The present explanation would be utterly misconceived if it were supposed to disparage mathematics. By calling the quantitative characteristic merely external and indifferent, we provide no excuse for indolence and superficiality, nor do we assert that quantitative characteristics may be left to mind themselves, or at least require no very careful handling. Quantity, of course, is a stage of the Idea: and as such it must have its due, first as a logical category, and then in the world of objects, natural as well as spiritual. Still even so, there soon emerges the different importance attaching to the category of quantity according as its objects belong to the natural or to the spiritual world. For in Nature, where the form of the Idea is to be other than, and at the same time outside, itself, greater importance is for that very reason attached to quantity than in the spiritual world, the world of free inwardness. No doubt we regard even spiritual facts under a quantitative point of view; but it is at once apparent that in speaking of God as a Trinity, the number three has by no means the same prominence, as when we consider the three dimensions of space or the three sides of a triangle;--the fundamental feature of which last is just to be a surface bounded by three lines. Even inside the realm of Nature we find the same distinction of greater or less importance of quantitative features. In the inorganic world, Quantity plays, so to say, a more prominent part than in the organic. Even in organic nature when we distinguish mechanical functions from what are called chemical, and in the narrower sense, physical, there is the same difference. Mechanics is of all branches of science, confessedly, that in which the aid of mathematics can be least dispensed with,--where indeed we cannot take one step without them. On that account mechanics is regarded next to mathematics as the science _par excellence_; which leads us to repeat the remark about the coincidence of the materialist with the exclusively mathematical point of view. After all that has been said, we cannot but hold it, in the interest of exact and thorough knowledge, one of the most hurtful prejudices, to seek all distinction and determinateness of objects merely in quantitative considerations. Mind to be sure is more than Nature and the animal is more than the plant: but we know very little of these objects and the distinction between them, if a more and less is enough for us, and if we do not proceed to comprehend them in their peculiar, that is their qualitative character.