In Chapter IV, Mill treats in greater detail the proof to which he believes utility is susceptible. This proof consists of a combination of moral intuition and analysis of our basic moral conceptions. In particular, he treats the moral concept of virtue through a utilitarian lens in order to justify the utilitarian foundation of morality.
Mill begins by reiterating the general remarks on proof he offered at the end of Chapter I. The upshot is that moral theory cannot be tested by scientific standards, but must rather be tested by its equivalent: a reasoned analysis of moral intuition. This is of course dependent upon the moral perceptions endowed by the conscience, which Mill introduced in the previous chapter.
The first account Mill gives of moral proof here is that the greatest happiness principle is morally intuitive. He compares this to sensory data, saying that moral facts are evidenced by sensing them inwardly just as evidence of a sound is in hearing it. In this way, Mill maintains, the greatest happiness principle is evidenced by everyone desiring happiness and seeing happiness as a good, meaning that morality as an aggregate of these inclinations would be represented as the greatest happiness principle.
Yet Mill recognizes that this is not a sufficient account of proof for utilitarianism by any means. He immediately anticipates an objection this line of reasoning invites: for utilitarianism to hold, people must only desire happiness and see no other virtues or objectives as good. Mill knows this is untrue, and cites as a particular case the fact that people desire virtue and the absence of vice.
Mill contends that this can actually bolster the argument in favor of utilitarianism because other apparent moral virtues are explicable within a purely utilitarian framework. The basic mode of his argument is that virtue, initially desired for the ends that it promotes, can become an object of intrinsic happiness in light of those ends. Thus virtue becomes an end to be sought in utilitarian pursuit of the greatest happiness.
The move Mill makes here is critical because, if accepted, it encapsulates virtually all moral mandates and general goals under the umbrella of utilitarianism. All moral ends, Mill argues, are so sought because they have become the object of happiness, much in the same way music or a desire for health might. In this framework, all moral considerations are underpinned by the greatest happiness principle.
Mill is well aware of the strength of this theory, and, having laid it out, has little else to say on the matter. He has presented the analytical tools for justifying a utilitarian framework of ethics. Having done so, he returns to people's rational faculties for the ultimate proof: if we practice disciplined self-consciousness and reflection on our motives and desires, he contends, there will be little doubt that his utilitarian account is true.
The pushback here is whether Mill's sweeping move of reducing all other morals to matters of utility is in fact justified. Given what a strong claim it is, Mill has a substantial burden of proof in defending it. It is not entirely clear that he meets this burden of proof.
In the spirit of the philosophical thought experiment, consider for a moment a classic anti-hero: someone who categorically does what is virtuous yet takes no pleasure from it. When pressed as to why he acts the way he does, he does not say, "I love virtue"; rather, he says, "I truly wish I did not do so, yet I must because this is my duty." What could a utilitarian do to account for this?
A similar example could be drawn from sacrifice. Suppose one jumps in front of a trolley to save people tied to the track and dies in the process. Is the best explanation of his action that he calculated the happiness of the multiple people on the track to be worth more than his own? It seems intuitively to be more reasonable to say that he was concerned with some moral principle such as the sanctity of life or an obligation to help victims.
A utilitarian may well have a response to this, but the point, simply put, is thus: we would most likely describe both of these people as doing moral good. How can we account for that if hedonism is the only explanation available to us?
In Mill's defense, we should note that there is a distinction between a theory of morals describing how morality functions, and what people consciously think in the process of making moral decisions. Mill seems to be more concerned with the former than the latter. All the same, it seems unclear how he could argue with simplicity from utilitarianism for either of these problem cases. Indeed, it might be easier for him to simply deny that these two people were acting morally.