As Jung says in the Face-to-Face interview with BBC in 1959, he was studying Kant during the early parts of his career in order to better understand human cognition. As Jung says: “I was studying Kant. I was steeped in it.”
Kant believed that sensing and intuition are factors that condition our conscious experience of reality. In a famous passage in the first Critique, Kant indicates what he takes a representation to be (A320/B376-77):
As will be seen here, Kant regards intuition as always objective and outwardly directed while he regards sensation as always subjective and pertaining directly to the subject. Thus, to Kant, intuition is always extroverted and sensation is always introverted.
Jung then improved upon Kant by showing how sensation can also be extroverted. Kant had said that sensations do not represent anything apart from the person sensing it. But this is only true when sensation is introverted, that is, when sensation becomes a repository for an impressionistic order of facts as it is in the introverted mode (Si).
But when sensation is extroverted (Se), it is in fact conditioned by outer objects in the same way as extroverted intuition (Ne). Of course it is true that Se is to some extent still dependent on the subject, but so is Ne; no two Ne users will experience exactly the same associations, even if subjected to the exact same stimuli. So in the extroverted mode, sensation is in fact steered by outer objects as much as any other extroverted function. In fact, Se is attracted by those objects that release the strongest sensation-stimuli. Thus, Kant was wrong to say that sensation can only pertain to the subject itself, for Se aims to represent the outer objects photographically, that is, on their own terms and with a purity of immediacy that is exclusive to the ES-P types.
Jung also showed how intuition could be introverted. Indeed in its introverted mode, it is intuition that does not represent anything that is distinct from the person experiencing that intuition. As has also been pointed out by J.H. van der Hoop in his book Conscious Orientation, this difference between extroverted and introverted intuition is exactly the reason why in philosophy INTPs tend to construct systems that are outside and apart from themselves, whereas INTJs tend rather to make a forceful case for something that is more directly dependent upon them as a subject. That is the difference, for example, between a Kant and a Nietzsche. It is also something we cover in our Dawkins vs. Hitchens infographic.
This same difference could also be visualized like this:
Finally, when Kant formulated his theory, why did he find that intuition is naturally extroverted while sensation is naturally introverted? Was he perhaps, as an Ne-Si type himself, projecting his own type on to all of humanity? We leave it to the reader to decide.