INTRODUCTION TO THE SECOND EDITION THE Principles of Mathematics " was published in 1903, and most of it was written in 1900. In the subsequent years the subjects of which it treats have been widely discussed, and the technique of mathematical logic has been greatly improved ; while some new problems have arisen, some old ones have been solved, and others, though, they remain in a controversial condition, have taken on completely new forms. In these circumstances, it seemed useless to attempt to amend this or that, in the book, which no longer expresses my present views. Such interest as the book now possesses is historical, and consists in the fact that it represents a certain stage in the development of its subject. I have therefore altered nothing, but shall endeavour, in this Introduction, to say in what respects 1 adhere to the opinions which it expresses, and in what other respects subsequent research seems to me to have shown them to be erroneous. The fundamental thesis of th
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