Syllogism

SYLLOGISM. - From the Greek οὐν-λόγος, λογισμός, it indicates a connection of ideas, discourse. The term, already used by Plato (Theaet., 189 d; Phil., 41 c), is employed in a generic sense to indicate reasoning (v.), illation, inference (a meaning also suggested, figuratively, by συλλέγειν, to gather; cf. the Latin colligere, to infer).

With Aristotle, to whom the systematic theory of the syllogism is owed, the term takes on a technical meaning: "a syllogism is a discourse in which, certain things having been posited, something other than these follows of necessity, because these things are so" (Anal. pr., I, 1, 24 b 19; cf. Top., I, 1, 106 a 25). This definition reveals the essential concept of the Aristotelian syllogism as an instrument of demonstration or apodeixis. While Platonic διαίρεσις or division (Soph., 253 d), as a dialectical method, does not possess formal necessity, and is therefore only an "impotent syllogism" (ἀσθενὴς συλλογισμός; Anal. pr., I, 31, 46 a 33), the syllogism, on the other hand, in its perfect form "needs nothing else but the premises to show the necessary consequence" (ibid., 1, 24 b 22). The Aristotelian definition extends to every form of formal reasoning; not, therefore, properly to induction (v.): although he sometimes uses the expression "syllogismus ex inductione" (Anal. pr., II, 23, 68 b 15). Aristotle in fact contrasts, in a technical sense, syllogism and induction (Anal. pr., loc. cit.; Top., I, 72, 104 a 13).

The logical structure of the syllogism as the typical form of deductive reasoning consists in the comparison of two terms (concepts, noemata) with a third in which their mutual belonging or exclusion is shown: the syllogism thus resolves itself into a mediated judgment (and therefore into a synthesis of judgments) where the agreement or disagreement between subject and predicate is derived from a pre-established relation of both to another common term. The syllogism therefore comprises three terms: subject and predicate, or the "extremes" (ἄκρα; the predicate, the major extreme: ὄρος πρόσος, τὸ μεῖξον; the subject, the minor extreme: ὄρος ἔσχατος, τὸ ἔλαττον) and the middle term (ὄρος μέσος, τὸ μέσον; cf. Anal. pr., I, 4). The terms are distributed into three propositions: two premises (προτάσεις, τὰ κείμενα, τὰ προτεινόμενα), the major (ἔξιμα) in which the predicate is referred to the middle, the minor (πρόληψις) in which the middle is referred to the subject; and the conclusion (ἐνταρά, τὸ συμπέρασμα) which expresses the relation of agreement or exclusion of the predicate with the subject: "When three terms stand to one another in such a way that the last is contained in the whole of the middle and the middle is contained or not contained in the whole of the first, there is necessarily a perfect syllogism that connects the extremes" (Anal. pr., I, 4, 25 b 32 ff.), e.g., mammals have pulmonary respiration, man is a mammal, therefore man has pulmonary respiration. The foundation of the logical force of the syllogism thus consists in the particular relation of predication or subordination that it establishes among the terms and that is expressed in the law: if a predicate belongs to a subject, the predicate of the predicate also belongs to it, or "whatever is said of the predicate must also be said of the subject" (Cat., 5, 3 b 4-5). This formula is nothing but an application of the principle of identity and non-contradiction and thus clarifies the universal formal necessity of the syllogism. Kant expressed it in analogous terms: "The first and universal law of every affirmative syllogism is... nota notae est nota rei ipsius; of every negative syllogism: ... repugnans notae repugnat rei ipsi" (Die falsche Spitzfindigkeit d. vier syllogistischen Figuren, § 2). The principle was also otherwise indicated by Aristotle in terms of extension: "what is said universally (καθόλου, κατὰ παντός) of a class must also be said singly of the individual subjects contained in the class: if every man is mortal, and Socrates is a man, Socrates is also mortal (the principle 'dictum de omni'; cf. Anal. post., I, 4, 72 a 28, and Anal. pr., I, 1, 24 b 27). The formula of 'identity' ('two things equal to a third are equal to each other'), although not absent in Aristotle (Top., VII, 1, 152 a 31; cf. Sum. Theol., 1ª, q. 28, a. 3 ad 1), does not, however, express his more precise way of understanding the relation among the terms of the syllogism; nor is it perhaps in itself the best, inasmuch as the relation among the terms, in the propositions of the syllogism, is not necessarily one of identity. From the nature of the syllogism Aristotle already deduced its fundamental law: "it is manifest that every demonstration must be through three terms and not more" (Anal. pr., I, 25, 41 b 35); this norm, together with the other, which requires the general acceptation of the middle term in at least one of the premises (the middle particular twice can resolve itself into two terms: cf. ibid., cap. 24, 41 b 7; and Anal. post., I, 11, 77 a 8-9: "if there is no universal term there will be no middle") was subsequently detailed in the well-known eight traditional rules.

