Deduction

DEDUCTION. - It may be understood in different ways: a) In a generic sense, which is also the one immediately suggested by the term, deduction is the process of reasoning by which one passes from one or more propositions to a new proposition formally contained in them, by virtue of a logical link or connection. Understood in this way, deduction embraces every kind of formal reasoning, that is, reasoning in which the conclusion follows by necessity of logical consequence from the premises. b) In a narrower sense, and one in fairly common use, deduction means the process of reasoning that goes from universal principles to particular truths; as such it is contrasted with induction (v.), which proceeds from particular facts to universal principles; and it constitutes the principal moment of the synthetic process, just as, in turn, induction constitutes that of the analytic process (v. ANALISI). c) Finally, since the most typical form of reasoning from the universal to the particular is the common syllogism, deduction is sometimes identified, though quite inexactly, with the syllogism (v.).

The narrow sense b) and c) takes its start from Aristotle, in whom ἀπόδειξις (demonstrative syllogism, and sometimes syllogism in general) is universally asserted as deduction of the particular from the universal and is contrasted with induction: ἀπόδειξις and ἐπαγωγή constitute precisely, according to Aristotle, the two essential forms of human learning, and the first goes from the universal to the particular, the second, inversely, from the particular to the universal (Anal. pr., II, 23, 68 b 13; Anal. post., I, 18, 81 a 40). This Aristotelian identification of deduction 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 of deduction of the particular from the universal is therefore also the path of demonstration, that is, scientific cognition of the particular traced back to the universality of the concept. The opposition between deduction and induction in the Aristotelian sense does not, however, have absolute value. The type of mathematical deduction can 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 the case is contained.

Kant, starting from the particular acceptation of the term in juridical language, calls transcendental deduction the explanation of the manner in which a priori concepts or pure forms of the intellect refer to experience and have validity for it. Unlike empirical deduction, which shows only how a concept is acquired by means of experience, transcendental deduction is a legitimation, on the basis of the a priori structure of reason, of the objective use of the categories. It is founded, according to Kant, 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).

Deduction understood as a process of synthetic development from universal principles has an essential task in the rational sciences (philosophy, mathematics, etc.), and an integrative but equally important one 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 of scientific ordering, by which the logical concatenation of concepts and judgments is brought to light, it claims an intrinsic value that is heuristic and extensile of knowledge. For if it is true that particular truths are objectively contained in universal principles, nevertheless they do not reveal themselves to thought except through the fecundity of deductive development (v. SILLOGISSO).

Ugo Viglino