Principia Mathematica

"The present work was originally intended by us to be comprised in a second volume of The Principles of Mathematics. With that object in view, the writing of it was begun in 1900. But as we advanced, it became increasingly evident that the subject is a very much larger one than we had supposed; moreover on many fundamental questions which had been left obscure and doubtful in the former work, we have now arrived at what we believe to be satisfactory solutions. It therefore became necessary to make our book independent of The Principles of Mathematics."

"We have found it necessary to give very full proofs, because otherwise it is scarcely possible to see what hypotheses are really required, or whether our results follow from our explicit premisses."

"From this proposition it will follow, when arithmetical addition has been defined, that 1 + 1 = 2."

"The above proposition [1 + 1 = 2] is occasionally useful."

"But why all these pages to prove that 1 + 1 = 2?""Hm … how shall I put it? It's the price you pay for being truly certain."

"I can remember Bertrand Russell telling me of a horrible dream. He was in the top floor of the University Library, about A.D. 2100. A library assistant was going round the shelves carrying an enormous bucket, taking down book after book, glancing at them, restoring them to the shelves or dumping them into the bucket. At last he came to three large volumes which Russell could recognize as the last surviving copy of Principia Mathematica. He took down one of the volumes, turned over a few pages, seemed puzzled for a moment by the curious symbolism, closed the volume, balanced it in his hand and hesitated …"

"As a work in mathematics, Principia Mathematica soon became obsolete. Symbolic logic is also a field of philosophy, and so the study of major works from the past has a special role unlike that of the study of the history of mathematics."

"He [Russell] said once, after some contact with the Chinese language, that he was horrified to find that the language of Principia Mathematica was an Indo-European one."

"It takes a huge chunk of this volume just to prove that 1 + 1 = 2. And a large part of that proof revolves around the problems of the finite and the infinite, and the paradoxes that Cantor's work had thrown up."