Mill continues to refine some of the issues that arise as a result of the stratification of types of pleasure, then addresses more general objections to the fundamentals of utilitarianism. The issues that Mill address here take two major forms: first, there is the issue that the establishment of a higher form of pleasure invokes the image of a paragon of humanity, prompting the issue of what it means for the moral theory that not everyone lives up to that paragon. Second, there is the matter of whether or not happiness is a plausible moral metric in the first place.
The first objection that Mill anticipates to his definition of higher pleasures is that men oftentimes choose a lesser, baser pleasure over a higher, intellectual pleasure. Mill sees this as a non-issue on the grounds that choosing a lesser pleasure does not necessarily mean it is valued more than the higher pleasure; rather, men will simply sometimes choose a more immediate, less valuable pleasure, all the while aware that they are choosing the less valuable pleasure. Mill explains the psychology of this as a weakness of character on the agent's part.
The second issue Mill fields is just how necessary the differentiation of this kind of pleasure is to the theory of utilitarianism. Interestingly, Mill posits that his exact account of different kinds of pleasures could actually be dispensed with, while still maintaining the theory of utilitarianism. His reason for this is that application of the greatest happiness principle alone would naturally tend towards a noble character by considering the happiness of others as much as one's own; in effect, this would yield the same result as explicit differentiation of kinds of pleasure.
Mill next considers arguments concerned with how much happiness humans can have, if any. The first such concern is whether humans can be happy at all. Mill first points out that this is not a real threat to the theory, because a sufficient component of the greatest happiness principle is the mitigation of unhappiness and pain, and so happiness need not actually be received for utilitarianism to function. He also points out that as happiness is not framed as a constant, implausible state of excitement, but rather as various transient pleasures, it is very hard to say that it can never occur.
The following concern is whether happiness could be the ultimate ends of humanity and the source of morality if so many have a moderate or otherwise small share of it. Mill's response is that two goal states of being, tranquility and excitement, reconcile people to happiness with less pleasure or more pain, respectively. He sees the only causes of a truly unsatisfactory life as a lack of intellectual cultivation, and selfishness.
With these fundamentals laid out, Mill is in a position to comment on the implications utilitarianism has for truly doing without happiness, vis-à-vis sacrifice of one's own happiness. The greatest happiness principle is crucial to this in one major way: it allows that one can morally sacrifice one's own happiness or interests insofar as the happiness or pain of others is concerned. Thus, one who jumps on a landmine to save others could be morally justified, but one who practices asceticism for reasons other than the happiness of others could not.
Of note in Chapter II is that Mill points out that some simply see that standards of utilitarianism as too high for humanity, even after seeing the principles clearly. Mill makes the point, but contends that this is no matter particular to utilitarianism, but rather a general feature of ethical theory: these are ethical tenets towards which people must strive, and the difficulty people have in following the ethical norms have no bearing on their validity.
A question here is where weakness of character fits into Mill's ethical model. According to Mill, people's pleasures and preferences form the basis from which morality is derived; to then make the move that people preferring pleasures that are morally lesser constitutes only weakness of character seems like suspiciously circular reasoning. If someone prefers a lesser pleasure, what ground is there for it being lesser?
A possible response is that the preference of the individual does not reflect the preference of the majority, an issue that also tracks in regards to democracy. A question to pose in this case is how people in the minority would be able to function morally, because their preferences would seem to necessarily put them in the moral wrong by nature of majority rule. It is difficult to say that such a moral denouncement would be anything but arbitrary.
In regards to Mill's response to the matter of whether or not feeling pleasure is possible, it is interesting to consider someone who can feel neither pleasure nor pain - say, someone who has for whatever tragic reason been left numb to all matters of pleasure and pain. How would such a person be treated in Mill's world? It seems as though they would not matter because the greatest happiness principle would not endow them with any moral status. One could see this as a problem for the moral framework set forth by Mill.
What of sacrifice? It is interesting to consider the degree to which a utilitarian could reasonably sacrifice one's own happiness. Competing concerns leave the answer anything but obvious, and probably outside the scope of Mill's treatise.
For example: someone who sacrifices a passionate career in the circus for a dispassionate career as a doctor could be said to surrender some of one's personal happiness for the happiness of others in an admirable way. But what about a doctor who jumped in front of a trolley to save five workers tied to the track? The five workers might have more capacity for happiness than the one doctor, but the doctor might also have been able to save more than five people throughout his professional career, had he not sacrificed himself. Despite these blind spots, Mill makes it clear that the capacity for pleasure, or the mitigation of pain, is at the heart of human morality.