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” andgive in consequence a valid conclusion from two particulars. This is due to the overlapping of the major and minor terms.