Henry Sidgwick, answered from the texts and cited to the page.
The question is broad, so let me give you the architecture as I understand it from the inside. My central project, set out in The Methods of Ethics, is to examine the three methods by which reflective persons actually reason about conduct: egoism, which directs each agent to pursue his own greatest good; intuitionism, which appeals to self-evident moral rules; and utilitarianism, which directs us toward the greatest happiness of all.
My aim was not to champion one against the others from the outset, but to press each until it either stood firm or gave way. The intuitional method, when examined carefully, yields something important. The common maxims of ordinary morality — keep promises, speak truth, requite benefits — prove too vague and exception-ridden to serve as genuine first principles.
But beneath them lie a very few axioms that do survive rigorous scrutiny. The axiom of justice holds that similar cases ought to be treated similarly. The axiom of prudence holds that mere position in time gives a good no greater rational claim. And the axiom of rational benevolence holds that the good of any one individual is of no more importance, from the point of view of the universe, than the good of any other.1
From these two latter intuitions — prudence and benevolence — one may deduce that each person is morally bound to regard the good of any other individual as much as his own.2 It is this axiom of rational benevolence that provides, in my view, the rational foundation for the utilitarian principle itself.3 So I arrive at utilitarianism not by rejecting intuition but by pressing through it.
The utilitarian first principle is one of the few intuitions that stand the test of rigorous criticism.4 Mill, by contrast, tried to prove the principle of utility by observing that people desire happiness — but that inference, from the fact of desire to the conclusion of desirability, is precisely where his argument requires supplementation of the kind my intuitional procedure supplies.5
Yet utilitarianism, once established, must still face the intuitionist who holds other formulae as independently self-evident — principles of truth, justice, and the rest. The utilitarian must show that these have only a dependent and subordinate validity: that they are general rules admitting of exceptions, that their fundamental notions are vague and need determination, and that when they conflict with one another some higher principle is required to adjudicate.6
The utilitarian standard is that higher principle. The honest difficulty — and I will not conceal it — is that rational egoism also presents itself to reflection with the character of self-evidence. That my own good on the whole is what I have most reason to promote seems, when I examine it, no less evident than the axiom of benevolence. Where the two coincide, there is no problem; where they part, I could find no self-evident principle to rank one above the other. That is the dualism of practical reason, and it is the finding my inquiry could not resolve.
the good of any one individual is of no more importance, from the point of view (if I may say so) of the Universe, than the good of any other; unless, that is, there are special grounds for believing that more good is likely to be realised in the one case than in the other.The Methods of Ethics
each one is morally bound to regard the good of any other individual as much as his own, except in so far as he judges it to be less, when impartially viewed, or less certainly knowable or attainable by him.The Methods of Ethics
the axiom of Rational Benevolence is, in my view, required as a rational basis for the Utilitarian system.The Methods of Ethics
This, it will be remembered, is the reasoning that I used in chap. xiii. of the preceding book in exhibiting the principle of Rational Benevolence as one of the few Intuitions which stand the test of rigorous criticism.The Methods of Ethics
I find the need of some such procedure to complete the argument very plain and palpable... 'The sole evidence it is possible to produce that anything is desirable, is that people do actually desire it.'The Methods of Ethics
The Utilitarian must, in the first place, endeavour to show to the Intuitionist that the principles of Truth, Justice, etc. have only a dependent and subordinate validity: arguing either that the principle is really only affirmed by Common Sense as a general rule admitting of exceptions and qualifications... and further, that the different rules are liable to conflict with each other, and that we require some higher principle to decide the issue thus raised.The Methods of Ethics