| (i) | Some S is not M1, | |
| All M2 is M1, | ||
| All M3 is M2, | ||
| All M4 is M3, | ||
| All P is M4, | ||
| therefore, | Some S is not P. | |
| (ii) | Some M4 is not P, | |
| All M4 is M3, | ||
| All M3 is M2, | ||
| All M2 is M1, | ||
| All M1 is S, | ||
| therefore, | Some S is not P. | |
Analysing the first of the above, and inserting the suppressed conclusions in square brackets, we have—375
| Some S is not M1, | |
| All M2 is M1, | |
| [therefore, | Some S is not M2,] |
| All M3 is M2, | |
| [therefore, | Some S is not M3,] |
| All M4 is M3, | |
| [therefore, | Some S is not M4,] |
| All P is M4, | |
| therefore, | Some S is not P. |
This is the only resolution of the sorites possible unless the order of the premisses is transposed, and it will be seen that all the resulting syllogisms are in figure 2 and in the mood Baroco. The sorites may accordingly be said to be in the same mood and figure. It is analogous to the Aristotelian sorites, the subject of the conclusion appearing in the premiss stated first, and the suppressed premisses being all minors in their respective syllogisms.
The corresponding analysis of (ii) yields the following:—
| Some M4 is not P, | |
| All M4 is M3, | |
| [therefore, | Some M3 is not P,] |
| All M3 is M2, | |
| [therefore, | Some M2 is not P,] |
| All M2 is M1, | |
| [therefore, | Some M1 is not P,] |
| All M1 is S, | |
| therefore, | Some S is not P. |
These syllogisms are all in figure 3 and in the mood Bocardo ; and the sorites itself may be said to be in the same mood and figure. It is analogous to the Goclenian sorites, the predicate of the conclusion appearing in the premiss stated first, and the suppressed premisses being majors in their respective syllogisms.
It will be observed that the rules given in the preceding section have not been satisfied in either of the above sorites, the reason being that the rules in question correspond to the special rules of figure 1, and do not apply unless the sorites is 376 in that figure. For such sorites as are possible in figures 2, 3, and 4, other rules might be framed corresponding to the special rules of these figures in the case of the simple syllogism.
It is not maintained that sorites in other figures than the first are likely to be met with in common use, but their construction is of some theoretical interest.[408]
[408] The examples given in the text have been purposely chosen so as to admit of only one analysis, which was not the case with the examples given in the first two editions of this work. The original examples were, however, perfectly valid, and further light may be thrown on the general question by a brief reply to certain criticisms passed upon those examples. The following was given for figure 2 (the suppressed conclusions being inserted in square brackets), and it was said to be analogous to the Aristotelian sorites:—