Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

WE ASSUME that one opposition is real and another logical—that is, opposition of things or of propositions. These two are related in such a way that real or physical opposition is, as it were, the object of logical opposition: the being and nonbeing that exist on the side of the thing and in the objects themselves are signified by opposed propositions. Although treating real opposition belongs to the metaphysician, since treating the oppositions of propositions belongs to the logician, the logician must also in some way touch on what pertains to the opposition of things, insofar as they are the objects of opposed propositions.

THE ANSWER, then, to the proposed difficulty, is that contradictory opposition, both in propositions and in things, both dialectical and physical, is the greatest among all oppositions.

For this conclusion see St. Thomas, Opusculum 37, c. 1,¹ and Metaphysics X, lecture 6.² The FOUNDATION is that the greater opposition is the one in which there is less agreement and one opposite destroys the other more. Opposites are then said to lack a middle because they lack every agreement by which they could agree in some way, whether on the side of the subject, through some third form mediating between the extreme opposing forms, or in any other way. It is clear, however, that only contradictory opposition absolutely and in every way destroys its opposite. The other oppositions do not destroy it so absolutely and simply, but leave something of it behind and thus retain some agreement; in this respect they have less opposition.

This is clear from examining each species of opposition, whether on the side of things or of propositions. In all of them some negation opposed to affirmation is found, but not as purely and absolutely as in contradiction. A contrary proposition, if it is physical, lies between two positive forms, which can be in the same subject either simultaneously, if they are in remiss degrees, or successively, if they are in intense degrees. Thus one contrary form does not wholly destroy the other or their agreement in the subject. Similarly, contrary opposition in propositions, which is dialectical opposition, does not remove everything in one proposition that is in the other, since it at least does not remove universality and distribution; contrary propositions must agree in this respect. Consequently, neither does the falsity of one destroy the falsity of the other, and so it is not a negation that absolutely denies and removes what is in the other extreme. Likewise, subcontrariety does not remove particularity and consequently does not remove truth: two subcontrary propositions are both particular and can both be true. Finally, privative opposition does not remove but leaves an aptitude for the opposite form; at least in this respect it leaves some agreement with its opposite. Relative opposition also does not include a negation by which one opposite removes the other. Rather, relatives exist together in nature and in cognition, and each posits³ being. For this reason the passage of St. Thomas in De potentia, q. 7, a. 8, ad 4,⁴ must be understood to say that in relatives one does not remove the other or include a negation of the other. It does not mean that a relation contains no negation of its correlate, but that it does not include that negation by way of removing and excluding the correlate from a subject. Rather, it presupposes that such a correlate exists, even though it is distinct in itself, is not that relation, and is related to it.

In contradictories, however, the negation of one is so pure and absolute that it removes every agreement with its opposite; it therefore leaves neither being nor aptitude, universality, nor particularity, but destroys the whole, as if by a malignant nature. Thus it is simply and absolutely the greater opposition intensively. Opposition is derived from it, as from the primary opposition, to the other oppositions, which have opposition only insofar as they have something of contradiction, as St. Thomas teaches in the cited places and in the chapter “On Opposites” in the Logic.⁵

THE ARGUMENTS ARE ANSWERED.

You will object, first: Contraries are maximally distant from one another; therefore they are maximally opposed, since opposition is a kind of distance. Hence opposites that are more immediate seem less opposed because they are less distant. But contradictories are immediate, because there is no middle between being and nonbeing.

Second: Contrariety destroys more than contradiction; therefore it is the greater opposition. The antecedent is clear because contrariety is more universal in negating, and therefore also in destroying. Contrary propositions consist of two universals, one denied and the other affirmed; therefore the negative is always universal, and consequently it denies and destroys more.

Third: Contraries entail contradictories both in logic and in physical things. In logic, the following inference holds: “Every man is white” and “No man is white”; therefore “Every man is white” and “Some man is not white,” which are contradictories. In physical things, hot and cold are contrary, yet from “hot” it correctly follows that something is not cold, which is contradictorily opposed to cold.

Fourth: All the other oppositions include contradiction and add something to it; therefore they are greater oppositions than contradiction alone. The antecedent is proved because they include negation and affirmation, and therefore contradiction, which is completed through affirmation and negation. All oppositions thus signify contradiction, are reduced to its principles, and are governed by it. Therefore they add something to contradictory opposition and are greater.

TO THE FIRST we reply that contraries are maximally distant within the same genus and inside one genus, whereas contradictories are distanced through negation in every genus and beyond every genus. Pure and absolute negation is outside every genus and thus negates every being; contradictories are therefore maximally distant and have no middle of agreement with the other extreme. Opposites are called immediate and maximally distant because they lack a middle of agreement. Things placed immediately, however, lack a middle of position and are therefore less distant in local distance. But we are not speaking here of this distance, but of the distance of incompatibility and opposition. In this respect being and nonbeing are more distant: they lack a middle—that is, agreement—because nothing is left that is not removed.

TO THE SECOND we say that universal negation in a contrary proposition destroys more extensively, as regards the mode of signifying distribution, but not more intensively or with respect to destroying everything posited in its opposite, both as to truth and falsity, universality and particularity, and so on. Contradiction removes everything in this way, whereas contrariety leaves something behind, namely universality and falsity. It is one thing to destroy more of one’s opposite and another to apply negation to more subjects by distributing it; contrariety does the latter, not the former.

TO THE THIRD we reply that contradictory opposition does not follow formally from the opposition of contraries, but follows as it were materially. Although a particular proposition that is the matter of the contradictory opposition to another universal proposition follows from one universal proposition, this inference does not arise from the contrary opposition between two propositions; rather, it is sufficiently deduced from only one universal proposition. Subcontraries do follow from contrary opposition: that is, the two particular propositions, one affirmed and one denied, which are subordinate to those universal propositions. But this opposition is lesser. Similarly, a contradictory does not follow formally from physical contrariety. For from cold there does not follow the absolute and simple negation of hot, but the negation of hot in this thing—that is, in cold insofar as it is cold—which is a negation in something positive and is therefore not absolute. For hot and cold can well coexist in the same subject in remiss degrees.

Second, there is no impossibility in a greater opposition following from a lesser one, when the greater stands as the origin and principle of the lesser; for the other oppositions arise from contradiction as from their principle. For example, specific distinction is less than distinction of things primarily diverse, yet the distinction of differences that are primarily diverse from one another is inferred from the distinction between two species, as it were a posteriori.

TO THE FOURTH we reply that the other oppositions add something to contradiction that diminishes opposition rather than increasing it, as can be seen in St. Thomas, Opusculum 37, c. 1.⁶ Since the negation of contradiction is pure and absolute, whereas the negation of contrariety and privation retains something of the positive opposite, it is clear that they diminish the account of opposition by diminishing the absolute account of negation and removal from the opposite.