exactly numerable, but in his being aboriginal and originative; in a word, in his self-activity, in his being a centre of autonomous social recognition; yet exactly numerable he indeed is, and must be, not confusable with any other, else his professed autonomy, his claim of rights and his sense of duty, can have no significance, must vanish in the universal confusion belonging to the indefinite. Nor, on the other hand, is it at all true that a number has to be a point or an instant, nor that things when numbered and counted are implicitly pinned upon points or, at all events, upon instants. It may well enough be the fact that in our empirical use of number we have to employ Time, or even Space, but it is a gaping _non sequitur_ to conclude that we therefore can count nothing but the placed and the dated. Certainly we count whenever we _distinguish_,--by whatever means, on whatever ground. To think is, in general, at least to "distinguish the things that differ;" but this will not avail except we keep account of the differences; hence the One and the Many lie in the very bosom of intelligence, and this fundamental and spontaneous contrast can not only rive Time and Space into expressions of it, in instants and in points, but travels with thought from its start to its goal, and as organic factor in mathematical science does indeed, as Plato in the _Republic_ said, deal with absolute being, if yet dreamwise; so that One and Many, and Many as the sum of the ones, makes part of the measure of that primally real world which the world of minds alone can be. If the contrast One and Many can pass the bounds of the merely phenomenal, by passing the temporal and the spatial; if it applies to universal being, to the noumenal as well as to the phenomenal; then the absolutely real world, so far as concerns this essential condition, can be a world of genuine individuals, identifiable, free, abiding, responsible, and there can be a real moral order; if not, then there can be no such moral world, and the deeper thought-conceptions to which we now approach must be regarded, at the best, as fair illusions, bare ideals, which the serious devotee of truth must shun, except in such moments of vacancy and leisure as he may venture to surrender, at intervals, to purely hedonic uses. But if the One and the Many are not dependent on Time and Space, their universal validity is possible; and it has already been shown that they are not so dependent, are not thus restricted.