Logic and Knowledge

By Bertrand Russell; Robert Charles Marsh | Go to book overview

1908
MATHEMATICAL LOGIC AS BASED ON
THE THEORY OF TYPES

In this paper, originally published in the AMERICAN JOURNAL OF MATHEMATICS, Russell offers his celebrated approach to the solution of a set of classical mathematical and logical problems involving the appearance of contradiction. The doctrine of types (as he then called it) was 'put forward tentatively' in the second appendix to THE PRINCIPLES OF MATHEMATICS, a valuable discussion from the point of view of history, since it shows us these ideas in the form they took shortly after they first came to Russell in the opening years of the century, although (in the words of the Introduction he wrote to the second edition of the PRINCIPLES in 1937) as 'only a rough sketch'. The paper reprinted here gives us what was in effect the finished theory, although these ideas are better seen in the larger context in which they reappear in the first volume of the PRINCIPIA MATHEMATICA (1910).

The theory of types has played such an important role in modern philosophy that it is pointless to comment further on its significance, other than to say that this paper is one of Russell's finest and universally acknowledged to be a masterpiece of recent philosophic thought.

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