The formula of humanity is stated as: "So act that you use humanity, whether in your own person or in the person of any other, always at the same time as an end, never merely as a means" (Ak. 4: 429). One of the immediately interesting points to note about this formula is how it effects the sense we have of means-ends relationships. In what Kant had earlier described as "hypothetical imperatives" there are two basic things at issue, either "skill" in terms of devising means to a given "technical" end or "prudence" through thinking about how to devise means to the pre-given end of happiness. In both situations the means-ends nexus is as we normally tend to think it. An end is given and we work out the best means to achieve it. Here, with the formula of humanity, we realise the import of the difference between such hypothetical imperatives and what is occurring in the case of the moral imperative. In the case of the latter we are working with a sense of end that cannot be distinguished from means as we do in hypothetical cases. Here "humanity" is treated as something that cannot be treated as a means to some further end but rather as an end-in-itself and this notion of an end-in-itself is one that we might term an "eschatological" sense of end. The normal instrumental notion of end is not strictly, as is often assumed, a "teleological" one since teleology as the generic name for purposes is not equivalent to instrumentality or at least need not be equivalent. The usual sense of ends is, however, clearly instrumental. By contrast with this notion if we think of an end as something that exists and not something we are aiming to bring about and assume that this end is one that we relate to as requiring modification of all notions of means then we have a radical conception. Since this is an "end-in-itself" it makes sense to me to think of it as an eschatological sense of end.
Now, after giving this formula, Kant looks again at the same four examples that were given to the formula of the universal law of nature. Again, the first two examples are cases of contradiction in conception and I don't want to consider these (suicide and false promising). But the second two were shown to have some odd characteristics in relation to the universal law of nature so now I want to consider them in relation to the formula of humanity. They are again given in the same order with cultivation of talents first. When presented in relation to the formula of humanity Kant adds an additional characterisation of the cases treated as involving contradiction in the will. They are now described as "meritorious" duties suggesting, correctly I think, that there is something about such duties that appears additional to the most minimal sense of duty.
In the case of cultivation of talents Kant mentions that "it is not enough that the action does not conflict with humanity in our person as an end in itself; it must also harmonize with it" (Ak. 4: 430). This requirement is like the shift, in Perpetual Peace, from the negative to the affirmative sense, of publicity. It would appear that the negative notion of lack of conflict with humanity in oneself is sufficient to rule out suicide but we require bringing in, when considering the case of "meritorious" duty, the additional notion of harmonization of the action with the sense of humanity as an end-in-itself. And it is by means of this move from a negative to a positive sense of relation to the formula that Kant justifies the need for cultivation of one's talents for, as he puts it, there are "predispositions" to "greater perfection" and to neglect these is not consistent with the "furtherance" of humanity.
The second example, concerning beneficence, makes the same basic move of invoking the distinction between negative and positive forms of relation to humanity and indicates that when we make this move we can see the need to act beneficently. Given that this example of beneficence has been studied at some length in contemporary writings on Kant's ethics I don't want to say too much more here. But what is apparent is that the extension of humanity to the positive harmonizing sense to include the ends of others is not exactly parallel to what is happening in the case of cultivation of talents. In the case of cultivation of talents I am considering a duty I owe to myself and hence the question concerns the status of humanity in my self. With the example of beneficence I have a duty to others and this requires thinking about the status of humanity in others and how it relates to humanity in myself. So in the case of beneficence Kant focuses on this relation and how it connects to the sense of furtherance of humanity: "the ends of a subject who is an end in itself must as far as possible be also my ends, if that representation is to have its full effect in me" (Ak. 4: 430).So the case of beneficence adds the question of how the representation of others as ends in themselves is to have its full effect and if we consider that we are led to endorse the need for beneficence whereas without such consideration we would be led to neglect the need for it.
If we now compare the treatment of the cases of contradiction in the will given when we are working with the formula of humanity to that given when we have the universal law of nature formula we can note some important differences. In the case of cultivation of talents the argument given from the universal law of nature seemed to in fact convert the moral imperative into a kind of prudential one. The treatment of this case with regard to the formula of humanity, by contrast, does not do this. The latter treatment does, however, still appear to invoke something from the earlier formula's treatment as Kant refers to predispositions to perfection and says that they "belong to the end of nature with respect to humanity in our subject" (Ak. 4: 430). This "end of nature" is not here made fuller so it is not clear from this text alone what Kant means but it does suggest that we are still, when we connect the formula of humanity to the example of cultivation of talents, thinking about nature as an important part of our considerations. It is not, though, a prudential reference that emerges but the need to think of how to go farther than preserving humanity and to the need to work out how to further it as well.
The case of beneficence again seemed to involve prudential considerations when considered in relation to the universal law of nature formula and such considerations are, once more, not present when the example of beneficence is considered in relation to the formula of humanity. Instead, a kind of imaginative extension of the relation I have to the sense of humanity in myself is required and this might point to the need to think about the role of such imaginative work in ethics but there is not here any kind of prudential consideration given as rather the question is how to ensure the understanding of others as ends-in-themselves is to have its full effect on me.
As was the case when these cases were treated in relation to the universal law of nature formula so also here when we are considering the formula of humanity we clearly get a sense of the importance of understanding purposes when we look at the cases of contradiction in the will. If willing, though, requires a conception at work not just of the world one would create in universalizing the maxim of my will but also a relation to what is capable of so willing then questions do appear to arise about the status of this reference to "humanity". The other point to note though is that the formulas of humanity do seem to have enabled a more consistent focus on moral imperatives than seems possible from the universal law of nature alone.