There are two "proofs" of freedom in Kant's Critique of Practical Reason; one is the formal proof and the other is the popular proof.*

[* The author's translation of this section along with his commentary can be found here. The back button must be used to return here.]

By way of short introduction, we note that in his Groundwork to the Metaphysics of Moral Kant will have certified that the notion of duty that we have could not have arisen through empirical means at all, and so is an idea (invention) of pure reason itself as it conceives a rational realm of free beings, and of the laws that would have to guide these beings. This does present a problem, of course, and much as in his earlier pursuit of the object of experience. The categories of understanding, like cause and effect, are our own inventions also, but they find application in the construction of the experience in which the object of experience then appears (like the constant “real” object we conceive of in comparison with the variable “visual” object we see with our eyes). Here with the moral law we dream up this idea of a rational and free realm and discover its law which is then called the moral law. But since this can never be discovered in any experience, but merely assigned to an experience as a causation, it requires a special deduction.

The Deduction of the Moral Human. Every being presupposes his own freedom in the reasonings that he undertakes from time to time to determine some rational course of action. But that does not make him subject to the moral law and he can still ask about his interest in complying with a moral law. "Why should I? What’s in it for me?" Now this interest cannot be shown empirically, for the most we can learn empirically is what produces pleasure and what produces pain, and the moral law is not presented in those terms at all, but by pure reason. What is necessary is a two-fold consideration of the human being, namely he is a being of natural necessity and at the same time he is a thinking actor. Man then puts himself into a natural frame of mind when he is explaining his actions of the past, and into an intelligible (spiritual?) frame of mind when he considers any action at hand. And in that latter frame of mind he can conceive of himself as a member of that free, rational realm and then he realizes his interest in the moral law, for now he sees that in that free, rational realm he would quite naturally comply with the moral law, and that the only reason he does not himself immediately do so is because he is also a member of the realm of nature where happiness is a factor and acts often contrary to the moral, i.e., he will automatically obey the law unless he has some reason not to. And so in this way it is possible that he could imagine himself as subject to a law in the form of a categorical imperative. This then establishes how a man must think of himself in order to be able to understand how such a law, a dreamed up thing, could be important for him. Then the actual proof takes place as described below.

Next Kant prepares for his proof in the Analytic of the Critique of Practical Reason. He finds reason functions by principles, theoretically or practically. There are three sorts of rules which are rationally practical: rules of efficiency, counsels of prudence (directed toward happiness) and categorical imperatives (the moral law). The incentives for the first two are self evident, but not the incentive of the moral law. He will find in the course of his proofs that the moral law is an incentive sufficient in itself.

Formal Proof* A scientist, to be entirely objective and consistent, must necessarily consider a person possessed by a mere idea as insane. John Locke’s mentions the case of the man who thought he were made of glass, even though he acted very rationally in accordance with that idea, e.g., he studiously avoided physical shock. Locke’s glass man is a lunatic. Even so is Don Quixote a lunatic, e.g., taking windmills for evil giants, even though he acted with great nobility and courage in light of his understanding. Even so consistent scientists find they must consider a man who is morally inclined to be suffering from a delusion of his own making and that he is then acting that delusion out in his life, like the glass man. But it is very strange then, observes Kant, that science does not treat moral people as lunatics but rather as persons of emulation. The reason for this, Kant then concluded, was because the scientist is imposed upon by the moral law (an invention of human reasoning itself--consider Genesis 3:22), i.e., he has respect for the law. Thus the universality of respect for the moral law in all human beings. Even science yields its objectivity in this case. **

[* Critique of Practical Reason, No. 6, 2nd Task, sentence 8 of paragraph 3.]

[** If a person had no respect for the moral law (a matter of experience, though with a priori anticipations), then the law as a command for conduct would be utterly inane, such as an arbitrary rule to stand on your head every Wednesday morning. And even though the rule, the moral law, is derived by pure reason when considering a realm of free beings, and as being the only rule which all people could agree on for a law, if the scientist were utterly devoid of a moral feeling (first evoked by the conception of the moral law), that would be no more meaningful than any other law. Perhaps it would be an interesting plaything if a person wanted to spend his time in dreaming up laws, e.g., the law of gravity or even a law of spirits. And so the fact that it is an objective law of pure reason does not mean that all beings will necessarily be imposed upon by it. Kant mentions possible beings, e.g., some angels, who might not be driven by this moral law.***]

[*** Religion Within The Bounds Of Reason Alone, Book One, I. Regarding The Original Structure For Good In Human Nature, footnote to sentence 1 of paragraph 1. ". . . The most rational heavenly being might still have need of certain incentives derived from objects of desire in order to determine his choice, even apply the most rational deliberation concerning the greatest sum of incentives as well as the means of attaining the determined objective through them, and still without even imagining the possibility of such a something as the moral, utterly commanding law which announces itself as itself an incentive and indeed the highest. . . ."]

Popular Proof There are two renditions of this. One is the gallows case and the other concerns rationalizations.

The Gallows Case.* A man will admit, under serious questioning, that he would be able to resist at any given moment his most “irresistible” delight in order to continue his own life. And so his life is more important than his delight. Then the same man is asked whether he would be willing to give up his life in order to avoid telling a lie by means of which an innocent man would be put to death. Now the man will likely not be immediately sure, but the very fact that he stops to consider the matter indicates that he is free and could conceivably give up his life in order to do what is right. So strong is the moral law within each person that a person will at least consider giving up his own life, what he treasures far beyond any delight. If a person were devoid of the moral law, asking him this question would prompt a look of surprise, much as though you had asked why he pulled his hand from a burning fire. He would have to ask you to repeat your question, so curious would it sound to his ears. And so it would be with the gallows case.

[* Critique of Practical Reason, No. 6, 2nd Task, sentences 10-13 of paragraph 3.]

The Rationalization Case. Each individual will find, upon introspection, that he is busy figuring out some excuse for having violated the moral law. He rationalizes his dereliction in terms of his own weakness or of some necessity. In this way he seeks to calm his conscience. But like the gallows case (and whereof it is merely a special case) this proves the moral law and freedom, for no rational being, who had no respect for the moral law (it being merely another arbitrary rule, one among many) would be able to spend an instant rationalizing any misconduct, for misconduct would be a meaningless term like the “uh” that we sprinkle our speech with all the time.*

[* Critique of Practical Reason, No. 7, Consequence and Remark, sentence 2 of paragraph 4.]

Conclusion. Kant has already established in his Critique of Pure Reason that it is easy enough to think freedom at the same time that you think natural necessity and the absense of freedom, and only in a different way. And so there is no reason why a person could not be free and exist in a naturally necessitated world, and so there is no reason for anyone to doubt their freedom. Not even scientists do that. And scientists hold themselves accountable to laws of ethics, which is contrary to everything scientists teach in the class (for it presupposes freedom).