Popper asserts that there are sources of knowledge, but there are equally sources of ignorance, which serve as provenance and explanation for the absence of knowledge.

To begin understanding why the absence of knowledge can have a source, Popper first explores historical methods of knowledge production. He breaks down two prominent European schools of thought in the Enlightenment: The British and Continental schools of philosophy. The British school, defended by philosophers such as Francis Bacon, John Locke, David Hume, and John Stuart Mill, insisted on classical empiricism, the idea that observation is at the core of knowledge. The Continental school of René Descartes, Baruch Spinoza, and Gottfried Wilhelm Leibniz argued that intellectual intuition and reasoning could also produce knowledge.

Despite the rivalry between these two schools, Popper believes they are more similar than different. He argues that neither approach is a true source of knowledge on its own. This is because both schools of thought incur the same problem of “ambiguous epistemology”—otherwise known as the theory of knowledge. The study of pure epistemology is often thought to be rational, as it probes the very nature and method through which knowledge is acquired. However, Popper observes that this is not necessarily true, because both the a priori (knowledge which proceeds from theoretical deduction) and a posteriori (knowledge which proceeds from experience or observation) approaches to reasoning ultimately rely on an act of faith, rather than rational reasoning.