CONTRADICTION. — The relation of opposition existing between the affirmation and negation of the same predicate with regard to the same subject, “simultanea eiusdem affirmatio et negatio.”
Contradiction, therefore, properly exists only between two judgments (explicit or implicit), and not between concepts, except insofar as two notions of opposing content—for example, just and unjust—are thought of together as referable to a subject, and thus as implying a virtual judgment. Between two judgments, contradiction may be formal-explicit (contradictio in terminis), when the affirmation and negation are explicit with regard to a formally identical predicate (the soul is spiritual—the soul is not spiritual), or merely material-implicit, when the second judgment expresses a new predicate that destroys the first (the soul is spiritual—the soul is generated by the body).
In the more strictly technical sense, in logic two propositions are called contradictory when one affirms or denies only that which is required and sufficient to cancel the first, so that no intermediate proposition can be placed between the two: this is the precise meaning of Aristotle, who defines ἀντίφρασις as “oppositio cuius inter utramque enunciationem non datur medium” (Anal. Post., I, 2, 72 a 12; cf. De Interpr., 6, 17, a 33 and Met., X, 4, 1055 b 1-2).
In this sense, two propositions are contradictory when one is universally affirmative or negative and the other respectively particularly negative or affirmative, for example, everything lives—something does not live. From two propositions of this kind arise special relations of mutual incompatibility, whereby they can be neither both true nor both false. This law, while of particular importance in the logic of propositions, is not without practical implications even in the theological disciplines, with regard, for example, to propositions proscribed by the Church’s magisterium. Their true formal meaning is readily grasped if one bears in mind that, for any condemned proposition, its contradictory—and only it—is necessarily true (v. LOGICA).
PRINCIPLE OF C. — Fundamental law of logical-metaphysical thought expressing the opposition between being and non-being, truth and falsity, yes and no. Its most common ontological formulation is: “nothing can at the same time be and not be,” or: “being is not non-being”; its logical formulation: “the same predicate cannot at the same time be affirmed and denied of the same subject.”
The history of the principle of c., also called by some the principle of non-c., follows the history of the various metaphysical conceptions of thought and reality, its meaning and value being determined in accordance with them. In the meantime, that it has universal validity as a logical-formal principle of thought seems to be denied by no one, since evidently logical thought cannot affirm just anything, assigning a meaning to that affirmation, without recognizing the antithesis between yes and no, “this” and “not-this.” This is what Aristotle vigorously affirmed against Heraclitus’s alleged denial: Impossibile est quem-piam putasse idem esse et non esse (Met., IV, 3, 1005 b 23). But for Aristotle the principle of c. is not merely an absolute necessity of logical thought, first among all principles, to which every demonstration must necessarily refer (loc. cit., 1005 b 33); it also has a distinctly ontological scope and significance. It is the very law of reality, founded upon the intrinsic determination of being, and first of all of the obetz, whereby, if “being a man” is something, it cannot be “being a non-man”; otherwise it would be equally valid to say “trireme” or “wall” or “man” (loc. cit., 4, 1007 b, 20-24). St. Thomas’s thought is identical, reaffirming the principle of c. as the first principle, rooted in the notion of being and non-being: Primum principium indemastrabile est quod non est simul affirmare et negare, quod fundatur super rationem entis et non entis (Sum. Theol., 1ᵃ-2ᵃᶜ, q. 94, a. 2, c.).
The crisis of the principle of c., which had already appeared in the history of philosophy with Heraclitus, reemerges much more acutely in modern philosophy. First of all, in the various empiricist tendencies. For these, once intellectual knowledge of reality has been devalued and regarded as having a purely empirical value, the principle of c., like every other general principle, is valid only as a norm of logical thought, whether it be a universal law intrinsic to the structure of the human mind (Goblot), or—as in certain forms of psychologism and sociologism—a mere psychic disposition arising from factual conditions of individual and social thought (L. Lévy-Bruhl).
Like empiricism, although through an opposed metaphysical conception, Hegelian dialecticism, by identifying reality with the logical process (becoming) of the idea, which is realized in a perpetual synthesis of opposing moments, necessarily arrives at the denial of the principle of c. in its Aristotelian-ontological meaning. Once the concept of reality is changed, so that it no longer signifies an intrinsic determination but instead carries within itself an internal opposition, the principle of c. also falls as an expression of the determination of being and remains, at most, as an expression of the perpetual dialectical movement of reality toward the overcoming of c. (cf. Hegel, La scienza della logica, I, Italian trans. by A. Moni, Bari 1925, pp. 74 ff., 103 ff.; II, pp. 50 ff., 69 ff.). The Hegelian conception essentially reappears in Gentile, for whom the principle of c. is indeed valid for pensiero pensato (object-thought), but not for pensiero pensante (subject-thought), “which, in its actuality, which is becoming or development, does indeed posit the identical as its own object, but precisely by means of the process of its development, which is not identity, that is, abstract unity, but... unity and multiplicity together, identity and difference” (G. Gentile, Teoria generale dello spirito, 5th ed., Florence 1938, p. 44). The Bergsonian intuitionism ultimately arrives at the denial of the ontological value of the principle of c.; it renews in a certain way the position of Heraclitus by affirming the real not as immobile being, but essentially as pure becoming.
Against these and analogous conceptions, traditional philosophy defends the Aristotelian-Thomist position: once reality is affirmed as positivity and as the ontic determination of pure act (infinite being), or of a unity of act and potency (finite being), there follows the absoluteness and validity, within being, of the principle of c., without which that positivity would be inconceivable and would vanish, dissolving being itself. Nor does this position preclude a dialectical conception of becoming. Becoming arises, in fact, from the tension present in imperfect and incomplete being, and therefore in its non-being, toward being and perfection. Now the fact that being a has a tension toward non-a in no way compromises the principle of c.; the tension toward non-a belongs to the structure and intrinsic determination of being a.
It would therefore be erroneous to interpret the principle of c. as the law of the immobility of being. Experience and metaphysics meet in the conception of being as nature and therefore as a principle of activity. But this activity, through which being tends by itself to expand and increase, is metaphysically defined by the interior structure of substance. It is because of this radical metaphysical determination of substance that the principle of c. extends to becoming itself.