Note 408 — Chapter VII
Reading edition
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:—
All A is B,
No C is B,
[therefore, No A is C],
All D is C,
[therefore, No A is D],
All E is D,
therefore, No A is E.
It has, to begin with, been objected that the above is Goclenian, and not Aristotelian, in form, “the subject of each premiss after the first being the predicate of the succeeding one.” This overlooks the more fundamental characteristic of the Aristotelian sorites, that the first premiss and the suppressed conclusions are all minors in their respective syllogisms. It has further been objected that the following analysis might serve in lieu of the one given above:—AaB, CeB, [∴ CeA,] DaC, [∴ DeA], EaD, ∴ AeE. No doubt this analysis is a possible one, but the objection to it is its heterogeneous character. The first premiss and the first suppressed conclusion are majors, while the last suppressed conclusion is a minor. Again, the first syllogism is in figure 2, the second in figure 1, and the third in figure 4. It must be granted that what has been above called a heterogeneous analysis is in some cases the only one available, but it is better to adopt something more homogeneous where possible. If the first premiss of a sorites contains the subject, and the last the predicate, of the conclusion, then the last premiss is necessarily the major of the final syllogism; and hence the rule may be laid down that we can work out such a sorites homogeneously only by treating the first premiss and all the suppressed conclusions as minors, and all the remaining premisses as majors, in their respective syllogisms. A corresponding rule may be laid down if the first premiss contains the predicate, and the last the subject, of the conclusion.
It will be found that a sorites in figure 4 cannot have more than a limited number of premisses. This point is raised in section 335.