SYLLOGISM. — From Greek σύν-λόγος, λογισμός, it indicates the connection of ideas, discourse. The term, already used by Plato (Theaet., 189 d; Phil., 41 c) in a general sense, denotes reasoning (v.), inference, deduction (a meaning also figuratively suggested by σύν-λόγος, to gather; cf. the Latin colligere, to infer).
With Aristotle, to whom the systematic theory of the s. is owed, the term assumes a technical meaning: “a s. is a discourse in which, certain things being posited, something different follows of necessity, by virtue of those things being posited” (Anal. pr., I, 1, 24 b 19; cf. Top., I, 1, 100 a 25). This definition reveals the essential concept of the Aristotelian s. as an instrument of demonstration or apodictic proof. Whereas the διαλεκτις or Platonic division (Soph., 253 d), as a dialectical method, lacks formal necessity and is therefore merely an “impotent s.” (ἀσθενής σύν-λόγος, Anal. pr., I, 31, 46 a 33), the s., in its perfect form, “needs nothing beyond the premises to show the necessary consequence” (ibid., I, 24 b 22). Aristotle’s definition extends to every form of formal reasoning; it does not, properly speaking, include induction (v.), although he sometimes uses the expression “syllogismus ex inductione” (Anal. pr., II, 23, 68 b 15). Aristotle, in fact, contrasts s. and induction in a technical sense (Anal. pr., loc. cit.; Top., I, 72, 104 a 13).
The logical structure of the s. as a typical form of deductive reasoning consists in the comparison of two terms (concepts, νοήματα) with a third in which their mutual inclusion or exclusion is shown: the s. thus resolves into a mediated judgment (and hence 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 s. therefore comprises three terms: subject and predicate, or “extremes” (ἄκρα: the predicate, greater extreme: ὁ πρῶτος, ὁ μέσος; the subject, lesser extreme: ὁ ἐσχάτης, ὁ ἐκείνης) and the middle term (ὁ μέσος, τὸ μέσον: cf. Anal. pr., I, 4). The terms are arranged in three propositions: two premises (προτάσεις, τὰ κείμενα, τὰ πρότασις/μέσα), the major (τὰ μέσα) in which the predicate is related to the middle term, the minor (πρόληψις) in which the middle term is related to the subject; and the conclusion (ἐπίσκοπος, τὸ συμπέρασμα) which expresses the relation of agreement or exclusion between the predicate and the subject: “When three terms are so related that the last is contained in the middle and the middle is contained or not contained in the first, there necessarily exists a perfect s. that connects the extremes” (Anal. pr., I, 4, 25 b 32 sgg.), e.g., all mammals have pulmonary respiration, man is a mammal, therefore man has pulmonary respiration. The foundation of the logical force of the s. thus lies in the particular relation of predication or subordination that it establishes between the terms, expressed in the law: “if a predicate belongs to a subject, it also belongs to the predicate of that subject,” or “whatever is said of the predicate must also be said of the subject” (Cat., 5, 3 b 4-5). This formula is but an application of the principles of identity and non-contradiction and thus clarifies the universal formal necessity of the s. Kant expressed it in similar terms: “The first and universal law of all affirmative reasoning is... nota notae est nota rei ipsius; of all negative reasoning: ... repugnans notae repugnat rei ipsius” (Die falsche Spitzfindigkeit d. vier syllogistischen Figuren, § 2). The principle was also expressed by Aristotle in terms of extension: “what is said universally (καθόλου, καταπαντός) of a class must also be said of each individual subject contained in the class: if every man is mortal, and Socrates is a man, then Socrates is also mortal” (the principle “dictum de omni”: cf. Anal. post., I, 4, 72 a 28, and Anal. pr., I, 24 b 27).
