ABSURD. — From the Latin *absurdus*, which in its proper sense had the same value as *absonus* (from the privative prefix *ab-* and *sonus*, sound), meaning out of tune, discordant, dissonant (cf. Cicero, *Tusc.*, II, 4; *Divinat.*, I, 9). In Italian, only the figurative sense has remained, in which the two Latin expressions were already commonly used. Thus, A. is transferred to signify a dissonance in the realm of thought and properly indicates—setting aside the somewhat broader and inexact meaning that the word assumes in common usage—everything that violates the norms and laws of logic, the principles of reason. It will therefore apply to an idea when it is constituted of logically incompatible elements, and to a judgment when it aims at a synthesis of subject and predicate that is impossible from the standpoint of the laws of rational thought. A. thus has a narrower field of reference than the false, to which ideas and judgments may refer in contrast not with the pure demands or principles of reason, but with reality or the order of existing things. If not everything that is false is A., the converse is true: for every philosophy that upholds the objectivity of reason, what is A. is also false, albeit in a purely formal order.
The empiricist school and psychologism, which have denied or cast doubt upon the objectivity of rational A., 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, perceiving that their very negation, as a judgment that posits itself, is not an absolute value and implies the universality of the objectivity of reason. In reality, the objectivity of rational principles is an intrinsic exigency of the nature of thought, which cannot be otherwise understood than as an expression of being and its relations, foremost among which is that of non-contradiction; in whose negation, in the end, directly or indirectly, every A. consists.
With regard to methods of argumentation, the argument *ad absurdum*, which proves the truth or falsity of a proposition from the falsity of a consequence, has been known since Aristotle. It comprises two different forms: the first, properly called proof *ad absurdum*, demonstrates the truth of a proposition from the false consequences that derive from its contradictory, a method frequently used in mathematics from Euclid onward; the second, better termed reduction to the absurd (Aristotle, ἀπαγωγὴ εἰς τὸ ἄδυσαντον, “reductio ad impossibile,” *Anal. Pr.*, I, 7, 20 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 unquestionable apodictic value: “to reduce a proposition to absurdity is to demonstrate its falsity” (Leibniz, *Nouveaux Essais*, IV, ch. 8, § 2).