What is the difference between a priori and a posteriori knowledge?

A priori knowledge is prior to sense experience (thus 'priori'). For example, even prior to actually going out into the world and doing experiments, one could simply close their eyes, think, and deduce that 2+2=4. One need not go out and check to make sure that wherever two boulders are lying next to two other boulders that there are, in fact, four boulders. Rather, such knowledge is known prior to any reference to the physical world or our five senses. Going back as far as Plato, many philosophers have thus argued that fundamental truths, such as mathematics, logic, morality and even the existence of God can be innately known by the mind prior to any actual experience of the world. Instead of turning outward and using our 5 senses to experience the world outside, a priori knowledge turns inward and reflects upon what we seem to already know prior to any actual experience of the world. In contrast, a posteriori knowledge is gained only after sense experience has already occurred (i.e., once sense experience is behind us or ‘posterior’). One could never close their eyes, look within, and discover that the Titanic sunk on April 15, 1912, or that water is two parts hyrdogen and one part oxygen. Rather, such knowledge can only be gained by actually going out into the world and using our five senses to experiment and find out the 'facts' of the matter. For thousands of years philosophers have debated whether a priori or a posteriori knowledge should be primary, with a posteriori knowledge taking a commanding lead during the Scientific Revolution through thinkers like Locke and Hume. However, many philosophers (such as Kant) argue that a priori and a posteriori knowledge must work together, and any theory of knowledge that leaves out either side of the equation is incomplete. For while a priori knowledge without reference to actual experience is prone to flights of imagination, a posteriori knowledge cannot even get off the ground unless our brain already has prior categories through which it can process our experiences (e.g., how could we think logically about our sense experiences unless we already possess basic logic from the very beginning?). It is a difficult question indeed.