Why is there a debate between rationals and empiricals? What are the differences between those two ways of thinking?
See in Stanford Encyclopedia of Philosophy :
The dabate between Rationalism and Empiricism dates back, in modern times, to XVII century :
"contnental" rationalists : Descarte, Leibniz, Spinoza
"british" empiricists : Locke, Hume.
From SEP :
"The dispute between rationalism and empiricism concerns the extent to which we are dependent upon sense experience in our effort to gain knowledge. Rationalists claim that there are significant ways in which our concepts and knowledge are gained independently of sense experience. Empiricists claim that sense experience is the ultimate source of all our concepts and knowledge."
One of the key-points of rationalist theory is :
The Innate Knowledge Thesis: We have knowledge of some truths in a particular subject area, S, as part of our rational nature.
The dispute his a fundamental one in modern philosophy, and culminated in the kantian attempt to synthetize the two points of view.
In XX century, the positivist school (Mach) and neo-positivism (see Vienna School) "revamped" the empiricist point of view, but significant scientific theory, like Generative Syntax of the american linguist and philosopher of language Noam Chomsky, have argued for the necessity of postulating an "innate capability" of human mind.
When you say "thinking" I imagine you mean "knowledge" and the process of informative manipulation with it; if that's so, you should read the works of Willard van Orman Quine, 'cause he proves that a prior (acquired by pure reasoning) knowledge just doesn't exist, e.g, that every knowledge it's just empirical (acquired from experience). For example, we know what will happen if we take a rock and smash it against the bathroom mirror; but we only know that because we have seen, in some moment of our lives, a smashed mirror, and the "act" of hitting with a rock. Other example is our dreams; if you never feel the experience of being shot, you'll never be able to dream about that feeling, because your brain never "felt" that, so he doesn't have the information about that experience. So, rational thinking, would be just deductions based on empirical knowledge, e.g., you can imagine, you can make hypothesis based on your sensorial experiences. That's were a lot of scientific reasoning occurs: we know if A happens, then it will imply B (A->B), and we know that if C happens, it will imply D (C->D), but what if A and C happens at the same time? We know what's gonna happen if we smash a rock in the mirror, but what if we smashed it against an object that we never seen beforer, we would be able to tell what's going to happen? NO! A good example of that it's the experiment https://www.youtube.com/watch?v=LyvfDzRLsiU, in which we can't know the result until we see it.