ASSURDO. — From Latin absurdus, which in its proper sense had the same value as absonus (ab privative, sonus, sound): out of tune, dissonant, discordant (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. A. is thus transferred to signify a dissonance in the sphere of thought and properly indicates, leaving aside the somewhat broader and less exact meaning that the word assumes in current usage, everything that offends logical norms and laws, the principles of reason. An idea will therefore be a. when it is constituted by logically incompatible elements; a judgment will be a. 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 falso, which may refer to ideas and judgments 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 a., the converse proposition is nevertheless true: for every philosophy that defends the objectivity of reason, whatever is a. is also false, even if, in itself, only in a purely formal order. The empiricist school and psychologism, which denied or called into question the objectivity of rational a., reducing logical norms to the contingency and relativity of psychological laws, must consequently arrive at the denial of scienza as a universal value. Without, however, perceiving that their own denial, insofar as it was a judgment asserted with absolute validity, implied the universality and objectivity of reason. In reality, the objectivity of rational principles is an intrinsic requirement of the nature of thought, which can be understood in no other way than as an expression of being and of its relations, the first among them being that of non-contradiction; in the denial of which, ultimately, every a. consists, directly or indirectly.
In relation to methods of argumentation, the argomento per a. 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 prova per a., demonstrates the truth of a proposition from the false consequences that follow from its contradictory, a method frequently used in mathematics since Euclid; the second, better called riduzione ad a. (Aristotle, ἀναγωνή 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 a. 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).