The book is framed as the search for a solution to a global problem that cannot be solved by the kinds of moral standards that command intuitive assent and work well within particular communities. Greene calls this problem the “tragedy of commonsense morality.” In a nutshell, it is the tragedy that moralities that help members of particular communities to cooperate peacefully do not foster a comparable harmony among members of different communities.
Morality evolved to enable cooperation, but this conclusion comes with an important caveat. Biologically speaking, humans were designed for cooperation, but only with some people. Our moral brains evolved for cooperation within groups, and perhaps only within the context of personal relationships. Our moral brains did not evolve for cooperation between groups (at least not all groups).
...To solve this problem Greene thinks we need what he calls a “metamorality,” based on a common currency of value that all human beings can acknowledge, even if it conflicts with some of the promptings of the intuitive moralities of common sense. Like others who have based their doubts about commonsense morality on diagnoses of its evolutionary pedigree, Greene thinks that this higher-level moral outlook is to be found in utilitarianism, which he proposes to re-name “deep pragmatism” (lots of luck). Utilitarianism, as propounded by Bentham and Mill, is the principle that we should aim to maximize happiness impartially, and it conflicts with the instinctive commonsense morality of individual rights, and special heightened obligations to those to whom one is related by blood or community. Those intuitive values have their uses as rough guides to action in many ordinary circumstances, but they cannot, in Greene’s view, provide the basis for universally valid standards of conduct.
No, they can't. But so what? Why should we feel obligated to seek a "universally valid standard" of conduct anyway? Why should the abstract category of species membership trump other considerations, not least of which Dunbar's number? What's wrong with a fatalist acceptance of a certain, irreducible amount of tragedy in the human condition? And thus we're back to metaphysics after all, where your answers, whatever they may be, are a product of those intuitive gut feelings, not a product of objective reason from a God's-eye perspective.
Alain de Botton, before he devoted himself full-time to his new, self-appointed position as secular existential shepherd to lost souls, offered a concise, illuminating summary of one particular philosopher's objection to utilitarianism:
Nietzsche's antipathy to alcohol explains simultaneously his antipathy to what had been the dominant British school of moral philosophy: Utilitarianism, and its greatest proponent, John Stuart Mill. The Utilitarians had argued that in a world beset by moral ambiguities, the way to judge whether an action was right or wrong was to measure the amount of pleasure and pain it gave rise to. The thought of Utilitarianism, and even the nation from which it had sprung, enraged Nietzsche:
European vulgarity, the plebianism of modern ideas [is the work and invention of] England. Man does not strive for happiness; only the English do that.
He was, of course, also striving for happiness; he simply believed that it could not be attained as painlessly as the Utilitarians appeared to be suggesting:
All these modes of thought which assess the value of things according to pleasure and pain, that is to say according to attendant and secondary phenomena, are foreground modes of thought and naïveties which anyone conscious of creative powers and an artist's conscience will look down on with derision.
An artist's conscience because artistic creation offers a most explicit example of an activity which may deliver immense fulfillment but always demands immense suffering. Had Stendahl assessed the value of his art according to the 'pleasure' and 'pain' it had at once brought him, there would have been no advance from L'Homme qui craint d'être gouverné to the summit of his powers. Instead of drinking beer in the lowlands, Nietzsche asked us to accept the pain of the climb.