[402] The distinction which follows is ordinarily applied to chains of reasoning only; but the reader will observe that it admits of application to the case of the simple syllogism also.

[403] On the distinction between progressive and regressive arguments, see Ueberweg, Logic, § 124.

An epicheirema is a polysyllogism with one or more prosyllogisms briefly indicated only. That is, one or more of the syllogisms of which the polysyllogism is composed are enthymematic. The following is an example:

All B is D, because it is C,
All A is B,
therefore, All A is D.[404]

[404] A distinction has been drawn between single and double epicheiremas according as reasons are enthymematically given in support of one or both of the premisses of the ultimate syllogism. The example given in the text is a single epicheirema; the following is an example of a double epicheirema:

All P is Y, because it is X ;
All S is P, because all M is P ;
therefore, All S is Y.

The epicheirema is sometimes defined as if it were essentially a regressive chain of reasoning. But this is hardly correct, if, as is usually the case, examples such as the above are given; for it is clear that in these examples the argument is only partly regressive.

370 324. The Sorites.—A sorites is a polysyllogism in which all the conclusions are omitted except the final one, the premisses being given in such an order that any two successive propositions contain a common term. Two forms of sorites are usually recognised, namely, the so-called Aristotelian sorites and the Goclenian sorites. In the former, the premiss stated first contains the subject of the conclusion, while the term common to any two successive premisses occurs first as predicate and then as subject; in the latter, the premiss stated first contains the predicate of the conclusion, while the term common to any two successive premisses occurs first as subject and then as predicate. The following are examples:

Aristotelian Sorites,—All A is B,
All B is C,
All C is D,
All D is E,
therefore, All A is E.
Goclenian Sorites,—All D is E,
All C is D,
All B is C,
All A is B,
therefore, All A is E.

It will be found that, in the case of the Aristotelian sorites, if the argument is drawn out in full, the first premiss and the suppressed conclusions all appear as minor premisses in successive syllogisms. Thus, the Aristotelian sorites given above may be analysed into the three following syllogisms,—