The formula of identity (“two things equal to a third are equal to each other”), though 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 most precise understanding of the relation between the terms of the s.; nor is it perhaps the best formulation in itself, since the relation between terms in the propositions of the s. is not necessarily one of identity. From the nature of the s., Aristotle already deduced its fundamental law: “it is clear that every demonstration must proceed through three terms and no more” (Anal. pr., I, 25, 41 b 35); this rule, together with the other that requires the middle term to be taken universally in at least one premise (a middle term twice particular may resolve 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 term), was later elaborated into the traditional eight rules.
Aristotle’s theory is further developed (Anal. pr., I, 4 sgg.) in the determination of the figures (σχήματα) and modes (τόποι) of the s. The “figure” depends on the different placement of the middle term in the premises; the “mode” 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 term is subject in the major premise and predicate in the minor; in the second, it is predicate in both; in the third, it is subject in both. For each figure, the laws of inference are determined, and a method is set forth for reducing syllogisms of the second and third figures to the type of the first, which Aristotle (wrongly, it seems: cf. W. D. Ross, op. cit., in bibl., pp. 49-50) considered the only perfect and independent form of s. To the three Aristotelian figures
a fourth was later added (attributed to Galen [v.]), in which the middle term is predicate in the major premise and subject in the minor, and which is therefore rather a transposition of the first. Taking into account the laws of the individual figures, the arrangement of the middle term and the premises according to quantity and quality allows for 19 different valid modes of s., expressed in medieval scholasticism (first, it seems, in the *Summulae logicales* of P. Ispanus) by mnemonic verses, *Barbara Celarent Dari Ferio*, etc.; where the vowels of each term indicate the propositions of the s. in one of the four figures (e.g., *Barbara* denotes a s. with three universal affirmative propositions in the first figure). In Aristotle’s treatment, a detailed exposition follows of *modal* syllogisms, in which the modality (necessity or contingency) of the subject-predicate relation is also expressed (cf. *Anal. pr.*, I, caps. 9-22).
From the standpoint of matter or content, Aristotle distinguishes demonstrative s. (σ. ἀποδεικτικός, φιλοσοφικός), which proceeds from universal and necessary premises (*Anal. post.*, I, 4, 72 a 7, and 6, 75 b s.) and is thus founded on “essence” (*Met.*, VII, 9; XII, 4, 1078 b 24), and which is extensively developed in the *Posterior Analytics*; dialectical s. in repose (σ. διαλεκτικός, ἐπιγενέργημα), which from probable premises attempts the discovery of truth; contentious or sophistic s. (σ. ἐριστικός, σοφισμός) which “seems to demonstrate” but in reality does not (v. *Sofisma*); and rhetorical s. (σ. ἐνθυμήμα; a term later used, from Boethius onward, with a different meaning), which proceeds from analogies and examples (cf. *Top.*, VIII, 11, 162 a 15 and I, 1, 100 a 27 sgg.; *Anal. pr.*, II, 27, 70 a 10; and *Rhet.*, I, 1, 1355 a 6 sgg.). The derived forms of the s. that represent mere variations (polysyllogism and sorites) are not explicitly considered by Aristotle (the sorites—though not the term—is mentioned in *Anal. pr.*, I, 23, 41 a 18, and developed already by Alexander of Aphrodisias [v.]); nor are analogous forms of deductive reasoning treated (the so-called “disjunctive s.,” conditional s., and dilemma).
Such, in general terms, is the Aristotelian theory of the syllogism, which remained substantially unchanged through the countless commentaries and later developments. Aristotle displayed a particular sagacity of mind; he himself emphasizes with satisfaction his discovery: “On the method of exposition we had nothing before us to present, and we should personally have to make long and laborious investigations” (*De soph. elench.*, 34, 18 4 b 1 sgg.). Hegel, while noting that the Aristotelian stimulus refers solely to the forms of finite and abstract thought, does not hesitate to qualify Aristotle as, in a certain sense, “the naturalist of the spiritual forms of thought,” and his logic as “a work that most honorably reflects the depth and vigor of abstraction of its discoverer” (*Lezioni sulla storia della filosofia*, Italian trans. by G. Codignola and G. Sanna, I, Florence 1932, p. 374). The having fixed the forms of thought “which branch out like a network of infinite mobility within concrete thought” was a masterpiece of empiricism, and this awareness is of absolute value (ibid., p. 383). Leibniz offers a similar evaluation: “Je tiens que l'invention de la forme des syllogismes est une des plus belles de l'esprit humain et même des plus considérables” (*Nouv. ess.*, IV, cap. 17, § 4).
