Page:The World and the Individual, First Series (1899).djvu/295

276 ideal objects, which may never come to be in valid Being at all. In fact, genuinely universal judgments, as Herbart and a good many more recent Logicians have taught, are essentially hypothetical in their true nature. But for that very reason, like the hypothetical judgments, the universal judgments, taken in their strictest sense, apart from special provisos, are judgments that undertake to exclude from the valid Reality certain classes of objects. To say that All A is B, is, in fact, merely to assert that the real world contains no objects that are A’s, but that fail to be of the class B. To say that No A is B is to assert that the real world contains no objects that are at once A and B. Neither judgment, strictly interpreted, tells you that A exists, but only that if it exists, it is B. Now those mathematical judgments, of whose endless wealth and eternal validity we have heretofore spoken, are very frequently, although by no means always, of the universal type. They refer to Being, — a Being of the third type, — and, when universal, they assert, about a realm of definite or relatively determinate, although still universal validity, or possibility, something that proves to be primarily negative, so far as its relation to its external object is concerned. They accomplish their assertions by means of the very fact that they undertake to exclude from the realm of externally valid Being, certain ideal combinations that, in the first place, would have seemed abstractly possible, if one had not scrutinized one’s ideas more closely. Thus, to know that universally 2 + 2 = 4, is to know that there nowhere exists, in all the realm of external validity, a two and a two that, when added, fail to give, as the result, four. In advance of