Kant analyses practical reason with the result telling us that the Categorical Imperative is the principle of pure practical reason and that autonomy lies at the root of morality.

Practical reason lays down imperatives which determine what constitutes rational and irrational conduct.
There are better and worse reasons for action.

The hypothetical imperatives depend upon desires and inclinations. These differ between persons hence they only apply contingently.
Hume believed that practical reason only issued these; upon this practical reason is only concerned with us taking the means to our ends (set by desire). It does not cast verdict on ends themselves.

Kant believed that ethics was a system of categorical imperatives.
Even if you desire to torture people, the command not to still applies to you.
They are unconditional with no exceptions.

Assuming that Kant is right about this, he tries to relate this to the content of everyday morals.
The result is the Formula of the Universal Law (I ought never to act upon a maxim unless it could be willed as a universal law).

Ethics is about acting on principles that all rational beings could act upon.
Thus, do not act in a way that involves making an exception of oneself.
It can also serve as a test for maxims of our own actions; we can purportedly provide ethical guidance to agents.

iv) Ask self: am I able to conceive of myself acting upon original maxim in the world where it is universalised?
If no, the maxim is impermissible to act upon.

Contradiction in Conception
It could be said that it is a logical contradiciton here generated by the way that we try to will our maxim in the world of the universalised maxim; the proposed world would be impossible/inconceivable.

If this is right the Formula of the Universal law will render permissible actions impermissible and impermissibile permissible.
Kill your rival example.

A main problem for the formula as mentioned earlier is that it may warrant permissible maxims impermissible such as leaving the football early.
Another problem is that it does not necessarily explain the agents maxims.

Some believe that we need to be more sympathetic towards Kant and feel that we just need a better understanding upon the relationship between the categorical imperative and rational agency.

i) All imperatives must make reference to ends.
ii) Hypothetical imperatives command us relative to contingent ends that we have have, set by inclination.
iii) Categorical imperatives must command us relative to a necessary end that we all share.
No such end could be set by an inclination.

Another argument is that as rational agents, we necessarily take our own rational agency as having a value above any of our discretionary ends.
Our valuing things presupposes that we take ourselves to have value.

However, there is a gap between claiming that we necesarily regard our own rational nature as having unconditional value and that we therefore ought to regard other rational natures in the same way.
Doubt the move from 'I value my rational agency' to 'I must value rational agency in others'.

Humanity and Content
The formula of humanity can plausibly deal with the 'problem' cases for the formula of the universal law. It is generally taken to entail strong injunctions against coercion, eg. rape and enslavement.
By coercing others, you are not representing their ability to make decisions about their own life and actions.

Imperfect Duties
-Developing talents and giving aid to those in need.
- Failing to do either of these does not obviously conflict with preserving or respecting rational nature as an end in itself; he does think that we have a duty to promote and foster rational nature.

Overall...
acting in a way that not everyone could is incompatible with respecting the freedom of other people.
However it is not obvious that the formulations pick out the same actions as permissible and impermissible; how then could they be equivalent?

Self-Imported Law
The categorical imperative is the law of practically rational beings (the principle of pure practical reason).
As practically rational beings, we are the authors of the law.
It is a law we impose on ourselves; this idea of self-legislation is autonomy. It is Kant's account of normativity.

For moral action, it must be possible to act on the basis of something that the will can provide; it is our law.
This is the proper object of respect.

Are we autonomous?
A free will and a will under moral laws are the same thing - Section 3.
There is an important connection between having a free will and autonomy hence subject to the categorical imperative.

Will is a kind of causality hence it must be law-governed for Kant.
A free-will must be law-governed. But to be free, it must be governed by its own law.
This is the postive conception of freedom; it sounds just like the definition of autonomy hence free will and a will under the moral law are the same.

One interpretation
Whenever I am deliberating about action I must presuppose that it is up to me how I act. This practical standpoint seems inescapable.
However acting under the idea of freedom does not imply that we are really free...

Kant tries to avoid this by saying that although we are members of the phenomenal world, thinking that all there is to the world is the phenomenal world is an inadequate conception of the world.
We have reason to/ are entitled to posit a noumenal realm wherein freedom is possible.

Note
Kant is not claiming that we are free.
this is metaphysically profligate.
Also, there is a potential incoherency between the worlds.