We will talk about what utilitarianism is, how the utilitarians argued for their view, and how they defended it against the most prominent type of objection they faced.
Utilitarianism is characterized by two elements:
A hedonistic account of good and bad: good and bad ultimately consist in pleasurable or painful feelings.
A consequentialist account of right and wrong: an action or policy is right if it produces better consequences than the alternatives and wrong if it does not.
You can see how this would work in practice by looking at Bentham, chapter 4, §V.
Generally speaking, the utilitarians support their view by arguing that it is implicit in common sense morality, meaning the moral codes that we all follow in our everyday lives. For the most part, they say, these codes are implicitly utilitarian: they work to produce the best results overall. When they do not work this way, according to the utilitarians, they should be regarded as irrational.
In making their points, the utilitarians had to adopt two different postures towards common sense morality. On the one hand, common sense morality provides the chief support for utilitarianism. The reason we are given for believing utilitarianism is that it is implicit in our common sense moral codes. We are supposed to be implicitly committed to utilitarianism, even if we are not aware of it.
On the other hand, the utilitarians try to show that our common sense moral codes are not all that we take them to be. For example, Mill challenges the common sense view of justice. We think that our beliefs about justice reflect independent standards of conduct that we call the principles of justice. In reality, he argues, our beliefs about justice are the product of a variety of internal psychological forces. They are not formed in response to any external standards at all. Thus when our ideas about justice conflict with utilitarianism, he maintains, only the utilitarian view will actually make sense.
In sum, the utilitarians both rely on common sense morality and undermine it. There is obviously some tension between these two things and it is not obvious that they can manage it.
Mill realized that the chief objection to utilitarianism is that it diverges too much from common sense morality, specifically concerning justice. Roughly speaking, if the social good comes into conflict with the interests of an individual, the social good will always win. That raises legitimate concerns about whether individual rights will be ignored in order to maximize utility for the group.
Mill takes three stabs at addressing this problem. In my opinion, the second and third are the most successful.
His second argument maintains that our common thinking about justice is muddled and frequently contradictory. Adopting utilitarianism, he maintains, is the only way to clean up the mess. Strictly speaking, he only shows that it is a way. If someone else were to come up with an equally sophisticated way of putting things in order, then this argument would not necessarily favor utilitarianism over that alternative. This is something that we will see John Rawls try to do later in the term.
Mill’s third argument is the familiar one that common sense ideas about justice are implicitly utilitarian. We think that justice requires respect for and enforcement of our rights. Our rights, in turn, protect our most important interests in personal security and property. But if an interest is genuinely important, Mill reasons, utilitarianism will want to protect it too: it promotes the good of the group by protecting the most important interests of the individuals that make up the group. Of course, people think that their individual rights trump the interests of the group too. But there, Mill says, they are just mistaken.