Human Knowledge: Its Scope and Limits (1948) is arguably the best defense of empiricism I've ever read. It is a philosophical position which I personally subscribe to and which is, I think, the most consistent doctrine of theory of knowledge available. Throughout the book, Russell meticulously argues for his position through analyzing alternative interpretations and theories and refuting them. Along the way he honestly states the flaws and limits of his own theories and acknowledges plurality of choice whenever this is factually the case.
The most important point here is that while Russell refutes all forms of idealism as valid epistemology, he does concede that instantaneous solipsism is as valid as his own empiricist theory of knowledge. The problem is, the solipsist refuses all common sense experiences - such as personal history, future expectations, the existence of other minds, etc. - and ends up in absurdities.
The book itself is written in a style that offers the reader lucidity, accessibility and comprehensiveness. As a whole, the book takes the reader by the hand on an analytical exploration of the scientific method and its concepts and it continuously builds on earlier results and conclusions. As one moves on one is offered summaries and short recapitulations of earlier points, which makes for easy reading and eases one into deeper understanding of the problems concerned. The only exception is Part V, which deals with probability theory and is rather theory-driven, so I think this part might be problematic for those readers that find mathematics hard to follow. Another major plus is that most chapters end with one or two paragraphs in which Russell summarizes the main arguments and conclusions of the chapter - which helps in returning to earlier parts of the book to better understand later, more complex parts.
Russell was besides a skilled lecturer a gifted writer and a very original thinker, and in Human Knowledge he combines all three to offer the reader a gem of philosophical exploration. It is rather sad that Human Knowledge is among Russell's lesser known works. (It's also, apart from his mathematical works, the biggest works - perhaps this plays a role...)
It would go too far to explicitly state all of Russell's analyses and conclusions, which would not fit in such a review. Let me summarize the end result:
Russell's problem revolves around the question: How is synthetic knowledge, inferred from personal experiences, possible? And if it's possible, what is the status of this knowledge?
The problem is this: knowledge of the physical and mental world is fundamentally private. We each experience sensations and recollections of things and persons. Science describes the physical and mental world as objectively out there. How are our private world and the world of science related? And what does it mean to know something about some thing in the world? In other words: what general principles are necessary in order to be able to establish scientific knowledge?
In logic and mathematics we deal with certain knowledge, yet all our knowledge in these spheres is, ultimately, tautological. That is, it doesn't offer us any information about the world. It is only when we apply mathematics to empirical data that science can take off. And these empirical data are rooted in the life of common sense. We are used to see A occur and then see B follow. Hence we infer that A causes B. As Hume already said: causality is nothing but habit. Now, we only see B, and infer that A caused B even though we missed A altogether. Are we allowed to claim this? If so, why? And how?
Relying only on empirical data (i.e. experience) leads to solipsism. So we have to find some general principles that allow us to form rational expectations about the future and unobserved events but that cannot be themselves part of this experience. Usually people now yell "induction!" But Russell is smart to notice that induction in itself is a tautology - it only states in a general form that past experiences allow for certain expectations. It is only when we substitute particular experiences for the empty variables that induction becomes useful. Yet when we do this, we already suppose induction to be valid. It seems we need more general principles that allow for induction as method to be used in science.
Russell in essence seeks to understand how we generate knowledge from personal experiences. And in this language is crucial. We denote objects and we express our attitudes in words (object-words and syntax words respectively). Sentences are complexes of these. Knowledge consists in us grasping certain propositions to be true and others to be false. That is, we align our beliefs to our experiences. Russell is looking for general, a priori principles as the foundation of human knowledge - and is thus, in effect, looking for the truth of universal propositions and existence-propositions. That is, he wants (1) propositions that are true and valid at all times and (2) propositions that state the existence of things (and ultimately all things in the universe) independent of personal experience. I.e. we know of things existing through testimony of others, through books, through historical sources, etc. and we also know of things existing that cannot be experienced by any human.
Now, both (1) and (2) are both necessary for human knowledge and, ultimately, unprovable. So why should we adopt them? Well, because they pay to be held true as general principles of all our knowledge. In the end, Russell falls back on our biological roots: forming habits and expectations out of past and present experiences - while allowing for continual re-adjustment of beliefs - is biologically adaptive. The alternative is to become a solipsist who not only denies the existence of others and the world, but also his/her own past and future.
Admittedly, this Russell's final answer might leave us somewhat unsatisfied. Yet he does claim many times in the book that all he's looking for is grounds for rational expectations that transcend common sense and open up the path to science. Science is a continuous progress of endless adjustments of these grounds, through experiences, which would be impossible without these unprovable principles.
To sum up: Russell offers five postulates that allow for scientific inferences (i.e. laws, theories, hypotheses, concepts, etc.) from experience. These principles cannot be proved yet without them, science would be impossible. The consequence of these principles is that all our knowledge of the physical and mental world is uncertain, inexact and partial. That is, all scientific knowledge is characterized by degrees of certainty and exactness; in some cases these degrees can be calculated (through applied mathematics - probability theory) but in most cases these degrees have to be estimated by rules of thumb or best guesses. Our knowledge of the world is biologically rooted, which means the major assumption is that it pays (evolutionarily speaking) to have true beliefs about the world. These beliefs manifest themselves in behavior - communication, action, etc. - that are guided by expectations about the future state of the world. Through the development of language, and ultimately logic and mathematics, human beings can overcome the primitive, pre-scientific knowledge of common sense; yet we can never obtain absolute and certain knowledge.
I'll probably re-read this book in the future, since it is so vast in its scope and so dense in its material. Throughout the book Russell uses examples from cosmology and biology to psychology and geography in order to illustrate his theories. This means that on his/her journey through the book a reader has to jump mentally from here to there and back again, and sometimes the sheer amount of information numbs the mind. I guess this is one of those books that offers new payments on every subsequent readings. (Which is what brilliant philosophy has to do, in my opinion).
Definitely recommended for anyone interested in these topics!