Practical reason is the faculty for determining the will, which operates by applying a general principle of action to one's particular situation. A principle is either a mere maxim if it is based on the agent's desires or a law if it holds universally. A principle that presupposes a previous desire for some object in the agent always presupposes that the agent happens to be the sort of person who cares for that sort of thing. But what the agent is interested in is contingent, and so that principle is no law.
Suppose this is right. Then what can the practical law possibly be? If I say that the law is to serve God, the principle can be attacked on its dependence on interest in God, if I say that the law is to seek the greatest good, the principle can be attacked on its dependence on interest in the greatest good, etc. The answer is that the source of the law-likeness of the practical law must lay not in its content, but solely in its law-like, that is, universally applicable, form.
Even if a law is law-like solely because of its form, it must still have some content, if it is to exist. The content must be nothing over and above the law's form, though, otherwise it will become dependent on what desires the law's possessor has. The law must then be: "so act that the maxim of your will could always hold at the same time as a principle in a giving of universal law."
Now Kant asks, is there anything else we can say about a will acting on the practical law? We can say that it is acting on the idea of a form of law, an idea of reason, and having nothing to do with the senses. So the moral will is independent of the world of the senses, the world where it might be constrained by one's contingent desires. It is, therefore, free. Reciprocally: if a will is free, then it must, as a will, be governed by a rule, and yet not a rule whose matter restricts the freedom of the will. The only appropriate rule is the rule whose matter is equivalent to its form, the categorical imperative. And so we see that following the practical law is being autonomous, or free, and vice- versa. The moral law expresses the positive content of freedom, while being free from influence is the negative content.
We are conscious of the operation of the moral law on us. It is through this consciousness that we are conscious of our freedom and not through a special feeling of having free will. Although normally our actions are determined by self-love's calculations, we realize that we are able to ignore self-love's promptings, however great, when moral duty is at stake. Consciousness of the moral law is a priori, not based on any particular observation and it cannot be analyzed further.
Kant closes the chapter by discussing Hume's supposed refutation of causation. Hume argued that we can never see one event cause another, rather, all we can see is one event follow another, and we leap to the conclusion that there is a deeper connection. Kant argues in the first Critique that Hume's argument does not work because it does not apply to things as appearances, that is, this, phenomenal, world. Yet with his claims about autonomy, Kant says that we can know something about the noumenal world. Specifically, we know that we are in it, causing what happens here. This is okay, though, he concludes, because such knowledge does not expand our knowledge of the world per se, because it is only practically, and not theoretically, useful.
The first chapter of the Analytic, which is set out in the form of a geometry treatise, is both long and dense, containing some of the most difficult arguments of the book. In a short series of theorems, Kant moves rapidly from the universality of the law to its motivation by form alone to its specific content, and then to the equation of that law with freedom.
For instance, we might question Kant's claim that any practical principle specified by its content and not its form could only hold contingently because it presupposes desire for that content. Suppose "Obey God" was my maxim. It is true that should I cease taking an interest in God, I will no longer be following this maxim. But that is not to say that the maxim no longer has a hold over me. If it was ever a law for me, it is could still be now. After all, if a maxim had to be in fact universally motivating to count as a law, then we know that there are no laws—people do not always act according to any one maxim, including the categorical imperative.
We might also find the discussion of the form and the matter of a maxim less than easy to understand. What is a form and what is a matter? Can there be two maxims with the same matter and different forms, or vice-versa? And how does Kant move from saying that the law-giving force of the maxim must lie in its form to saying that its matter can be nothing but an expression of that form? These questions are not necessarily unanswerable, but the technical tone of the theorems suggests a rigor that makes surprising our need for conjecture to generate answers.
Another question this chapter brings up is how Kant can understand evil. If the free will is the moral will and vice-versa, how can immoral action be anything but un-free and therefore not blameworthy? If in acting on self-love, I am being determined by events in the phenomenal world like an automaton, why should I be any more blameworthy than an automaton? These questions are addressed, though perhaps only partially, in Kant's 1793 Religion within the Limits of Reason Alone, where he distinguishes between two senses of "will" and so understands acting immorally, or unfreely, as actively and freely causing oneself to be unfree.
Kant's practical law, the law of acting only under a maxim that could hold universally, holds a strong resemblance to the negative version of the Golden Rule, "What you would not have done to you, do not do that unto others." And yet Kant's law is different and original in that it is meant to be based on its formal universality, unlike either the positive or negative versions of the Golden Rule. The categorical imperative's similarity to the Golden Rule might be seen as an obstacle to fairly assessing the categorical imperative because it borrows a superficial plausibility from the resemblance. On the other hand, Kant might hold the Golden Rule's popularity to be due to its similarity to the one true moral law.