The author attempts to create a brief and accessible guide to the problems of philosophy. He introduces philosophy as a repeating series of (failed) attempts to answer the same questions: Can we prove that there is an external world? Can we prove cause and effect? Can we validate any of our generalizations? Can we objectively justify morality? He asserts that philosophy cannot answer any of these questions and that any value of philosophy must lie elsewhere than in offering proofs to these questions.

Focusing on problems he believes will provoke positive and constructive discussion, Russell concentrates on knowledge rather than metaphysics: If it is uncertain that external objects exist, how can we then know of them but by probability? There is no reason to doubt the existence of external objects simply because of sensory data.

The book also looks at the question of mathematical truths and philosophy within mathematics, particularly the question of how pure mathematics is possible.

Russell guides the reader through his famous 1910 distinction between knowledge by acquaintance and knowledge by description and introduces important theories of Plato, Aristotle, Ren