Many formulations of utilitarian consequentialism famously lead to a range of "repugnant conclusions", such as:
- it would be moral to execute an innocent person if this act could deter at least two future murders
- the Mere Addition paradox, that a world containing the largest number of people whose lives were just marginally better than insufferable has a high amount of total utility
- the Utility Monster
etc. There is a famous "repugnant conclusion" following from Kant's well-known categorical imperative in the following form:
Act only according to that maxim by which you can at the same time will that it should become a universal law
From this follows that if the Gestapo shows up at one's door, one should not lie when they ask if one is hiding a wanted Jew.
Kant proposed other formulations of the categorical imperative, such as the Humanity Formulation:
The practical imperative, therefore, is the following: Act so that you treat humanity, whether in your own person or in that of another, always as an end and never as a means only.
Now to Kant, these were seemingly interchangeable, and the categorical rejection of lying could be derived from this second form. But at first glance, it doesn't seem that e.g. the imperative to never only treat a person as a means to and end, but always as an end in themselves would automatically lead one to give up a fugitive just so one doesn't have to lie, particularly when considering side effects (see e.g. this).
What are the canonical counterexamples brought forward against Kant's Categorical Imperative in the form of the Humanity Formulation, that one should always treat people as ends in themselves, never merely as means to an end?