But unfortunately the position for him [viz., Henry Sidgwick] was not so simple as this. He had also to consider the relation between Egoistic and Universalistic Ethical Hedonism, and here he finds an insuperable difficulty. If it be admitted that there is a Total or Universal Good, then it is no doubt my duty to aim at maximising this and to regard the Good which resides in me and my experiences as important only in so far as it is a part of the Total Good. In that case I must be prepared to sacrifice some or all of my Good if by that means and by that only I can increase the Total Good. But the consistent Egoist will not admit that there is a Total or Universal Good. There is my Good and your Good, but they are not parts of a Total Good, on his view. My duty is to aim at maximising my Good, and to consider the effects of my actions on your Good only in so far as they may indirectly affect mine. Your duty is to aim at maximising your Good, and to consider the effects of your actions on my Good only in so far as they may indirectly affect yours. It is plain that there is no logical inconsistency in this doctrine. And Sidgwick goes further. He says that it is plain that X is concerned with the quality of X's experiences in a way in which he is not concerned with the quality of Y's experiences, whoever Y may be. And it is impossible to feel certain that this distinction is not ethically fundamental. Thus Sidgwick is left in the unfortunate position that there are two principles, each of which separately seems to him self-evident, but which when taken together seem to be mutually inconsistent.
(C. D. Broad, Five Types of Ethical Theory [London and Henley: Routledge & Kegan Paul, 1930], 158-9)
Note from KBJ: Egoism and utilitarianism are rival normative ethical theories. Each is internally consistent, as Sidgwick saw. Some people are attracted to egoism; some are attracted to utilitarianism. Some people are appalled by egoism; some are appalled by utilitarianism. It is folly to try to "prove" one theory or "disprove" the other. Nor does it make sense to say that one theory is "true" and the other "false." Normative ethical theories aren't the sorts of things that can be true or false. So what can philosophers contribute? They can elaborate the theories (distinguishing, for example, between act egoism and rule egoism); they can draw out the implications of each theory, so that others can decide which (if any) to subscribe to; and they can defend a theory from criticism. John Stuart Mill (1806-1873), for example, did all of these things with respect to utilitarianism. He also tried to "prove" utilitarianism, while simultaneously denying that such a thing is possible. Almost nobody is convinced by his attempted proof.
