Historically, philosophers working on the theory of knowledge began by adopting some dogmatic criterion of how we know about the world and then said that some bodies of knowledge do not tell us about the world because they do not meet this criterion. For example, our knowledge of the world is based on experience, but mathematics is based on reason rather than experience, so mathematics just gives us analytical tools, not knowledge of the world.
This book begins by looking at some of the historical theories, and then it takes the opposite approach to develop its own theory of epistemology. First, it looks at the different types of knowledge we actually have: mathematics and logic, the sciences, empirical knowledge, direct knowledge of our own consciousness. Then it looks at what they have in common to generalize about the basis of our knowledge, showing that the distinction between analytic and empirical knowledge is not as sharp as philosophers have believed.
Along the way, it refutes one of the most influential errors in the history of philosophy. Berkeley and Hume argued that our knowledge of the world is based on sense perceptions, so we cannot know that there objects in the world that cause these perceptions, only that the perceptions themselves exist. But we also have proprioceptions of our bodies as objects in space: seeing an object, we not only have a perception of the object but may also have a proprioception that we are turning our head toward the object, focusing our eyes on it, and so on. Berkeley and Hume overlooked our proprioception of our bodies in space, so they concluded that we cannot know that there are objects in space.