CONTRADICTION. — The relation of opposition existing between the affirmation and the negation of the same predicate in relation to the same subject, “simultaneous affirmation and negation of the same thing.”
Contradiction, therefore, properly exists only between two judgments (explicit or implicit), and not between concepts, except insofar as two notions of opposite content, e.g., just—unjust, are thought together as referable to a subject, thus implying a virtual judgment. Between two judgments, then, contradiction can be formal-explicit (contradictio in terminis), when the affirmation and negation is explicit in relation 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 a more strictly technical sense, in logic two propositions are called contradictory when one affirms or denies only what is required and sufficient to annul the first, so that no middle proposition can be placed between the two: this is the precise meaning given by Aristotle, who defines the ἀντιφάσεις as “opposites between which no middle term can be placed” (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 a universal affirmative or negative and the other a particular negative or affirmative respectively, e.g., every thing lives—something does not live. Between two propositions of this kind there arise special relations of mutual incompatibility such that not only can they not both be true, but neither can they both be false. A law which, while having particular importance in the logic of propositions, is not without practical repercussions even in theological disciplines, in relation, for example, to the propositions prescribed by the magisterium of the Church, whose true formal meaning is easily grasped when it is borne in mind that of any condemned proposition, the contradictory—and only this—is necessarily true (see also LOGIC).
PRINCIPLE OF CONTRADICTION. — Fundamental law of logical-metaphysical thought expressing the opposition between being and non-being, the true and the false, the yes and the 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 contradiction, also called by some the principle of non-contradiction, follows the history of the various metaphysical conceptions of thought and reality, its meaning and value being determined in function of these. Meanwhile, that it holds universally as a logical-formal principle of thought seems not to be denied by anyone, since it is evidently impossible for logical thought to affirm anything, giving this affirmation a meaning, without recognizing the antithesis between the yes and the no, the “this” and the “not-this.” This is what Aristotle vigorously affirmed against the pretended negation of Heraclitus: “It is impossible that anyone should think the same thing to be and not to be” (Met., IV, 3, 1005 b 23). But for Aristotle the principle of contradiction is not only an absolute necessity of logical thought, the first among all principles to which every demonstration must necessarily refer (loc. cit., 1005 b 33), but has a strictly ontological import and meaning. It is the very law of the real, founded on the intrinsic determination of being, and first of all of ousia, so that if something is the being of man, this cannot be the being of non-man; if not, it would be as much to say “tirere” or “wall” or “man” (loc. cit., IV, 1007 b, 20-24). Identical is the thought of St. Thomas, who reaffirms the principle of contradiction as the first, rooted in the notion of being and non-being: “The first indestructible principle is that it is not possible simultaneously to affirm and deny, which is founded on the reason of being and non-being” (Sum. Theol., 1a-2ae, q. 94, a. 2, c.).
The crisis of the principle of contradiction, already adumbrated in the history of philosophy with Heraclitus, reappears much more acutely in modern philosophy. And first of all in the various empiricist trends. For these, in devaluing intellectual knowledge of reality, deemed of merely empirical value, the principle of contradiction, like every other general principle, no longer holds except as a norm of logical thought, whether it be a universal and intrinsic law of the structure of the human mind (Goblot), or (as in some forms of psychologism and sociologism) a genuine psychic attitude born of factual conditions of individual and social thought (L. Lévy-Bruhl).
As with 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 perennial synthesis of opposed moments, necessarily arrives at the negation of the principle of contradiction in its Aristotelian-Thomist ontological meaning. Once the concept of reality is changed, no longer as intrinsic determination but as bearing within itself internal opposition, the principle of contradiction 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 contradiction (cf. Hegel, La scienza della logica, I, Italian trans. by A. Moni, Bari 1925, pp. 74 ff., 103 ff.; II, pp. 59 ff., 69 ff.). The Hegelian conception substantially returns in Gentile, for whom the principle of contradiction holds indeed for thought thought (thought-object), but not for thinking thought (thinking-subject), “which in its attitude is different and development, posits indeed as its own object the identical, but precisely through 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). Finally, the intuitionism of Bergson arrives at the negation of the ontological value of the principle of contradiction, renewing in a certain way the position of Heraclitus by affirming the real not as immobile being, but essentially as pure becoming.
Against these and similar conceptions traditional philosophy defends the Aristotelian-Thomist position: affirmed reality as the positive and ontic determination of pure act (infinite being), or of the synolon of act and potency (finite being), there follows the absoluteness and validity within being of the principle of contradiction, without which that positivity would be unacceptable and would dissolve being. Nor is a dialectical conception of becoming precluded by this position. For becoming arises from the tension that is in imperfect and incomplete being, and therefore in its non-being, toward being and perfection. Now the fact that being tends toward non-being in no way prejudices the principle of contradiction, since this tension toward non-being is included in the intrinsic structure and determination of being a.
It would therefore be erroneous to interpret the principle of contradiction in the sense of a law of the staticity of being. Experience and metaphysics meet in the conception of being as nature and therefore as a principle of activity. But this activity, in which being tends by itself to expand and increase, is metaphysically defined by the inner structure of substance. It is by this radical metaphysical determination of substance that the principle of contradiction extends even to becoming itself.