Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

Some think that the division into affirmative and negative is accidental, because it is a division according to the quality of proposition, while quality presupposes the essence and substance of a thing. The quality of proposition consists in affirming and denying, just as quantity consists in universality and particularity. Others think it is analogical because it is given according to priority and posteriority: affirmation is prior to negation. As for the division into universal and particular, almost everyone agrees that it is accidental.

NEVERTHELESS, the express view of St. Thomas is that the division of proposition into affirmative and negative is univocal, a division of genus into species. He says so in On Interpretation 1, lecture 8,¹ and more clearly in opusc. 48, treatise On Enunciation, chapter 6. It is clear from St. Thomas’s view that this division is essential and univocal. In the treatise On Enunciation, chapter 6,² after saying that it is a division of genus into species, he adds below that “this division pertains to the quality of enunciation, namely its essential quality, insofar as a difference signifies a ‘what sort of thing.’”

THE FOUNDATION of this view: To prove that the division is univocal, St. Thomas argues against Alexander that the affirmative and negative alike participate in the essential character of enunciation, namely “to signify what is true or false.” For an affirmative proposition signifies what is true or false just as properly and essentially as a negative proposition does.

That the division is essential rather than accidental is proved from the fact that it is a division according to the essential form of proposition, which is the copulation of the extremes signifying truth, insofar as it is grounded in their agreement or disagreement with one another. For before the agreement or disagreement of the extremes, no substance of enunciation can be conceived. The very character of enunciation is first conceived and constituted essentially when the extremes are understood as united in relation to truth. Therefore an essential difference in the character of this union produces an essential difference in the character of enunciation. It is for this reason that a hypothetical proposition differs essentially from a categorical one: it differs in its character and manner of copulating and composing. But negative copulation differs essentially from affirmative copulation, since negation is essentially opposed to affirmation, in that it wholly destroys it.

I SAY, SECOND: The division of proposition according to quantity, namely into universal, particular, and so on, is not essential but accidental.

WE PRESUPPOSE that quantity is not found in every proposition, but only in a proposition consisting of a common term. If its subject is singular, the proposition has no quantity, because quantity in propositions is considered according to the extension of the subject to more or fewer things. A singular proposition, however, has no extension, since it applies to only one thing; hence it is as if indivisible in the genus of propositional quantity.

FROM THIS IT IS CLEARLY INFERRED that this division according to quantity is accidental. First, because it is not taken according to what is essential in proposition, namely the signification of truth or the copulation of the extremes, but according to the extension of the subject in it to the things to which the predicate can apply. Second, because if the whole essence of proposition can be found in an individual without that quantity, as in a singular proposition, then the division according to quantity is not essential.

BUT IF YOU SAY: Some propositions can differ in species solely by reason of quantity. For example, if you say “Every human being is white” and “Some human being is white,” the first is false and the second true, solely by reason of quantity. Therefore different quantity produces an essential and specific difference.

It is answered by denying the antecedent, because truth and falsity are not essential differences, as we said above.³ Hence, from the mere fact that one proposition is true and the other false because quantity varies, it does not follow that they are essentially different. This is especially true with respect to the essential difference of proposition on the side of form and artful composition; in this respect there is no essential difference between those two propositions. But on the side of matter, namely because the thing signified is different, there is no impediment to some propositions differing specifically because they signify things distinct in species. This is not by reason of quantity: even if they have the same quantity, they differ in species in this way, as when you say “Every human being is an animal” and “Every horse is neighing.”

THE OBJECTIONS ARE ANSWERED.

First it is argued to prove that proposition is not rightly divided into affirmative and negative. For affirmation and negation are explained through being and nonbeing: one affirms by saying that something is, and denies by saying that it is not. But nothing common, nor any third middle term, can be given between being and nonbeing, since they are immediately opposed. Therefore this division is neither good nor univocal, since nothing is univocal with respect to being and nonbeing.

And it is confirmed because affirmation and negation are presented according to priority and posteriority. Affirmation is prior to negation, for negation is grounded in affirmation, as is clear from Aristotle, On Interpretation 1, chapter On Enunciation,⁴ and St. Thomas there, lecture 8.⁵ Therefore this is not a division of genus into species, but of an analogate into analogates. The consequence is clear, because the species of one genus are simultaneous by nature, as is said in the Postpredicaments;⁶ therefore one cannot give a division of genus by species that stand to one another as prior and posterior.

IT IS ANSWERED that some are badly troubled by this argument, but without foundation. For I grant that there is no middle between being and nonbeing, nor can anything common be abstracted from them. But there can be something common abstracted from “signifying being or nonbeing,” namely signifying complex extremes and uniting them, which are afterward determinately signified as united by affirmation or negation: one signifies being, the other nonbeing. Thus being and nonbeing themselves are opposed contradictorily, whereas affirmative signification and negative signification are not opposed contradictorily but contrarily, because each signification is positive. They stand as two species of artful and complex signification, and this complex enunciative signification is the common character between them.

To the confirmation it is answered from the teaching of St. Thomas, On Interpretation 1, lecture 8,⁷ and opusc. 48,⁸ where he solves this very argument: not every priority and posteriority constitutes analogy. This is clear in the species of number: one number is prior to another, and yet they are univocally numbers. Potency, habit, and act likewise have a character of priority and posteriority, yet they are univocally qualities. Rather, the priority that makes things participate unequally in a superior character—so that in one it is found primarily and in its own right, and in another in a qualified way and accidentally—makes for analogy, as “being” with respect to substance and accident, and “healthy” with respect to an animal and a plant; for in one it is found priorly, in the other posteriorly. The species of one genus are said to be simultaneous by nature in the simultaneity of their participation in the superior character, not in the simultaneity of their existence with one another.

