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# syllogism

A syllogism (properly, a categorical syllogism) is the inference of one proposition from two premises. An example is: all horses have tails; all things with tails are four-legged; so all horses are four-legged. Each premise has one term in common with the conclusion, and one term in common with the other premise. The term that does not occur in the conclusion is called the middle term. The major premise of the syllogism is the premise containing the predicate of the conclusion (the major term), and the minor premise contains its subject (the minor term). So the first premise of the example is the minor premise, the second the major premise, and ‘having a tail’ is the middle term. The four kinds of proposition distinguished in syllogistic reasoning are universal affirmatives (all men are mortal), called A propositions, particular affirmatives (some men are sick), called I propositions, universal negatives (no men are trustworthy), called E propositions, and particular negatives (some men are not lawyers), called O propositions. This enables syllogisms to be classified according to the form of the premises and the conclusions (see also square of opposition ). The other classification is by figure, or way in which the middle term is placed in the premises. The conclusion is always of subject–predicate (S–P) form, and the middle term is M. The four figures are illustrated in the diagram:
syllogism.jpg
The example given was a syllogism of the first figure. Mnemonics, in the form of names with the vowels indicating the A, E, I, O, forms, help students to remember the valid forms, called moods of the syllogism. Valid syllogisms of the first figure are Barbara (AAA), Celarent (EAE), Darii (AII), and Ferio (EIO); of the second, Cesare, Camestres, Festino, and Baroco; of the third, Darapti, Disamis, Datisi, Felapton, Bocardo, and Ferison; and of the fourth, Bramantip, Camenes, Dimaris, Fesapo, and Fresison. Rules exist for converting one form to another, and every valid syllogism may be converted to a syllogism of the first figure. Another set of rules concerns the distribution of terms. Roughly, a term is distributed if it covers all of its class. A test is whether the proposition containing the term must remain true if the term is qualified. Thus ‘all men are mortal’ distributes the term ‘man’ because it implies that all blind men are mortal; ‘not every animal is useful’ does not distribute ‘animal’ because it does not imply that not every farmyard animal is useful. A syllogism cannot be valid unless the middle term is distributed at least once, and any term distributed in the conclusion must be distributed in its premise. Although the theory of the syllogism dominated logic until the 19th century, it remained a piecemeal affair, able to deal with only a relatively small number of valid forms of argument. There have subsequently been rearguard actions attempting to extend the power of syllogistic reasoning, but in general it has been eclipsed by the modern theory of quantification (see also predicate calculus ), which gives greater expressive power for less complexity.

Philosophy dictionary. . 2011.

### Look at other dictionaries:

• Syllogism — Syl lo*gism, n. [OE. silogisme, OF. silogime, sillogisme, F. syllogisme, L. syllogismus, Gr. syllogismo s a reckoning all together, a reasoning, syllogism, fr. syllogi zesqai to reckon all together, to bring at once before the mind, to infer,… …   The Collaborative International Dictionary of English

• syllogism — late 14c., from O.Fr. silogisme a syllogism, from L. syllogismus, from Gk. syllogismos a syllogism, originally inference, conclusion, computation, calculation, from syllogizesthai bring together, premise, conclude, lit. think together, from syn… …   Etymology dictionary

• syllogism — index corollary Burton s Legal Thesaurus. William C. Burton. 2006 …   Law dictionary

• syllogism — ► NOUN ▪ a form of reasoning in which a conclusion is drawn from two given or assumed propositions (premises); a common or middle term is present in the two premises but not in the conclusion, which may be invalid (e.g. all dogs are animals; all… …   English terms dictionary

• syllogism — [sil′ə jiz΄əm] n. [ME silogisme < MFr < L syllogismus < Gr syllogismos, a reckoning together < syllogizesthai, to reckon together, sum up < syn , together + logizesthai, to reason < logos, word: see LOGIC] 1. an argument or form …   English World dictionary

• Syllogism — A syllogism (Greek: συλλογισμός – syllogismos – conclusion, inference ) is a kind of logical argument in which one proposition (the conclusion) is inferred from two or more others (the premises) of a certain form. In antiquity, there were… …   Wikipedia

• syllogism — /sil euh jiz euhm/, n. 1. Logic. an argument the conclusion of which is supported by two premises, of which one (major premise) contains the term (major term) that is the predicate of the conclusion, and the other (minor premise) contains the… …   Universalium

• SYLLOGISM —    the TRADITIONAL term used in DEDUCTIVE LOGIC for an argument with a specific structure that includes two PROPOSITIONS and a conclusion. On the basis of its formal structure a syllogism may be judged logically VALID. If the propositions are… …   Concise dictionary of Religion

• syllogism — /ˈsɪlədʒɪzəm / (say siluhjizuhm) noun 1. Logic an argument with two premises and a conclusion. Both the premises of a categorical syllogism are categorical propositions, containing just three distinct terms between them, e.g. all men are mortal… …   Australian English dictionary

• syllogism — UK [ˈsɪləˌdʒɪz(ə)m] / US [ˈsɪləˌdʒɪzəm] noun [countable] Word forms syllogism : singular syllogism plural syllogisms a statement that consists of three facts, the third of which is proved by the first two …   English dictionary