Sausage Grinder epistemology

Epistemology is the study of knowledge. How do we know what we know? What is the source of that "knowing"? Its limits? What about its structure? Well that is the purpose of epistemology, to answer questions like that. Before Immanuel Kant, there were two camps in this study of philosophy: rationalists and empiricists. Parmenides, Plato, Augustine, and Leibniz would be seen as rationalists. Heraclitus, Aristotle, Aquinas, Bacon, Locke, and Hume would be empiricists.

Rationalism

Above I mentioned two words that need defining: rationalists and empiricists. What is a rationalist? A rationalist claims there are significant ways we gain knowledge and concepts independently of sense experience. The key to understanding both camps in epistemology is to remember: it's all about sense experience. Your view on how important the role sense experience plays in our gaining concepts and knowledge will put in one of these camps.

So we now know rationalists claim there are other ways than through sense experience that we gain concepts and knowledge. What are those other ways? From the Stanford Encyclopedia of Philosophy: "First, they argue that there are cases where the content of our concepts or knowledge outstrips the information that sense experience can provide. Second, they construct accounts of how reason in some form or other provides that additional information about the world." Further, rationalists claim we have innate ideas that are "before experience." This knowledge is part of our rational nature, so it's not gained by intuition, deduction, or experience because it was there all along. Our experiences can trigger or set-off that knowledge, but experience didn't provide us with the knowledge itself. Rationalists disagree on how we gained this a-priori knowledge. Some say God stamped it on us at creation. Others say we gained it in an earlier existence, while there are those who say it was gained through natural selection.

Empiricism 

You can probably guess empiricism is all about. Yep, it's all about sense experience. John Locke claimed that the human mind at birth is a "tabula rasa" or blank slate, which means we are born with a mind without inclinations. Empiricists argue for a posteriori knowledge, that sense experience is the ultimate source of all our concepts and knowledge. From the SEP, "Empiricists present complementary lines of thought. First, they develop accounts of how experience provides the information that rationalists cite, insofar as we have it in the first place. (Empiricists will at times opt for skepticism as an alternative to rationalism: if experience cannot provide the concepts or knowledge the rationalists cite, then we don't have them.) Second, empiricists attack the rationalists' accounts of how reason is a source of concepts or knowledge." As I said before, sense experience is "ultimate" for the empiricist, there is no other foundation for knowledge. At this point, it's important to note that empiricists do not think we have empirical knowledge, but that our only avenue for knowledge, if at all, is by experience. 

Transcendental Method 

Yes, there has been a third way and this way was achieved by Immanuel Kant with his transcendental method of knowledge. Kant more or less took the best of both camps (rationalist and empiricist) to establish his method. Sense experience was the starting point for Kant. He disagreed with the rationalists' innate ideas, such as Descartes, but he distinguished between "prior to experience" knowledge and innate ideas with mental categories; a two-step approach if you will. For fear of over-simplifying I will give a link to Kant's method. We have mental categories of things that Kant would call "appearances" and then we have "things in themselves," i.e. things that are absolutely real. 

Kant's words: 

"T]he objective validity of the categories, as a priori concepts, rests on the fact that through them alone is experience possible (as far as the form of thinking is concerned). For they then are related necessarily and a priori to objects of experience, since only by means of them can any object of experience be thought at all. 

The transcendental deduction of all a priori concepts therefore has a principle toward which the entire investigation must be directed, namely this: that they must be recognized as a priori conditions of the possibility of experiences (whether of the intuition that is encountered in them, or of the thinking). Concepts that supply the objective ground of the possibility of experience are necessary just for that reason." 

You can think of Kant's method as a sausage grinder: sensations going into mental categories. What comes out of the sausage grinder? Knowledge. Kant argues that the categories are necessary for experience; without the mental categories we would have no way to experience anything. Do you think Kant's philosophy helped epistemology by finding a bridge between the camps? Or do you think he even made a bridge? One thing is certain: his method changed philosophy, so much so that philosophers to this day have various interpretations of the transcendental method, disagreeing over this aspect and that aspect. One could say this method created a crisis in philosophy and not just a change.

Kant's method is heavy reading to be sure, but it's also enjoyable (if you like philosophy that is) even though the method's complexity is high on the complex scale.

I highly recommend reading the links underneath "further reading" if you're interested in epistemology. 

Further reading
Rationalism vs Empiricism

Transcendental method (SEP) here is the method in Wikipedia

Immanuel Kant: Critique of Pure Reason

As always, a fair amount of resources can be found here at Apologetics 315.