Note 389 — Chapter VI

Archbishop Thomson’s definition of the disjunctive syllogism—“An argument in which there is a disjunctive judgment” (Laws of Thought, p. 197)—must be regarded as too wide if, as is usually the case, an affirmative judgment with a disjunctive predicate is considered disjunctive. It would include such a syllogism as the following,—B is either C or D, A is B, therefore A is either C or D. The argument here in no way turns upon the alternation contained in the major premiss, and the reasoning may be regarded as an ordinary categorical syllogism in Barbara, the major term being complex.

Logicians have not, as a rule, given any distinctive recognition to arguments consisting of two disjunctive premisses and a disjunctive conclusion; and Mr Welton goes so far as to remark that “both premisses of a syllogism cannot be disjunctive since from two assertions as indefinite as disjunctive propositions necessarily are, nothing can be inferred” (Logic, p. 327). It is, however, clear that this is erroneous, if an argument consisting of two hypothetical premisses and a hypothetical conclusion is possible, and if a hypothetical can be reduced to the disjunctive form. As an example we may express in disjunctives the hypothetical syllogism given on page 348: Either Q is not true or R is true, Either P is not true or Q is true, therefore, Either P is not true or R is true. Here questions of modality are left on one side. They would not, however, in any case materially affect the argument.