"Pure" vs. "empirical" use of cognitive faculties in the case of reason

Characterize the difference between the “pure” and “empirical” use of the cognitive faculties, especially but not only in the case of reason.

A lot of Kant’s critique is centered on pure reason versus empirical knowledge and many problems and questions arise for Kant when dealing with both pure and empirical knowledge.  First, we need to distinguish between a priori and a posteriori knowledge.  A priori is knowledge that is independent of experience and the senses.  A posteriori is knowledge that is dependent on experience.  Next we need to distinguish between analytic and synthetic judgments.  Analytic means that the predicate is contained in the subject.  For example, “A bachelor is an unmarried man”.  The predicate (unmarried man) is already contained in the subject (bachelor).  Analytic judgments are necessarily true because the negation leads to a contradiction.  Also, analytic judgments are then connected to the a priori.  On the other hand, synthetic judgments do not have the predicate contained in the subject.  For example, “Bachelors find early graves”.  We cannot know the predicate based solely on the subject.  Synthetic judgments are then connected to the a posteriori.  Now that we know analytic judgments go with a priori and synthetic judgments go with a posteriori, we can finally distinguish between pure and empirical.  Empirical knowledge is a type of knowledge that is both synthetic and a posteriori.  In other words, empirical knowledge is dependent on experience.  Kant then opposes empirical with “pure”.  The notion of pure is independent of experience or anything sensible.  As we know, Kant is critiquing pure reason, or reason independent of experience.  As far as the cognitive faculties go, there seems to be some trouble when coining either the sensibility or understanding as empirical or pure.  This is what Kant struggled with because he tried to prove that synthetic a priori judgments are possible.  Synthetic a priori judgments are independent on experience but also must be a posteriori because they are synthetic.  How is this possible?  Well, that question has been one of the most highly debated topics for philosophers and it has had much influence on philosophy since Kant’s time.  It is also the main problem with pure reason and a priori synthetic judgments must be proven possible to also get insight into pure reason.  Pure reason seems like a contradiction because you are mixing experience with no experience, synthesis with analytics, and pure with empirical.  It looks pretty messy but it is the main point of Kant’s critique.  How can we gain insight without experiencing?  In conclusion, pure and empirical are opposite but, when it comes to reason, Kant investigates the possibility of pure reason, or gaining insight without experience by using synthetic a priori judgments.