(1)  All B is C,
All A is B,
therefore, All A is C ;
(2)  All C is D,
All A is C,
therefore, All A is D ; 371
(3)  All D is E,
All A is D,
therefore, All A is E.

Here the premiss originally stated first is the minor premiss of (1), the conclusion of (1) is the minor premiss of (2), that of (2) the minor premiss of (3); and so it would go on if the number of propositions constituting the sorites were increased.

In the Goclenian sorites, the premisses are the same, but their order is reversed, and the result of this is that the premiss originally stated first and the suppressed conclusions become major premisses in successive syllogisms. Thus, the Goclenian sorites given above may be analysed into the three following syllogisms,—

(1)  All D is E,
All C is D,
therefore, All C is E ;
(2)  All C is E,
All B is C,
therefore, All B is E ;
(3)  All B is E,
All A is B,
therefore, All A is E.

Here the premiss originally stated first is the major premiss of (1), the conclusion of (1) is the major premiss of (2); and so on.

The so-called Aristotelian sorites[405] is that to which the 372 greater prominence is usually given; but it will be observed that the order of premisses in the Goclenian form is that which corresponds to the customary order of premisses in a simple syllogism.[406]

[405] This form of sorites ought not properly to be called Aristotelian; but it is generally so described in logical text-books. The name sorites is not to be found in any logical treatise of Aristotle, though in one place he refers vaguely to the form of reasoning which the name is now employed to express. The distinct exposition of this form of reasoning is attributed to the Stoics, and it is designated sorites by Cicero; but it was not till much later that the name came into general use amongst logicians in this sense. The form of sorites called the Goclenian was first given by Professor Rudolf Goclenius of Marburg (1547 to 1628) in his Isagoge in Organum Aristotelis, 1598. Compare Hamilton, Logic, I. p. 375; and Ueberweg, Logic, § 125. It may be added that the term sorites (which is derived from σωρὸς, a heap) was used by ancient writers in a different sense, namely, to designate a particular sophism, based on the difficulty which is sometimes found in assigning an exact limit to a notion. “It was asked,—was a man bald who had so many thousand hairs; you answer, No: the antagonist goes on diminishing and diminishing the number, till either you admit that he who was not bald with a certain number of hairs, becomes bald when that complement is diminished by a single hair; or you go on denying him to be bald, until his head be hypothetically denuded.” A similar puzzle is involved in the question,—On what day does a lamb become a sheep? Sorites in this sense is also called sophisma polyzeteseos or fallacy of continuous questioning. See Hamilton, Logic, i. p. 464.

[406] The mistake is sometimes made of speaking of the Goclenian sorites as a regressive form of argument. It is clear, however, that in both forms of sorites we pass continuously from premisses to conclusions, not from conclusions to premisses.

A sorites may of course consist of conditional or hypothetical propositions; and it is not at all unusual to find propositions of these kinds combined in this manner. Theoretically a sorites might also consist of alternative propositions; but it is not likely that this combination would ever occur naturally.

325. The Special Rules of the Sorites.—The following special rules may be given for the ordinary Aristotelian sorites, as defined in the preceding section:—
(1) Only one premiss can be negative; and if one is negative, it must be the last.
(2) Only one premiss can be particular; and if one is particular, it must be the first.