ABSURD. - From the Latin absurdus, which in its proper sense had the same value as absonus (from the privative ab and sonus, sound), out of tune, dissonant, discordant (cf. Cicero, Tusc., II, 4; Divinat., I, 9). In Italian only the figurative sense has survived, in which the two Latin expressions were already commonly used. "Absurd" thus comes to signify a dissonance in the field of thought, and denotes properly — setting aside the somewhat broader and less exact meaning that the word assumes in current usage — everything that offends the norms and laws of logic, the principles of reason. It will therefore be an absurd idea when it is constituted of logically incompatible elements, an absurd judgment when it aims at a synthesis of subject and predicate that is impossible from the standpoint of the laws of rational thought. The absurd thus has a narrower field of reference than the false, to which ideas and judgments may refer that are in conflict with reality or the order of existing things, but not with the pure requirements or principles of reason. If not everything that is false is absurd, the converse proposition is nonetheless true: for every philosophy that defends the objectivity of reason, what is absurd is also false, even if, in itself, in a purely formal order. The empiricist school and psychologism, which have denied or called into doubt the objectivity of the rational absurd, reducing logical norms to the contingency and relativity of psychological laws, must consequently arrive at the negation of science as a universal value. Without, however, noticing that their very negation, insofar as it was a judgment positing itself with absolute value, implied the universality and objectivity of reason. In reality the objectivity of rational principles is an intrinsic requirement of the nature of thought, which cannot be understood otherwise than as an expression of being and of its relations, the first among them being that of non-contradiction; and every absurd consists, at bottom, directly or indirectly, in the negation of this.
In relation to methods of argumentation, the argument by absurdity has been known since Aristotle; it proves the truth or falsity of a proposition from the falsity of a consequence. It comprises two distinct forms: the first, properly called proof by absurdity, demonstrates the truth of a proposition from the false consequences that derive from its contradictory — a method frequently used in mathematics since Euclid; the second, better called reduction to absurdity (Aristotle, ἀναγωγή εἰς τὸ ἀδύνατον, "reductio ad impossibile", Anal. Pr., I, 7, 29 a, 30; ibid., 6, 28 b, 21), demonstrates the falsity of a proposition by bringing to light the false or absurd consequences to which it logically leads. This indirect form of argumentation, when rigorously conducted, is of undoubted apodictic value: "réduire une proposition à l'absurdité c'est démontrer sa contradictoire" (Leibniz, Nov. Ess., IV, c. 8, § 2).