The Principles of Mathematics - Later Reviews

Later Reviews

In 1959 Russell wrote My Philosophical Development, in which he recalled the impetus to write the Principles:

It was at the International Congress of Philosophy in Paris in the year 1900 that I became aware of the importance of logical reform for the philosophy of mathematics. ... I was impressed by the fact that, in every discussion, showed more precision and more logical rigour than was shown by anybody else. ... It was that gave the impetus to my own views on the principles of mathematics.

Recalling the book after his later work, he provides this evaluation:

The Principles of Mathematics, which I finished on 23rd May, 1902, turned out to be a crude and rather immature draft of the subsequent work, from which, however, it differed in containing controversy with other philosophies of mathematics.

Such self-deprecation from the author after half a century of philosophical growth is understandable. On the other hand, Jules Vuillemin wrote in 1968

The Principles inaugurated contemporary philosophy. Other works have won and lost the title. Such is not the case with this one. It is serious, and its wealth perseveres. Furthermore, in relation to it, in a deliberate fashion or not, it locates itself again today in the eyes of all those that believe that contemporary science has modified our representation of the universe and through this representation, our relation to ourselves and to others.

Russell's Principles of 1903 also looms large in Ivor Grattan-Guinness' study of the roots of modern logic.

In 2006, Philip Ehrlich challenged the validity of Russell's analysis of infinitesimals in the Leibniz tradition. A recent study documents the non-sequiturs in Russell's critique of the infinitesimals of Gottfried Leibniz and Hermann Cohen.