Contradiction

CONTRADICTION. - The relation of opposition existing between the affirmation and the denial of one and the same predicate in relation to one and 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 opposite content, e.g., just - unjust, are thought together as referable to a subject, and thus as implying a virtual judgment. Between two judgments, moreover, contradiction can be formal-explicit (contradictio in terminis), when the affirmation and denial 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, two propositions are called contradictory in logic when one affirms or denies only as much as is required and sufficient to cancel the first, so that between the two it is not possible to place an intermediate proposition: this is the precise meaning of Aristotle, who defines ἀντίφρασις: «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 universal affirmative or negative and the other particular respectively negative or affirmative, e.g., everyone lives - something does not live. From two propositions of this kind there arise special relations of mutual incompatibility by which not only can they not both be true, but they cannot both be false either. A law which, while it has a particular importance in the logic of propositions, is not without practical repercussions also in the theological disciplines, in relation, for example, to the propositions proscribed by the magisterium of the Church, whose true formal meaning is easy to grasp, bearing in mind that of any condemned proposition, the contradictory one, and only this one, is necessarily true (v. also LOGICA).

PRINCIPLE OF CONTRADICTION

Fundamental law of logical-metaphysical thought expressing the opposition between being and non-being, the true and the false, 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"; the logical formulation: "one and the same predicate cannot at the same time be affirmed and denied of one and the same subject."

The history of the principle of c., called by some also that of non-c., follows the history of the various metaphysical conceptions of thought and reality, its meaning and value being determined as a function of these. In the first place, that it holds universally as a logical-formal principle of thought seems to be denied by no one, since logical thought evidently cannot affirm just anything, giving that affirmation a meaning, without recognizing the antithesis between yes and no, the "this" and the "not-this." This is what Aristotle vigorously affirmed against the supposed negation of Heraclitus: 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 only an absolute necessity of logical thought, first among all principles, to which every demonstration must necessarily refer (loc. cit., 1005 b 33), but has a plainly ontological scope and meaning. It is the very law of the real, founded on the intrinsic determination of being, and in the first place of the obetz, whereby, if "being a man" is something, this cannot be "being a non-man"; otherwise one might just as well say "trireme" or "wall" or "man" (loc. cit., 4, 1007 b, 20-24). Identical is the thought of St. Thomas, who reaffirms the principle of c. as the first, 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, reappears far more acutely in modern philosophy. And first of all in the various empiricist currents. For them, once the intellectual knowledge of reality has been devalued, held to be of purely empirical value, the principle of c., like every other general principle, no longer holds except 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 attitude born of factual conditions of individual and social thought (L. Lévy-Bruhl).

Like empiricism, though 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 opposite moments, necessarily arrives at the negation of the principle of c. in its ontological-Aristotelian meaning. Once the concept of reality is changed, which no longer holds as intrinsic determination but rather bears within itself an internal opposition, the principle of c. too falls as an expression of the determination of being and remains, at most, as an expression of the perennial dialectical movement of reality toward the overcoming of c. (cf. Hegel, La scienza della logica, I, trans. it. by A. Moni, Bari 1925, pp. 74 ff., 103 ff.; II, pp. 50 ff., 69 ff.). The Hegelian conception returns substantially in Gentile, for whom the principle of c. indeed holds for thought thought (thought-as-object), but not for thinking thought (thought-as-subject), "which in its actuousness that is becoming or development, indeed posits 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). Finally, the Bergsonian intuitionism arrives at the negation of the ontological value of the principle of c., 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 analogous conceptions traditional philosophy defends the Aristotelian-Thomist position: once reality is affirmed as positivity 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 c., without which that positivity would be inconceivable and would vanish, dissolving being. Nor in this position is a dialectical conception of becoming precluded. 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 a has a tension toward non-a does not in the least prejudice the principle of c., since the tension toward non-a falls within the structure and intrinsic determination of being a.

It would therefore be erroneous to interpret the principle of c. 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 of itself to expand and increase, is metaphysically defined by the interior structure of substance. It is by this radical metaphysical determination of substance that the principle of c. extends to becoming itself.

Ugo Viglino