By invading many areas traditionally covered by philosophy, modern science has made philosophy increasingly irrelevant, and has presented it with the challenge to legitimate itself. This challenge has not been successfully met, so much so that several scientists, and even some philosophers, have concluded that philosophy is dead and has dissolved into the sciences. The question then arises whether philosophy can still be fruitful, and what kind of philosophy can be such. This book attempts to give an answer to this question, reviving the ancient view that philosophy is the acquiring of knowledge. This involves rethinking knowledge and methods to acquire knowledge, including mathematical knowledge, which raises special problems. In addition to describing the aim of the book, the introduction briefly describes the parts and the individual chapters of the book, and outlines some conventions adopted in the book.