The first Chapter of Mill's treatise covers a general outline of his argument. He briefly discusses his reasons for writing the treatise, his goals for the work, and the moves he will make in arguing for his specific brand of utilitarianism.
Mill begins with a discussion of theories and first principles, drawing an analogy between the sciences and the study of morality. He contends that science is done by moving from first principles to general theory, whereas the order of reasoning is reversed in the case of morality. The reason for this is that the objects that take morality - i.e., actions - are determined by theory on the part of the agent, and principles are to be derived therefrom.
Mill describes the difficulty posed by the first principles of morality, particularly due to contention as to whether morality exists a priori (independent of experience) or a posteriori (dependent upon empirical evidence). The problem here, he contends, is an issue with where the authority of moral judgments stems from. He comes down on the side of a posteriori reasoning because he sees the maxims of a priori moral reasoning as being derived in a manner that is unjustified and out of touch with reality.
To illustrate the point made about a priori moral reasoning, Mill takes German philosopher Immanuel Kant as a brief example. The famous categorical imperative of Kant's ethics hold that one ought only to act in a manner that might be willed into a universal maxim. Mill contends that this imperative allows all sorts of immoral behavior to be justified, unless considerations of utility are taken into account.
This critique of Kant serves as Mill's segue into utilitarianism. He acknowledges that he will be putting all other ethical theories aside in considering the theoretical structure of utilitarianism. While he does not delve into reasons for this, one might assume that he sees an argument that Kant, the most popular deontologist, depends upon consequentialist concerns of utility, and is sufficient for the pursuit of utility thereafter.
Mill frames his paper by discussing the proof to which moral theory is susceptible, given that it cannot be proven in the typically understood meaning of direct proof. The proof that Mill plans to implement essentially amounts to an appeal to reason, depending upon the participatory analysis of a thoughtful reader. The line of argumentation is predicated upon the notion that evidence can be strengthened by the assent of one's intellectual faculties in learning about the evidence.
With that background, Mill outlines the course he will take in the body of his treatise. The beginning of the treatise is populated by clarifications and Mill's own revisions to utilitarian theory, designed so as to respond to objectors to utilitarianism while also laying a groundwork for Mill's own theory. The latter part of the treatise is devoted to more nuanced points of proof of utilitarianism, and how it fits into concepts like virtue and justice.
Though this section is brief, it is important to pay attention to the particulars because Mill is effectively framing the lens through which his moral discourse will be defined. As such, it is our opportunity as readers to vet and debate the most basic premises upon which Mill's work is founded.
There are a few points on which we could press Mill. One question is whether he actually has the order of analysis regarding first principles and general theory right. He does note that science is founded on underlying metaphysical theory; why, we might ask, does he not draw an analogy between this and grounding ethical analysis on underlying metaethical theory?
We will not pursue this line of questioning very much further because Mill's theory is not particularly concerned with the scope of metaethics; nonetheless, at the outset we ought to be aware that he is making certain assumptions about what moral truth exists and how we can come to know it. He does believe that moral truths exist and, though he makes a point of appealing to reasoned analysis beyond moral intuition, there is a question as to what difference this distinction makes, given that the object of our analysis is only our basic moral intuitions.
Without delving too much into a defense of Kantian ethics, we should acknowledge that Mill is probably using a straw man whenever he refers to Kant. His point is that ethical precepts divorced of pragmatic considerations do not translate well into actual ethical practices. Those looking for a precise refutation of Kant here are not liable to find it.
While these thoughts could be framed as critiques of Mill, it is probably more useful to see them as understanding with greater precision what Mill is trying to drive at. Utilitarianism is a theory of how basic human moral sentiments are translated into moral action; Mill's point in this first section is simply to make that sentiment relation apparent, and to emphasize that analysis of sentiment cannot be divorced from considerations of action.