The Aristotelian theory develops further (Anal. pr., I, 4 ff.) in the determination of the figures (πῆλματα) and the moods (τόσοι) of the syllogism. The "figure" depends on the different position of the middle in the premises; the "mood" on the arrangement of the premises according to their quantity and quality (universality and particularity, affirmation and negation). Aristotle distinguishes three figures: in the first the middle is subject in the major and predicate in the minor, in the second it is predicate in both, in the third it is subject in both. For each of the figures the laws of inference are determined and the method is then set out for reducing syllogisms of the second and third figures to the type of the first, held by Aristotle (wrongly, it seems: cf. W. D. Ross, op. cit., in bibl., pp. 49-50) to be the only perfect and independent form of syllogism. To the three Aristotelian figures a fourth was later added (attributed to Galen [v.]), in which the middle is predicate in the major and subject in the minor, which is therefore rather a transposition of the first. Taking into account the laws of the individual figures, the arrangement of the middle and of the premises according to quantity and quality allows 19 different moods of correct syllogism, expressed, in medieval scholasticism (for the first time, it seems, in the Summulæ logicales of P. Hispanus) with the mnemonic verses, Barbara Celarent Darii Ferio etc.; where the vowels of the individual terms indicate the propositions of the syllogism in one of the four figures (e.g., Barbara a syllogism with three universal affirmative propositions, in the first figure). In the Aristotelian treatment there follows an extensive exposition of modal syllogisms, in which is also expressed the modality (necessity or contingency) of the subject-predicate relation (cf. Anal. pr., I, caps. 9-22). From the point of view of matter or content Aristotle distinguishes the demonstrative syllogism (σ. ἀποδεικτικώς, φιλοσόφημα) which proceeds from universal and necessary premises (Anal. post., I, 4, 72 a 7, and 6, 75 b 5) and is therefore founded on "essence" (Met., VII, 9; XII, 4, 1078 b 24) and of which an ample development is given in the Posterior Analytics; the dialectical or inquisitive syllogism (σ. διαλεκτικώς, ἐπιχείρημα) which from probable premises "attempts" the search for truth; the contentious or sophistic syllogism (σ. ἀριστικώς, σόφισμα) which "seems to demonstrate" but in reality does not demonstrate (v. SOPHISM) and the rhetorical syllogism (σ. ἐγπορικώς, ἐνθυμήμα; the latter term used afterwards, from Boethius onward, with another meaning) which proceeds from analogies and examples (cf. Top., VIII, 11, 162 a 15 and I, 1, 100 a 27 ff.; Anal. pr. II, 27, 70 a 10; and Rhet., I, 1, 1355 a 6 ff.). The derived forms of the syllogism that represent a simple variation of it (polysyllogism and sorites) are not explicitly considered by Aristotle (the sorites — though not the term — is hinted at in Anal. pr., I, 23, 41 a 18, and developed already in Alexander of Aphrodisias [v. I]); nor are the analogous forms of deductive reasoning treated (the so-called "disjunctive" syllogism, the conditional syllogism and the dilemma).

Such, in general outline, is the Aristotelian theory of the syllogism, which thereafter remained substantially unchanged through the countless later commentaries and developments. Aristotle displayed in it a particular keenness of genius and himself emphasizes with satisfaction his discovery: "on the manner of syllogizing we had nothing before us to set forth and had personally to undertake long and laborious researches" (De soph. elench., 34, 18 a 1 ff.). Hegel, while noting that Aristotelian syllogistic refers solely to the forms of finite and abstract thought, does not hesitate to describe Aristotle as, in a certain sense, "the naturalist of the spiritual forms of thought," and his logic as "a work that does the highest honor to the profundity and the vigor of abstraction of its discoverer" (Lectures on the History of Philosophy, Ital. trans. by G. Codignola and G. Sanna, II, Florence 1932, p. 374). To have fixed the forms of thought "which branch out like a net of infinite mobility" in concrete thought "was a masterpiece of empiricism: and this awareness has absolute value" (ibid., p. 383). Leibniz's assessment is analogous: "je tiens que l'invention de la forme des syllogismes est une des plus belles de l'esprit humain et même des plus considerables" (Nouv. ess., IV, ch. 17, § 4).

