Kant presented his response to Hume in three books – the Critique of Pure Reason (1781), Critique of Practical Reason (1788) and Critique of the Power of Judgment (1790) – that have come to be known, respectively, as the first, second and third critique. The enterprise Kant undertakes in these books is often referred to, unsurprisingly, as critical philosophy. The position that results from this undertaking is called transcendental idealism. Kant claims that transcendental idealism successfully rebuts Hume's scepticism without reverting to dogmatic rationalism, and that it is the only philosophical option that remains tenable in the wake of a thorough critique of reason.

According to Kant, a complete and successful critique of reason must answer exactly three questions:

1. What can I know?

2. What should I do?

3. What may I hope?

The first, epistemological, question is the subject of the Critique of Pure Reason, the book that broke Kant's decade of silence and introduced his philosophical revolution. In that work, Kant is concerned to survey the extent of our possible knowledge by determining precisely the capacities and limits of theoretical rationality. Like Hume, Kant aims to deflate unwarranted and superstitious beliefs that exceed our powers of justification. At the same time, however, Kant aims to show that Hume's scepticism regarding theoretical rationality is itself unjustified, by demonstrating that there are indeed matters of fact that can be known to be necessarily true by means of reason alone. In the course of this demonstration, Kant also claims to defeat Hume’s determinism, by proving that one of the things we can know is that we cannot know whether or not we are free.