syllogism

syllogism a mode of argument that forms the core of the body of Western logical thought. Aristotle defined syllogistic logic, and his formulations were thought to be the final word in logic; they underwent only minor revisions in the subsequent 2,200 years. Every syllogism is a sequence of three propositions such that the first two imply the third, the conclusion. There are three basic types of syllogism: hypothetical, disjunctive, and categorical. The hypothetical syllogism, modus ponens, has as its first premise a conditional hypothesis: If p then q; it continues: p, therefore q. The disjunctive syllogism, modus tollens, has as its first premise a statement of alternatives: Either p or q; it continues: not q, therefore p. The categorical syllogism comprises three categorical propositions, which must be statements of the form all x are y, no x is y, some x is y, or some x is not y. A categorical syllogism contains precisely three terms: the major term, which is the predicate of the conclusion; the minor term, the subject of the conclusion; and the middle term, which appears in both premises but not in the conclusion. Thus: All philosophers are men (middle term); all men are mortal ; therefore, All philosophers (minor term) are mortal (major term). The premises containing the major and minor terms are named the major and minor premises, respectively. Aristotle noted five basic rules governing the validity of categorical syllogisms: The middle term must be distributed at least once (a term is said to be distributed when it refers to all members of the denoted class, as in all x are y and no x is y ); a term distributed in the conclusion must be distributed in the premise in which it occurs; two negative premises imply no valid conclusion; if one premise is negative, then the conclusion must be negative; and two affirmatives imply an affirmative. John Venn, an English logician, in 1880 introduced a device for analyzing categorical syllogisms, known as the Venn diagram. Three overlapping circles are drawn to represent the classes denoted by the three terms. Universal propositions ( all x are y, no x is y ) are indicated by shading the sections of the circles representing the excluded classes. Particular propositions ( some x is y, some x is not y ) are indicated by placing some mark, usually an "X," in the section of the circle representing the class whose members are specified. The conclusion may then be read directly from the diagram.

syllogism Logical argument consisting of three categorical propositions: two premises and a conclusion. It was devised by Aristotle to establish the conditions under which the conclusion of a deductive inference is valid or not valid. A valid conclusion can only come from premises that are logically related to each other. Examples of syllogisms are as follows: All men are mortal; John is a man; therefore John is mortal (valid); All trees have leaves; a daffodil has leaves; therefore a daffodil is a tree (invalid).

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.