Second it is argued: The same thing divided cannot be divided by two essential divisions, since essential differences divide a genus equally and are opposed to one another in an adequate way within the same genus. But proposition is divided essentially into categorical and hypothetical, as was said in the preceding article; therefore it cannot again be divided essentially into affirmative and negative, since one division is not contained under the other.

And this is confirmed because the species of genera that are not subordinated cannot be the same, as is said in the Antepredicaments.⁹ But categorical and hypothetical are genera that are not subordinated; therefore they cannot be divided by the same essential differences. Yet each can be divided into affirmative and negative, and, in turn, both affirmative and negative can be divided into categorical and hypothetical. Therefore these divisions cannot be essential, but are accidental.

IT IS ANSWERED, first, that there is no difficulty in the same thing being divided immediately by several essential divisions when the divisions are inadequate—that is, when an essence is constituted by several formalities, each of which can be divided into certain species. This is the teaching of St. Thomas, Summa theologiae I–II, question 95, article 4, body, where he says that “there are many things belonging to the character of human law, according to any one of which human law can properly and in its own right be divided.” There he enumerates different divisions of human law that are per se and essential, according to inadequate considerations. Indeed, in divisions of the categories it is not necessary for every division to be made into two adequate species; it can be made into several species by which the same genus can be divided. For example, animal can be divided into walking and flying, and again into crawling and swimming, and into many diverse essential species. Similarly, quality is divided immediately into habit and disposition, potency and incapacity, and so on.

Second, one can answer that affirmation and negation are not an immediate division of proposition, but its subdivision. For proposition is first divided into categorical and hypothetical, and categorical proposition into affirmative and negative. St. Thomas took this from the Philosopher, On Interpretation 1, chapter On Enunciation,¹⁰ lecture 8,¹¹ saying that “one enunciation is one simply, another is one by conjunction.” He immediately adds: “Another subdivision of enunciation is that, if an enunciation is one, it is either affirmation or negation.” This will be explained more fully just below.

To the confirmation it is answered from this last solution that the antepredicamental rule has no place here, since the division into categorical and hypothetical and the subdivision of the categorical into affirmative and negative involve genera subordinated to one another.

And when it is urged that hypothetical proposition too is divided into affirmative and negative, the answer is, first, that hypotheticals are not said to be affirmative or negative per se, except by reason of the categorical propositions of which they consist. For the hypothetical copulas themselves are not properly denied; rather, verbal copulas are denied, and from their negation hypothetical propositions too are made negative. Hence, when contradictories are formed among hypotheticals, negations are placed in the categorical copulas, not in the hypothetical ones (unless perhaps negation is placed before the whole enunciation). For example, if you say this conjunctive proposition, “Peter runs and John reads,” its contradictory will be this disjunctive proposition: “Peter does not run, or John does not read.” Master Soto rightly observes this in Summulae 3, chapter 9, note 5, where the hypothetical copulas, namely the terms “and” and “or,” are not denied in either place.

Second, it is answered that if a hypothetical proposition is divided per se into affirmative and negative, this affirmation and negation is very different from the affirmation and negation that divides categorical proposition, because categorical and hypothetical copulas are very different; therefore they cannot receive affirmation and negation according to the same character. For a categorical copula is a verb, whereas the copula of a hypothetical proposition is a mode, such as “and,” “or,” or “if.” It is like quality, which as a disposition in its genus is divided into permanent disposition, which is habit, and passing disposition, which is merely disposition; yet when quality is also divided into passion and passible quality according to whether it is permanent or passing, it is not divided by the same differences of permanence and transience as disposition, but by different ones.

Finally it is argued: Some propositions are at once affirmative and negative, or of mixed quality, such as this proposition: “Peter is and was not white.” Therefore this division is not essential, because two essential differences cannot belong to the same individual. Nor can one say that this is two propositions rather than one, for it consists only of one subject and predicate and can be judged with a single judgment. Therefore it is formally one, although it can be virtually multiple, since many propositions can be formed from it.

And this is confirmed because affirmative and negative propositions can be synonymous, such as “A human being is rational” and “A human being is not irrational”; therefore they are of the same species. The consequent is clear because they regard the same object, and species is taken from the object.

IT IS ANSWERED that propositions of mixed quality virtually contain two propositions, because they are as it were twofold, although they are said of the same subject, since the copula is multiplied. Nevertheless, because it is formally one proposition, a proposition of mixed quality that entails an affirmative proposition will be said to belong to the species of affirmative propositions, and the one that is entailed by a negative proposition will belong to the negative species, as we said in the text, in the chapter on the divisions of proposition.¹² Thus one proposition is not constituted formally in two species, but formally in only one; virtually, however, since it is twofold, it belongs to two.

To the confirmation it is answered that although those two propositions are of the same species on the side of matter, or of the subject considered materially, nevertheless they are different on the side of form and the artful mode of enunciating. In this way they are of the same species posterioristically, but different prioristically. For from the same object and matter one can form an enthymeme and a syllogism, which are different in species in the character of artful discourse and consequence, but then will be of the same character posterioristically.