I've been looking again at the Groundwork lately and was led to reflect on some questions concerning the way the "examples" work the first time they are told in the second section of it. The whole story of these "examples" is a complicated one that has attracted much commentary though more heat has been generated on the whole than light. So let's just begin by defining parameters before going on.
Firstly, the examples are introduced on two occasions after two distinct formulas. The second time is after the statement of the formula of humanity and I'd like to return to the discussion there on another occasion. However, the first time is after the formula of universal law has been stated but it is not this formula, in its classical statement, that is tested by them. This point is not always recognised but strikes me as significant. So, let's first reconstruct what happens with the formula prior to the statement of the examples and then cut to a point that is of interest about the treatment of these examples.
With regard to the formulas, what happens first is that Kant gives the formula of universal law as arising merely from connecting the concept of the law to its formula. This produces the classic statement: "act only in accordance with that maxim through which you can at the same time will that it become a universal law" (Ak. 4: 421). This is what is generally known as the formula of universal law (FUL) and many philosophers and commentators have come to the view that it doesn't work or is in some, very important way, problematic. However, Kant doesn't himself work with this formula in relation to the examples that he gives shortly after. This is despite statements about deriving all imperatives of duty from "this single imperative as from their principle" (Ak. 4: 421). What happens next is that Kant begins to discuss the universality of the law in relation to the representation of effects. In other words, Kant thinks about the law as something that could work in a causal nexus. After raising this prospect, Kant goes on to discuss how representation of such a causal nexus is equivalent to speaking about "nature" as nature is, "the existence of things insofar as it is determined in accordance with universal laws". The culmination of this discussion is that Kant next formulates what he terms "the universal imperative of duty" and this takes the much less familiar form: "act as if the maxim of your action were to become by your will a universal law of nature" (Ak. 4: 421).
It is this second formulation and not the classic FUL that is then tested in relation to the "examples" and nor is this insignificant for how the examples are treated. Before looking at that treatment, and particularly the division within it, it is worth pointing out that if FUL were related directly to duties then one would expect a test to emerge that would only relate to universality and nothing else. However, as we will see, the switch from FUL to reference to a "universal law of nature" (or ULN) ensures that Kant can discuss something more than merely universality alone even though the form of universality is still crucial in what he says.
The four examples that follow involve maxims connected to suicide, promising, the cultivation of talents and beneficence. Now, whether one likes what Kant says about suicide and promising or not the treatment of them is relatively straightforward. With these examples Kant alleges that adopting maxims of a certain sort is not consistent with treating the maxims in question as universal laws of nature since, if that is how they are treated, the conception of this nature would involve a self-contradiction. This is often stated as meaning that these maxims involve a "contradiction in conception" and this is alright so long as it is understood the conception is not within the maxims as such but the maxims understood as universal laws of nature.
The second two maxims are much more complicated since, in the cases of someone declaring they will not cultivate their talents as in the case of someone who refuses to act beneficently, there is not the same self-contradiction involved in the picture of nature that would ensure if these maxims were taken as universal laws of it. Instead, the contradiction is often said to be a contradiction in the will that would be asked to will these maxims. Now, how does this alleged contradiction in the will in question relate to the notion of a universal law of nature?
With the first case, of cultivation of talents, Kant pictures the person in question not bothering to work on themselves for the purposes of self-improvement basically because they would prefer instead to devote themselves to "idleness, amusement, procreation", which is summed up as "to enjoyment" (Ak. 4: 423). In this case it is apparent that the motivation in question is one of acting in accord with inclinations alone, something previously discussed in this section of the Groundwork. Alright, but what's wrong with that in relation to universal law? Surely it would be possible to will a nature that had such action in accord with inclination into being? It is not ruled out since, as Kant puts it, such a nature could "subsist". So the nature in question is a possible nature, unlike the nature ruled out in the case of the first two examples. But, the problem is said to be, although the conception of this nature is not itself an impossible one, we could not wish to live in a world that was governed by such laws so acting in accordance with a maxim that would, if universalised produce it, is not in accord with our will. Why not? Because, says Kant, as a rational being we "necessarily will" that all our capacities be developed since they serve both ourselves and others "for all sorts of possible purposes".
This point seems to be one, however, of indicating the imprudence of willing a nature governed by such a law. In such a nature there would be innumerable purposes that we wouldn't be able to carry out due to our not having adopted the means of developing them. So it is not, as it were, in our best interests to will in this way. The appeal then would appear to be to those best interests and to rule out a certain kind of disposition due to the way it will later affect our prospects. This may well not be the strongest type of consideration that could be given here!
The last of the examples, concerning beneficence, takes the case of someone who says he won't help others and is quite willing, in return, not to have them help him. Again, if such a disposition is used as the basis of a maxim of universal law of nature then it appears that we could well find that nature thereby would "subsist". The problem, again, is supposed to be that we couldn't "will" such a nature to be. The reason, on this occasion, why there is taken to be a problem with "willing" this as a universal law of nature is that we rule out the prospect, in advance, of being able to call out for help however dire our need. Since we have no way of knowing how dire that need may be there is a sense in which we have acted to prevent it being possible that we can achieve sustenance. Again, the problem seems here to be that such a maxim is not a prudent one. That is, the argument seems to show that the kind of end we have in view here, as the basis of a hypothetical imperative, is one that defeats itself in relation to certain necessary outcomes of it. And, once again, this doesn't seem like the kind of thing we would expect Kant to say.
However, what is of interest with these examples and the way they are treated here is how they focus very definitely on purposes and their consistency. It is the consistency of certain kinds of purpose that is being questioned with the device of the universal law of nature. The device of the universal law of nature may not be the best one to deal with this but what is shown by the fact that it is purposes that are being so treated is the centrality of purposes to Kant's considerations.