§ 808. It is sometimes more appropriately called the chain-argument, and map be defined as-- A train of reasoning, in which one premiss of each epi-syllogism is supported by a pro-syllogism, the other being taken for granted. This is its inner essence. § 809. In its outward form it may be described as--A series of propositions, each of which has one term in common with that which preceded it, while in the conclusion one of the terms in the last proposition becomes either subject or predicate to one of the terms in the first. § 810. A sorites may be either-- (1) Progressive, or (2) Regressive. _Progressive Sorites_. All A is B. All B is C. All C is D. All D is E. .'. All A is E. _Regressive Sorites_. All D is E. All C is D. All B is C. All A is B. .'. All A is E. § 811. The usual form is the progressive; so that the sorites is commonly described as a series of propositions in which the predicate of each becomes the subject of the next, while in the conclusion the last predicate is affirmed or denied of the first subject. The regressive form, however, exactly reverses these attributes; and would require to be described as a series of propositions, in which the subject of each becomes the predicate of the next, while in the conclusion the first predicate is affirmed or denied of the last subject. § 812. The regressive sorites, it will be observed, consists of the same propositions as the progressive one, only written in reverse order. Why then, it may be asked, do we give a special name to it, though we do not consider a syllogism different, if the minor premiss happens to precede the major? It is because the sorites is not a mere series of propositions, but a compressed train of reasoning; and the two trains of reasoning may be resolved into their component syllogisms in such a manner as to exhibit a real difference between them. § 813. The Progressive Sorites is a train of reasoning in which the minor premiss of each epi-syllogism is supported by a pro-syllogism, while the major is taken for granted. § 814. The Regressive Sorites is a train of reasoning in which the major premiss of each epi-syllogism is supported by a pro-syllogism, while the minor is taken for granted. _Progressive Sorites_. (i) All B is C. All A is B. .'. All A is C. (2) All C is D. All A is C. .'. All A is D. (3) All D is E. All A is D. .'. All A is E. _Regressive Sorites_. (1) All D is E. All C is D. .'. All C is E. (2) All C is E. All B is C. .'. All B is E. (3) All B is E. All A is B. .'. All A is E. § 815. Here is a concrete example of the two kinds of sorites, resolved each into its component syllogisms-- _Progressive Sorites_. All Bideford men are Devonshire men. All Devonshire men are Englishmen. All Englishmen are Teutons. All Teutons are Aryans. .'. All Bideford men are Aryans.