A syllogism is an artificial, logical arrangement of a natural deductive process known as argumentation. It was invented and perfected by aristotle, although other Greek thinkers, particularly Theophrastus, the Stoics and the Megarians, made substantial additions. In the Middle Ages the syllogism became identified with scholastic method, and it was much ridiculed by the founders of modern science in the 17th century. Recent studies, however, including those in symbolic logic, have vindicated the concern of ancient and medieval thinkers for this instrument of human thought. In its apodictic form, or dem onstration, the syllogism is man's most powerful device for the attainment of truth and certitude (see logic, history of).
Nature and Kinds of Syllogism. The argumentation expressed by a syllogism involves three elements: the antecedent, or truth already known; the conclusion or new truth; and the inference of the mind connecting these two. In the syllogism, the antecedent is made up of propositions called premises, usually two in number. The conclusion is also a proposition, preceded by a "therefore" to signify the act of inference. While inference itself is not artificial, since it is a natural act of the mind (called rea soning), the forced disposition of the antecedent and conclusion according to logical laws is artificial, that is, it is imposed on the mind by mind itself in order to attain truth more easily and with less error. Thus syllogism is a logical tool that makes the natural deductive process more accurate, much as learning to eat correctly is an artificial imposition that assists the natural process of nutrition.
The two principal types of syllogism are the categorical and the hypothetical. The difference lies in the formal structure and the type of inference, as is explained below.
Categorical Syllogism. The categorical syllogism is defined as an argumentation in which two terms are compared with a third term in the antecedent, and the conclusion states that the two terms agree or do not agree with each other. An example is the following:
All things composed of matter are corruptible.
But all men are things composed of matter.
Therefore all men are corruptible.
In this example, the first two propositions constitute the antecedent; the proposition "Therefore all men are corruptible" is the conclusion. The subject term of the conclusion, "men," is the minor term and the premise that contains this term is called the minor premise. The predicate term, "corruptible," is the major term and the premise that contains it is called the major premise. The term repeated in both premises but not found in the conclusion, that is, "things composed of matter," is known as the middle term.
The categorical syllogism is validated by two basic principles of logic, the so-called dictum de omni and dictum de nullo. The first states that whatever is distributively and universally predicated of some subject must be affirmed of all included under that subject; the second states that whatever is universally and distributively denied of a subject must be denied of all included under that subject (see predication). These principles are similar to the mathematical propositions: two things equal to a third are equal to each other, and two things not equal to a third are not equal to each other.
Rules for the Syllogism. From the nature of the categorical syllogism certain laws follow that govern its use. These may be summarized as follows: (1) There can be only three terms in such a syllogism, one of which (the middle term) cannot appear in the conclusion. From this law, logicians deduce that only four "figures" of the categorical syllogism are possible. The following shows the four figures of the categorical syllogism and the possible arrangements of the subject term (S), the predicate term (P) and the middle term (M):
(2) A term in the conclusion cannot have a wider extension than in the premises, for the effect cannot be greater than the cause. (3) The middle term must be used universally at least once, otherwise one cannot be certain that this subject term is included under this predicate term. (4) If one premise is negative or particular, the conclusion must be negative or particular. (5) When both premises are negative or particular, no conclusion is possible.
Mnemonics and the Laws. When these rules are applied to the various figures of the categorical syllogism, only a limited number of forms, or moods, are found to be valid within each figure. These valid moods can be recognized with the aid of the following mnemonics or memory aids, devised by logicians for this purpose:
First Figure: Barbara, Celarent, Darii, Ferio.
Second Figure: Cesare, Camestres, Festino, Baroco.
Third Figure: Darapti, Felapton, Disamis, Datisi, Bocardo, Ferison.
Fourth Figure: Bamalip, Calemes, Dimatis, Fesapo, Fresison.
The first three vowels in these mnemonics indicate whether the major premise, the minor premise, and conclusion, in order, are A, E, I, or O (see proposition). Some of the consonants, similarly, indicate how various moods can be reduced to the four basic moods of the first figure. The first figure is considered the most perfect, because it best illustrates the principles on which the categorical syllogism is based, while the mood Barbara, being composed of three universal affirmative propositions, is regarded as the most perfect form of the first figure.
Related Forms. The polysyllogism is a series of categorical syllogisms so arranged that the conclusion of the previous syllogism becomes a premise of the next. The enthymeme is a categorical syllogism with one premise merely implied; it is employed with great effect in rhet oric. The singular syllogism, called an expository syllogism if the singular term is the middle term, is a post-Aristotelian development; its validity as a form of categorical syllogism is controverted. The sorites is a categorical syllogism resulting from a concatenation of middle terms. The modal syllogism is made up of propositions that have a modality apart from being true or false, such as, necessary, possible, or problematical; while not much discussed in traditional logic, it is undergoing extensive development in symbolic logic (see logic, symbolic; mode).
Hypothetical Syllogism. The hypothetical syllogism is defined as an argumentation that has a hypothetical proposition as a major premise. Hence the basic forms of this syllogism derive from the forms of the hypothetical proposition, namely, conditional, disjunctive and alternative. The conditional syllogism, most important among the hypotheticals, has two valid figures: one posits the condition in the minor premise, and then posits the conditioned in the conclusion; the other denies the conditioned in the minor premise, and denies the condition in the conclusion. The frequent use of the other possibilities constitutes the fallacy of consequence.
See Also: deduction; first principles; proof;
Bibliography: i. m. bochenski, A History of Formal Logic, tr. i. thomas (Notre Dame, Ind. 1961). s. caramella, Enciclopedia filosofica, 4 v. (Venice-Rome 1957) 4:615–620. r. eisler, Wörterbuch der philosophischen Begriffe, 3 v. (4th ed. Berlin 1927–30) 2:757–771. j. a. oesterle, Logic: the Art of Defining and Reasoning (2d ed. Englewood Cliffs, N.J. 1963). v. e. smith, The Elements of Logic (Milwaukee 1957). e. d. simmons, The Scientific Art of Logic (Milwaukee 1961).
syl·lo·gism / ˈsiləˌjizəm/ • n. an instance of a form of reasoning in which a conclusion is drawn (whether validly or not) from two given or assumed propositions (premises), each of which shares a term with the conclusion, and shares a common or middle term not present in the conclusion (e.g., all dogs are animals; all animals have four legs; therefore all dogs have four legs). ∎ deductive reasoning as distinct from induction: logic is rules or syllogism.DERIVATIVES: syl·lo·gis·tic / ˌsiləˈjistik/ adj.syl·lo·gis·ti·cal·ly / ˌsiləˈjistik(ə)lē/ adv.