The Enlightenment, described as a "rebellion against authority", has for the longest time lacked an epistemology that would enable the systematic rejection of all claims to authority. Popper's critical rationalism was the first philosophy to offer such a systematically anti-authoritarian epistemology. The fulcrum of this philosophy is deductive logic, which is taken as a basis for a new explanation, and defence against criticism, of Popper's falsificationism. Some of Popper's concepts, however, need to be improved upon, especially "truth", "objectivity", and "World 3". Thus made to cohere more stringently with the rest of critical rationalism, these concepts are taken as a basis for expanding Popper's epistemology. It is shown how it is possible to gain objective knowledge in wider areas, e.g. the social sciences, the problems of the Open Society, and ethics. Thus, an outline is presented for how to develop specifically critically-rational approaches to some philosophical areas of interest, in particular ethics and the problem of free will.