Nevertheless, from antiquity onward (Sextus Empiricus, *Pyrrh. Hypot.*, II, 14, 1996), a fundamental objection has been raised against the syllogism: the major premise presupposes the particular conclusion, and thus as a demonstrative process the syllogism involves a vicious circle. To be able to say that “every man is mortal,” one must already know that “Socrates is mortal.” The uselessness of the syllogism for science is then reiterated by Bacon (*Nov. org.*, I, 13-14) and by Carnesius, who asserts that to construct a syllogism one must already have its matter beforehand; hence, with the syllogism one learns nothing new, and dialectic “is altogether useless for those desirous of investigating the truth of things” (*Reg. ad direct. ingenii*, 10, ca. finem). Locke develops this critique at length, maintaining that the syllogism, “if it serves to demonstrate the connection between proofs,” “does not, however, give any aid to our reason... in finding proofs and making new discoveries”: the syllogism shows the connection between two extremes once a middle term is posited, “but that connection which the middle term has with either extreme no syllogism shows nor can show” (*Ess.*, IV, cap. 17 § 4, 6; see Leibniz’s reply in *Nouv. Ess.*, IV, cap. 17). This objection was taken up thoroughly by J. Stuart Mill (q.v.): “a reasoning from the general to the particular cannot as such prove anything; for from a general principle we cannot infer other particulars except those already assumed as known by the principle itself” (*System of logic*, II, cap. 3). In the syllogism, according to Mill, there is therefore no *inference*. When the syllogism is constructed, the inference is already complete; and thus the syllogism serves only as a *test* of the correctness of our inductive processes: it is not a method of discovery, but of interpretation and proof; and in this lies its irreplaceable utility.
Mill’s difficulty partly arose from the erroneous empiricist presupposition of reducing the universal (q.V. *Universali*) to a mere collection or sum of individuals. It does not, however, seem possible to deny all foundation to the objections raised against the syllogism. In particular, the syllogism in purely extensional terms (every man is mortal – Socrates is a man – therefore Socrates is mortal) is substantially equivalent to a simple relation of subalternation between a general proposition and a particular one. Nor, generally, does the syllogistic *form* constitute the natural mode of inference for thought. The movement of thought is realized through the connection 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 takes place through the perceptive power of the mind, which does not unfold in an explicit syllogism but rather involves it within the substance of its intuitive-discursive act. Aristotle himself noted that for the invention of the middle term—on which alone depends the true progressive moment of knowledge, and which is prior to the formulation of the syllogism and not achieved through it—“sagacity” (ἀγχίνοια) is required (*Anal. post.*, I, 34, 89 b 10). For this reason, the syllogistic schema is of no valid assistance, nor does it in fact intervene in the living and creative effort of thought, which proceeds through analysis, comparisons, direct confrontations of concepts and things, thereby discovering the indefinite relations of reality (τὰ λεχθέντα τῶν λόγων of Plato: *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 finds its necessary logical clarification; and thus, as rightly attributed to Aristotle, it is the instrument of science as demonstration (q.v.).
In Hegelian idealism, since the real is rationality, the syllogism, as the only possible form of rational content, assumes an absolute evaluation: “the syllogism is the *essential reason of being of every truth*,” and “everything is a syllogism” (*Enc.*, § 181). For G. Gentile, the syllogism, as an expression of objectified and abstract thought, is determined by the law of identity; hence circularity in the demonstrative process is inevitable. If, therefore, “the nature of thought thought, governed by the principle of identity, is fully expressed in the syllogism,” it nonetheless has value only as “a moment in the dialectic of the act of thought” (*Sistema di logica*, I, Florence 1940, p. 258).