DEDUZIONE. — It may be understood in different ways: a) In the generic sense, which is also the one immediately suggested by the term, d. is the process of reasoning whereby, from one or more propositions, one passes to a new proposition formally contained in them, by virtue of a logical bond or connection. Understood in this way, d. encompasses every kind of formal reasoning, that is, reasoning in which the conclusion follows necessarily from the premises by logical consequence. b) In a narrower and fairly common sense, d. means the process of reasoning that proceeds from universal principles to particular truths; as induction (v.), which proceeds from particular facts to universal principles; and it constitutes the principal moment of the synthetic process, just as induction, in turn, constitutes that of the analytic process (v. PSICANALISI). c) Finally, since the most typical form of reasoning from the universal to the particular is the common syllogism, d. is sometimes identified, though quite inaccurately, syllogism (v.).
The restricted senses b) and c) originate with Aristotle, for whom ἀπόδειξις (demonstrative syllogism, and at times syllogism in general) is universally affirmed as the d. of the particular from the universal and contrasted with induction: ἀπόδειξις ἐπταγόνῃ constitute, according to Aristotle, the two essential forms of human learning, the former proceeding from the universal to the particular, the latter, conversely, from the particular to the universal (Anal. pr., II, 23, 68 b 13; Anal. post., I, 18, 81 a 40). This Aristotelian identification of d. with demonstrative syllogism is rooted in the metaphysical function that he attributes to the universal, as the essential principle of the particular and the concrete: the process, therefore, of d. of the particular from the universal is also the way of demonstration, that is, scientific knowledge of the particular brought back to the universality of the concept. The opposition between d. and induction in the Aristotelian sense does not, however, have absolute validity. The type of mathematical d. may in fact proceed from the particular to the universal, as, for example, when, from a property referring to a determinate case, one derives by an apodictic logical process the general formula in which that case is contained.
Kant, starting from the particular meaning of the term in juridical language, calls transcendental d. the explanation of the way in which a priori concepts, or pure forms of the intellect, relate to experience and have validity for II. Unlike empirical d., which shows only how a concept is acquired through experience, transcendental d. is a legitimization, on the basis of the a priori structure of reason, of the objective use of the categories. According to Kant, it is founded on the principle that pure concepts must be recognized as the a priori conditions of the possibility of experience and of its very objects (cf. Critica della Ragion pura, Bari 1940, part 1, pp. 119–28).
D. understood as a process of synthetic development from universal principles has an essential task in the rational sciences (philosophy, mathematics, etc.) and in the integrative sciences, but is equally important in the physical sciences, despite the repeated attempts at devaluation on the part of empiricism. Although it serves principally as a method of proof and scientific organization, whereby the logical concatenation of concepts and judgments is brought to light, it asserts an intrinsic heuristic and extensive value for knowledge. For although it is true that particular truths are objectively contained in universal principles, they nevertheless reveal themselves to thought only through the fecundity of deductive development (v. SILLOGISSO).