Against the syllogism, nevertheless, a fundamental accusation has been brought since antiquity (Sextus Empiricus, Pyrrh. Hypot., II, 14, 1996): the universal major premise presupposes the particular conclusion and therefore, as a demonstrative process, the syllogism involves a vicious circle: in order to say that "every man is mortal" one must already know that "Socrates is mortal" as well. The uselessness of the syllogism for science is then repeated by Bacon (Nov. org., I, 13-14) and by Descartes, who asserts that in order to construct a syllogism one must have its matter beforehand: therefore by the syllogism nothing new is learned, and "vulgar" dialectic is entirely useless "rerum veritatem investigare cupientibus" (Reg. ad direct. ingenii, 10, ca. finem). The critique is developed at length by Locke, for whom the syllogism, "if it serves to demonstrate the connection between the proofs," "yet gives no help to our reason... in finding proofs and making new discoveries": the syllogism shows the connection between two extremes, given a middle term, "but that connection which the middle term has with one or the other of the extremes, no syllogism shows nor can show" (Ess., IV, ch. 17 §§ 4, 6; see Leibniz's reply in Nouv. Ess., IV, ch. 17). The objection was taken up thoroughly by J. Stuart Mill (v.): "a reasoning from the general to the particular cannot as such prove anything; for from a general principle we can infer no other particulars than those which the principle itself assumes as known" (System of Logic, II, ch. 3). In the syllogism, therefore, according to Mill, there is no inference. When the syllogism is constructed, the inference has already been completed; and hence the syllogism serves only as a test of the correctness of our inductive processes: it is not a method of research, but of interpretation and proof; and in this lies its irreplaceable usefulness.

Mill's difficulty arose, in part, from the erroneous empiricist presupposition of reducing the universal (v. UNIVERSALI) to a pure collection or sum of individuals. It does not seem, however, that every foundation must be denied to the objections against the syllogism. In particular, the syllogism in purely extensional terms (every man is mortal — Socrates is a man — Socrates is mortal) amounts substantially to a simple relation of subalternation between a general proposition and a particular proposition. Nor, generally, does the syllogistic form constitute the natural mode of the inference of thought. The movement of thought is effected through the connection that it discovers between a fact and a value, between the particular and the universal or between the universal and the particular. And, at the moment of research, this discovery is accomplished through the perceptive power of the mind, which does not unfold in an explicit syllogism, but rather involves it in the substance of its intuitive-discursive act. Aristotle himself noted that for the invention of the middle term — in which alone consists the truly progressive moment of knowledge, and which is prior to the formulation of the syllogism and is not accomplished by it — "sagacity" is required (ἀγχίνοια: Anal. post., I, 34, 89 b 10). For this reason the syllogistic schema is of no valid help, nor does it in fact intervene in the living and creative effort of thought, which proceeds by analysis, comparisons, direct confrontations of concepts and things, thus discoursing through the indefinite relations of the real (Plato's κοινωνία τῶν λόγων: Soph., 253 d, 257 a). And yet the essential structure of the syllogism underlies the deductive process of thought, which in the syllogism and its schemas rediscovers its clarification and logical necessity and therefore, as Aristotle rightly held, the instrument of science as demonstration (v.).

In Hegelian idealism, since the real is rationality, the syllogism, as the only possible form of rational content, assumes an absolute valuation: "the syllogism is the essential reason for being of every truth," and "everything is a syllogism" (Enc., § 181). In G. Gentile the syllogism, as an expression of objectified and abstract thought, is determined by the law of identity: circularity in the demonstrative process is therefore inevitable. If, accordingly, "the nature of thought thought, governed by the principle of identity, is fully expressed in the syllogism," it nevertheless has value only as a "moment of the dialectic of the act of thinking" (Sistema di logica, I, Florence 1940, p. 258).

1925, pp. 127-78 (cf. Enc., §§ 181-70); W. Leibniz, Nouv. est., IV, ch. 17; Italian trans., II, Bari 1926, pp. 244-69; G. Calogero, I fondamenti della logica aristotelica, Florence 1927, pp. 209-47; J. De Tonquédec, La critique de la connaissance, 2nd ed., Paris 1929, pp. 375-435; J. M. Le Blond, Logique et méthode chez Aristote, ibid. 1930, pp. 57-106; J. Fröbes, Logica, Rome 1940, pp. 187-265; W. D. Ross, Aristotele, Italian trans. by A. Spinelli, Bari 1946, pp. 45-72; F. H. Bradley, The principles of logic, I, 2nd ed., reprint, Oxford 1950, p. 243 add., and II; J. Locke, Essay on human knowledge, IV, ch. 17; Italian trans., II, Bari 1931, pp. 374-401, see also LOGICA; RAGIONAMENTO.

Ugo Viglino