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THE DISJUNCTIVE JUDGMENT. 497 is not B we can say it is C, but only if we have already sub- sumed this particular thing under A ; the proof must always rest on this assumption. This is one way of stating the objections to the value of the disjunctive syllogism. Mr. Bosanquet has indeed gone so far as to assert that the dis- junctive syllogism is no inference, but that the whole of the inference is contained in the major premiss the disjunctive judgment which is itself an inference. This is surely mis- leading, and I shall try to show that the disjunctive syllogism has a certain limited value in science but that the value of the inference lies wholly in the modus tollendo ponens. The judgment which we are here considering may be, for want of a better name, styled the divisive disjunction. In matters of empirical knowledge it is, as Sigwart (Logic, i., p. 230, Eng. Trans.) points out, preceded by the divisive judgment ' Some A is B and some A is C '. Both predi- cates are considered as actual or realisable. It is what Mr. Keynes (Formal Logic, p. 232, third edition) refuses to regard as a true alternative, but merely an " alter- native synthesis of terms ". Mr. Bosanquet however (Logic, i., p. 345) thinks it to be the " true or ideal disjunction" ; it is a "generic judgment whose content is developed or interrelated by the aid of hypothetical ". It is, of course, different from the ' disjunction of ignor- ance '. We may have judgment of both types about the same subject. Thus we may say * The triangle is either equilateral, isosceles or scalene ' a true divisive disjunction and again, * the triangle is either an arbitrary fiction of the imagination or an objective determination of reality '.. In divisive disjunctions the subject is used distributively or as a system of interrelated parts or functions ; in disjunc- tions of ignorance, on the other hand, the subject is viewed non-distributively, i.e., as an individual in the strict sense. If ' the signal light is either red or green ' is not a disjunction of ignorance, it must be a predication about the functions of the signal light and tell us that sometimes it shines green and at other times red. Now Mr. Bosanquet's objection to the disjunctive syl- logism is that the minor premiss adds no content to the disjunctive major. But is this so ? Surely we can specify in the minor under what conditions the signal shows either red or green. We may say " With the lever in the cabin so, the signal cannot be green, hence it is red ". Or again, if our subject be a genus ' A,' we may say, ' All A is either B or C,' but in the minor we are not limited to this ' A ' as a subject ; surely we may specify our subject 32