Page:Philosophical Review Volume 3.djvu/150

Nor do these two instances exhaust the whole case. There is a third case, different from both the current formula and the one just explained. If I mean by my proposition, or its sign, the whole and no less than the subject, as in the combined use of "any and every," and "each and every," and occasionally the world "all," the relations of Opposition must stand as in Fig. 2.

But a still more complicated result occurs when we take the particular proposition, or the term "some" to mean something else than what is assumed in the ordinary view. As already stated, in the usual acceptation of formal logic, "some" means a part, and it may or may not be all; but in actual practice it often, if not most frequently, means only a part, or not all, and this fact very greatly alters the whole relation of Opposition. Sir William Hamilton, looking at this matter, went so far as to propose that this meaning of the term be adopted as the proper one for formal logic. The relations of Opposition expressed by it would be as in Fig. 3. This shows us nothing but a relation of contradiction all the way through, except in the case of I and O, and we can understand why Hamilton desired to establish this usage as the proper one, because it so greatly simplifies the principles for practice. He did not live, however, to develop his doctrine.