546 w. BLAIR NEATBY: EXISTENTIAL IMPORT OF PROPOSITIONS. It seems to me, therefore, that the view that every categorical proposition implies the existence of its subject, a view which appears, as already stated, to be required by the very nature of the case, is strongly confirmed by an examination of the alleged exceptions ; for we have seen that the selected propositions that are categorical in form without implying the existence of the sub- ject, not only admit of easy and natural expression in hypothetical form, but are not true propositions, in the sense of accurately and adequately expressing a judgment, until they have been so ex- pressed. There is one class of propositions that is possibly an exception. I refer to propositions of which the very object is to deny the existence of the subject. If these propositions are real exceptions it is of no consequence, since our rule will not seem less simple and satisfactory when stated with the requisite qualification, as follows : Every categorical proposition implies the existence of its subject, unless it explicitly denies it. But however little objection there is to admitting an exception in such a sense, it is far from certain that we ought to do so. If I say, The Olympian gods have no existence, I cannot mean to deny an existence that I have implied a score of times before in various statements about them. I must be speaking of a totally different order of existence, viz., existence in the universe of actual things ; and this seems all that is intended to be denied. There will then be no ground for questioning that there is in such propositions an existential implication in reference to the appro- priate universe. Confirmation of the view maintained in this paper is furnished by the simple consideration that any proposition that does not imply the existence of its subject must needs siqypose it. The hypothetical nature of the proposition is then not far to seek. A further confirmation may be obtained by a glance at proposi- tions that present themselves in a hypothetical form. If we ex- press in categorical form as many of these as we can, we shall find that whenever the resulting proposition does not imply the existence of its subject, it does not express (without alteration or loss) the meaning of the original proposition ; in other words, the hypo- thetical clause is essential to the expression of the judgment. This indicates that the distinction between categorical proposi- tions and hypothetical propositions is real and vital ; and the simplest test that can be supplied lies in the implication of the existence of the subject in every true categorical. In a true (or pure) hypothetical, on the other hand, nothing is taken for granted. If we discarded the terms Categorical and Hypothetical, we could not alter the fact that all propositions now included under either of them fah 1 into two distinct classes, composed respectively of those that have existential implication and those that have it not, and that those that have it not can never find unequivocal ex- pression without a hypothetical clause. W. BLAIR NEATBY.
