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544 W. BLAIR NEATBY: soever class usually imply the existence of the subject ; that some universal propositions, both negative and affirmative, are excep- tions, but that the rule holds good universally in the case of both particular and singular propositions. The following selection from Dr. Keynes' list of examples will be found, I believe, sufficiently representative : All candidates arriving five minutes late are fined one shilling ; Who steals my purse steals trash ; An honest miller has a golden thumb ; A planet moving in a hyperbolic orbit can never return to any position it once occupied ; No unicorns have ever been seen. Now most at any rate of these and the other alleged exceptions are hypothetical propositions, some such clause as, If such there be, If any one should, etc., being plainly understood. So clearly is this the case that speakers who affect great precision make a point of expressing a clause of the kind, and the only objection ever made against doing so is that it savours of a pedantic accuracy. Dr. Keynes anticipates this objection, and rules it out on grounds that seem to me altogether unsatisfactory. He says that the point at issue is "whether we ever meet with propositions in ordinary discourse which are categorical in form, and yet are hypothetical so far as the existence of their subjects is concerned" ; and he says that " this point must be decided in the affirmative ". But surely when we examine for logical purposes the usages of speech, it is material to us to know whether a usage is exact or slovenly, correct or incorrect ; or rather, it is understood that we have to do only with correct usages, since otherwise we can have no guarantee that a given proposition is after all the expression of a judgment. Now it is of vital importance to observe that these propositions as they stand may perfectly well imply the existence of the sub- ject. A Cambridge man, relating various circumstances that had come under his notice at the University, might very well say : Freshmen are treated as inferior creatures ; Candidates that arrive late at the examinations are fined ; The lowest Junior Optime gets a wooden spoon. Here the existential implication is quite clear. How is it that the same form of words can be also used to express a radically different judgment? Simply because sometimes the connexion in which the words occur implies a hypothetical clause so powerfully that it is waste of time to express it. This means that the judgment is partly expressed, and partly left to be under- stood. But if ambiguous statements are allowed in the witness- box, I do not see why erroneous statements (i.e., statements expressing a totally different judgment from that intended) should not also be admitted, and then there is no end to the confusion. I contend that Logic, as the Science of Eeasoning, has nothing to do with any proposition that is not the sufficient and unequivocal expression of a judgment. The above is no picked case. Take the negative example : No unicorns have ever been seen. The words might conceivably be