On Kant's Introduction of FUL in the Groundwork

This is an informal piece of writing for PHILOS 151B taught by Prof. Dewitt at UCLA.

After introducing the concept of a categorical imperative (CI) in Section II of the Groundwork (G), Kant immediately goes on to show that the Formula of Universal Law (FUL) is the only possible CI. (G420-421) His argument for this is extremely concise: A CI only contains the law it represents and the necessity that the maxim must conform to that law. Since the concept of CI does not limit the law in any way, the only part of the concept of law remaining in the concept of CI is its universality. "There is therefore only a single categorical imperative, and it is this: act only according to that maxim through which you can at the same time will that it become a universal law. (FUL)"

On my first few readings, I understood everything in this argument, except how it gets to the conclusion: Why can't a will be necessarily commanded to follow some law other than mere universality itself (he didn't say that such a practical law is impossible)? Also, suppose there are multiple practical laws (he didn't say that's impossible), why can't it be the case that each of them commands my will using their own CIs (so that we can have more than one CI)?

There seem to be huge gaps in this argument, despite of how Kant so confidently gives it. I know I sound stupid, but this question has been confusing me for more than two months.

Here is the only possible solution I can think of to fill this gap: If we assume that for a CI to be necessarily commanding, it is not only required for the law it represents to be universal, but it is also required for the cognition of this particular CI to be analytic, i.e., even if we know nothing synthetic about what the practical law is, we can still cognize this CI. Only in this case, a CI can only contain the concepts already lying in the concept of CI, which are the law of universality and the maxim's necessary conforming to the law; and in this case alone, can the CI formulated by FUL be the only possible CI. However, this requirement still seems to be unreasonable, and for this reason I tend to believe that Kant made a mistake here. But this is not fatal to his theory: the formula of autonomy (FOA), which is shown to be necessary in section three, seems to be equivalent to FUL, so at least FUL does represent a CI, though not necessarily the only one.

Note that the "analytic" here cannot be replaced by "necessary": what if one can cognize more than one practical law a priori? what if one can cognize, completely a priori, a practical law that is stronger than mere universality? (Kant did not say they are impossible) Since Kant's usual account (e.g. KrV B3) assumes "necessary" to be equivalent to "a priori", in these cases one would be able to cognize such law(s) necessarily, and it's unclear how the necessary cognition of a CI including such law(s) would need anything more than that.