There are, then, wholes which possess the property that their value is different from the sum of the values of their parts, and the relations which subsist between such parts and the whole of which they form a part have not hitherto been distinctly recognised or received a separate name. Two points are especially worthy of notice. (1) It is plain that the existence of any such part is a necessary condition for the existence of that good which is constituted by the whole. And exactly the same language will also express the relation between a means and the good thing which is its effect. But yet there is a most important difference between the two cases, constituted by the fact that the part is, whereas the means is not, a part of the good thing for the existence of which its existence is a necessary condition. The necessity by which, if the good in question is to exist, the means to it must exist is merely a natural or causal necessity. If the laws of nature were different, exactly the same good might exist, although what is now a necessary condition of its existence did not exist. The existence of the means has no intrinsic value; and its utter annihilation would leave the value of that which it is now necessary to secure entirely unchanged. But in the case of a part of such a whole as we are now considering, it is otherwise. In this case the good in question cannot conceivably exist, unless the part exist also. The necessity which connects the two is quite independent of natural law. What is asserted to have intrinsic value is the existence of the whole; and the existence of the whole includes the existence of its part. Suppose the part removed, and what remains is not what was asserted to have intrinsic value; but if we suppose a means removed, what remains is just what was asserted to have intrinsic value. And yet (2) the existence of the part may itself have no more intrinsic value than that of the means. It is this fact which constitutes the paradox of the relation which we are discussing. It has just been said that what has intrinsic value is the existence of the whole, and that this includes the existence of the part; and from this it would seem a natural inference that the existence of the part has intrinsic value. But the inference would be as false as if we were to conclude that, because the number of two stones was two, each of the stones was also two. The part of a valuable whole retains exactly the same value when it is, as when it is not, a part of that whole. If it had value under other circumstances, its value is not any greater, when it is part of a far more valuable whole; and if it had no value by itself, it has none still, however great be that of the whole of which it now forms a part. We are not then justified in asserting that one and the same thing is under some circumstances intrinsically good, and under others not so; as we are justified in asserting of a means that it sometimes does and sometimes does not produce good results. And yet we are justified in asserting that it is far more desirable that a certain thing should exist under some circumstances than under others; namely when other things will exist in such relations to it as to form a more valuable whole. It will not have more intrinsic value under those circumstances than under others; it will not necessarily even be a means to the existence of things having more intrinsic value; but it will, like a means, be a necessary condition for the existence of that which has greater intrinsic value, although, unlike a means, it will itself form a part of the more valuable existent. (§ 19 ¶ 1)