s secondary signification, since what the name signifies is found in it as in a subject and material recipient. For example, “man” signifies human nature primarily and immediately, and mediately everything in which that nature is found, that is, all human individuals. Simple supposition, then, is taking a term for its primary and immediate signification so precisely that it does not pass to the secondary signification and the things in which the primary is found, but stands precisely for the primary signification. It is therefore simple and precise supposition: it stands for the immediate and primary signification, not as a double supposition that passes to the secondary and mediate signification. When I say “Man is a species,” “man” is not taken for individuals, but for man as such, abstracting from individuals. Hence it does not follow: Man is a species; therefore Peter is a species. Appellation is therefore always involved in simple supposition, because the predicate belongs to the subject under some precision and formality by which it does not descend to individuals.

Personal supposition is taking a term for individuals, or for the things signified materially and mediately. It is called personal because it belongs, as it were, to the persons or supposits of a thing. For example, when we say “Every man is an animal,” this also belongs to individuals, and descent is valid: therefore this man is an animal, and so forth. Hence personal supposition permits ascent and descent, unlike simple supposition.

SECOND, personal supposition is divided according to its order to the verb or copula into essential or natural supposition and accidental supposition. Natural supposition is taking a term for all the things for which it is naturally apt to be taken; in other words, taking it for that to which the predicate belongs intrinsically and essentially, as in “Man is an animal,” where the verb “is” abstracts from time in its verification. Accidental supposition is taking a term only for those of which it is verified according to the demand of the verb; in other words, taking it for that to which the predicate belongs not intrinsically but accidentally, as in “Man is just” and “man disputes.”

THIRD, supposition is divided on the side of signification into common and singular. Common supposition is taking a common term for its inferiors, as in “Man disputes.” Singular or discrete supposition is taking a singular term for a singular thing, as in “Peter disputes” or “this man disputes.”

FOURTH, common supposition is divided on the side of signs into determinate and confused. Determinate supposition is taking a common term that is indefinite or affected by a particular sign, as in “Man disputes” or “a certain man disputes.” Confused supposition is taking a common term with a universal sign or a special sign of confusion, as in “Every man disputes” or “Only man disputes.” Confused supposition is twofold: distributed and confused only. Distributed supposition is taking a common term immediately affected by a sign of distribution, as in “Every man disputes”; “man” stands distributively. Confused-only supposition is taking a term mediately affected by an affirmative universal sign or by a special sign of confusion. An example of the first is “Every man is an animal,” where “animal” stands confused only. Examples of the second are “Only man disputes” and “An eye is required for seeing,” where “man” and “eye” stand confusedly. In the next chapter we shall explain the special signs of confusion. Confused-only supposition is either disjunct or collective. Disjunct supposition is the kind illustrated by the examples just given. Collective supposition is affected by a collective sign, as in “All the apostles are twelve” and “All the planets are seven”; “apostles” and “planets” stand confusedly and collectively.

The difference among these suppositions is also commonly recognized by the descent or ascent appropriate to each. Determinate supposition takes disjunctive descent; distributed supposition, conjunctive descent; confused-only supposition, disjunct or collective descent. What conjunctive and disjunctive ascent, and disjunct and collective ascent, will be explained in the next book, chapters 2 and 3.

Since ascent and descent belong only to personal supposition, because they proceed with reference to individuals—to which we descend from the universal, or from which we ascend to the universal—and only personal supposition is taken for individuals, different kinds of personal supposition are best distinguished by the different descent and ascent to individuals. Since descent and ascent are as it were a kind of motion, a term under which we can descend and ascend immediately and independently of another is said to supposit or stand movably. When descent or ascent cannot be made immediately, but depends on resolving another term (resolution being the same as descent and ascent), the term is said to stand immovably. Disjunct and collective descent are not considered a resolution of the term simply, since descent is not made through propositions more evident in truth, as resolution requires, but by enumerating the same term. For example, in “Every man is an animal,” disjunct descent applies to “animal”: every man is this or that or that other animal. In “A horse is required for riding,” disjunct descent under “horse” is: this or that horse is required for riding. Such enumeration does not further manifest or resolve the truth, but only enumerates the terms. Likewise, “All the apostles are twelve” is resolved as follows: these and those, and so on, are twelve.