Yet Prof. Sidgwick holds that Egoism is rational; and it will be useful briefly to consider the reasons which he gives for this absurd conclusion. The Egoist, he says (last Chap § 1), may avoid the proof of Utilitarianism by declining to affirm, either implicitly or explicitly, that his own greatest happiness is not merely the ultimate rational end for himself, but a part of Universal Good. And in the passage to which he here refers us, as having there seen this, he says: It cannot be proved that the difference between his own happiness and another’s happiness is not for him all-important (IV. ii. § 1). What does Prof. Sidgwick mean by these phrases the ultimate rational end for himself, and for him all-important? He does not attempt to define them; and it is largely the use of such undefined phrases which causes absurdities to be committed in philosophy (§ 60 ¶ 1)

Is there any sense in which a thing can be an ultimate rational end for one person and not for another? By ultimate must be meant at least that the end is good-in-itself—good in our undefinable sense; and by rational, at least, that it is truly good. That a thing should be an ultimate rational end means, then, that it is truly good in itself; and that it is truly good in itself means that it is a part of Universal Good. Can we assign any meaning to that qualification for himself, which will make it cease to be a part of Universal Good? The thing is impossible: for the Egoist’s happiness must either be good in itself, and so a part of Universal Good, or else it cannot be good in itself at all: there is no escaping this dilemma. And if it is not good at all, what reason can he have for aiming at it? how can it be a rational end for him? That qualification for himself has no meaning unless it implies not for others; and if it implies not for others, then it cannot be a rational end for him, since it cannot be truly good in itself: the phrase an ultimate rational end for himself is a contradiction in terms. By saying that a thing is an end for one particular person, or good for him, can only be meant one of four things. Either (1) it may be meant that the end in question is something which will belong exclusively to him; but in that case, if it is to be rational for him to aim at it, that he should exclusively possess it must be a part of Universal Good. Or (2) it may be meant that it is the only thing at which he ought to aim; but this can only be, because, by so doing, he will do the most he can towards realising Universal Good: and this, in our case, will only give Egoism as a doctrine of means. Or (3) it may be meant that the thing is what he desires or thinks good; and then, if he thinks wrongly, it is not a rational end at all, and, if he thinks rightly, it is a part of Universal Good. Or (4) it may be meant that it is peculiarly appropriate that a thing which will belong exclusively to him should also by him be approved or aimed at; but, in this case, both that it should belong to him and that he should aim at it must be parts of Universal Good: by saying that a certain relation between two things is fitting or appropriate, we can only mean that the existence of that relation is absolutely good in itself (unless it be so as a means, which gives case (2)). By no possible meaning, then, that can be given to the phrase that his own happiness is the ultimate rational end for himself can the Egoist escape the implication that his own happiness is absolutely good; and by saying that it is the ultimate rational end, he must mean that it is the only good thing—the whole of Universal Good: and, if he further maintains, that each man’s happiness is the ultimate rational end for him, we have the fundamental contradiction of Egoism—that an immense number of different things are, each of them, the sole good.—And it is easy to see that the same considerations apply to the prhase that the difference between his own happiness and another’s is for him all-important. This can only mean either (1) that his own happiness is the only end which will affect him, or (2) that the only important thing for him (as a means) is to look to his own happiness, or (3) that it is only his own happiness which he cares about, or (4) that it is good that each man’s happiness should be the only concern of that man. And none of these propositions, true as they may be, have the smallest tendency to shew that if his own happiness is desirable at all, it is not a part of Universal Good. Either his own happiness is a good thing or it is not; and, in whatever sense it may be all-important for him, it must be true that, if it is not good, he is not justified in pursuing it, and that, if it is good, everyone else has an equal reason to pursue it, so far as they are able and so far as it does not exclude their attainment of other more valuable parts of Universal Good. In short it is plain that the addition of for him for me to such words as ultimate rational end, good, important can introduce nothing but confusion. The only possible reason that can justify any action is that by it the greatest possible amount of what is good absolutely should be realised. And if anyone says that the attainment of his own happiness justifies his actions, he must mean that this is the greatest possible amount of Universal Good which he can realise. And this again can only be true either because he has no power to realise more, in which case he only holds Egoism as a doctrine of means; or else because his own happiness is the greatest amount of Universal Good which can be realised at all, in which case we have Egoism proper, and the flagrant contradiction that every person’s happiness is singly the greatest amount of Universal Good which can be realised at all. (§ 60 ¶ 2)