INCOMPLETE SYLLOGISMS AND IRREGULAR ARGUMENTS. (1) Enthymeme. First, second and third orders. Natural form. (2) Epicheirema. Single, double. (3) Polysyllogism. Prosyllogism, episyllogism. (4) Sorites. Progressive, regressive. Two rules of each. (5) Irregular Arguments. Quantitative, plurative. =7. SUMMARY.= (1) An enthymeme is a syllogism in which one of the three propositions is omitted. Suppressing the major premise gives an enthymeme of the _first_ order; omitting the minor gives one of the _second_ order; while omitting the conclusion gives one of the _third_ order. The enthymeme is really the natural form of expression. Enthymemes of the first order are the most _common_ while those of the third order are the most _emphatic_. (2) An epicheirema is a syllogism in which one or more of the premises is an enthymeme. An epicheirema is said to be _single_ when but one premise is an enthymeme, and _double_ when both premises are enthymemes. (3) A polysyllogism is a series of syllogisms in which the conclusion of the _preceding_ syllogism becomes a premise of the _succeeding_ one. The one of the series whose conclusion becomes a premise is termed a prosyllogism; while the one which uses the conclusion as a premise is called an episyllogism. (4) A sorites is a series of syllogisms in which all the conclusions are omitted except the last one. The two kinds of sorites are the progressive and regressive. The progressive uses the “minor” as its first premise and adopts the form of the _fourth_ figure, whereas the regressive uses the “major” as its first premise and adopts the form of the _first_ figure. The two rules of the progressive sorites are, (1) “The first premise may be particular, all the others must be universal”; (2) “The last premise may be negative, all the others must be affirmative.” The two rules of the regressive are, (1) “The first premise may be negative, all the others must be affirmative”; (2) “The last premise may be particular, all the others must be universal”. (5) Irregular arguments are such as yield valid conclusions and yet do not conform to the syllogistic rules. The quantitative argument expresses quantity and contains four terms. This argument is based on the principle, “What ever is greater than a second thing which is greater than a third thing is itself greater than a third thing.” Plurative arguments are introduced by “more” or “most” and give in consequence a valid conclusion from two particulars. This is due to the overlapping of the major and minor terms. =8. REVIEW QUESTIONS.= (1) Define and illustrate an enthymeme. (2) Illustrate the enthymemes of the three orders and point out their distinct uses. (3) Why should the enthymeme demand closer thought than the ordinary syllogism? (4) Define and illustrate the epicheirema. (5) Of what use is the epicheirema? Illustrate.