Note 407 — Chapter VII

Sir William Hamilton indeed professes to give sorites in the second and third figures, which have, he says, been overlooked by other logicians (Logic, II. p. 403). It appears, however, that by a sorites in the second figure he means such a reasoning as the following,—No B is A, No C is A, No D is A, No E is A, All F is A, therefore, No B, or C, or D, or E, is F ; and by a sorites in the third figure such as the following,—A is B, A is C, A is D, A is E, A is F, therefore, Some B, and C, and D, and E, are F. He does not himself give these examples; but that they are of the kind which he intends may be deduced from his not very lucid statement, “In second and third figures, there being no subordination of terms, the only sorites competent is that by repetition of the same middle. In first figure, there is a new middle term for every new progress of the sorites; in second and third, only one middle term for any number of extremes. In first figure, a syllogism only between every second term of the sorites, the intermediate term constituting the middle term. In the others, every two propositions of the common middle term form a syllogism.” But it is clear that in the accepted sense of the term these are not sorites at all. In each case the conclusion is a mere summation of the conclusions of a number of syllogisms having a common premiss; in neither case is there any chain argument. Hamilton’s own definition of the sorites, involved as it is, might have saved him from this error. He gives for his definition, “When, on the common principle of all reasoning,—that the part of a part is a part of the whole,—we do not stop at the second gradation, or at the part of the highest part, and conclude that part of the whole, but proceed to some indefinitely remoter part, as D, E, F, G, H, &c., which, on the general principle, we connect in the conclusion with its remotest whole,—this complex reasoning is called a Chain-Syllogism or Sorites” (Logic, I. p. 366). In connexion with Hamilton’s treatment of this question, Mill very justly remarks, “If Sir W. Hamilton had found in any other writer such a misuse of logical language as he is here guilty of, he would have roundly accused him of total ignorance of logical writers” (Examination of Hamilton, p. 515).