How does Kant derive The Formula of an End in Itself, The Formula of Autonomy, and The Formula of the Kingdom of Ends from the The Formula of the Universal Law?
So far, this is my understanding of it.
The first formulation: Don't do anything that logic would not allow to be universalized.
For example, if everyone stole what they wanted to steal, then no one would recognize property rights so there would be no property, and if there is no property there can be no stealing. So, it is not logically possible to make stealing a universal imperative.
The second formulation: Always treat everyone as an end in themselves, never just as a means to an end.
P1. Suppose an actor acts as though he were an end in himself, and as though others were not ends in themselves.
P2. All acts must accord with universilizable principle.
P3. An imperative is what one must or must not do.
C1. Universalizing P1 produces a logically impossible principle.
For example, that impossible principle might read, 'All persons' actions ought to reflect the fact that they are ends in themselves, and that no other persons are ends in themselves'.
- C2. Accordingly one must not act as though others are not ends in themselves, so it is an imperative that people act as though others are ends in themselves.
The third formulation: Act that your will can regard itself at the same time as making universal law through its maxim.
- P1. An agent must act so that her will is free to express (regard) itself through action.
- P2. Suppose an agent acts in a way that constrains the expression of another agent's will.
- C1. Any universalization of P2 is inconsistent with P1.
The fourth formulation: I don't see how the fourth formulation differs from the third formulation.
Are any of these formulations mistaken? How does the third formulation differ from the fourth?