Logic and Knowledge

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

1901
THE LOGIC OF RELATIONS

In his autobiographical essay MY MENTAL DEVELOPMENT Russell says: 'The most important year in my intellectual life was the year 1900, and the most important event in that year was my visit to the International Congress of Philosophy in Paris.'* He travelled to Paris with Whitehead, his former teacher and then colleague, and they were both struck by the skill shown in the discussion of mathematical and logical problems by Peano and his pupils. Impressed, Russell went home to master Peano's works and particularly his notation. Its influence on the later Russell-Whitehead notation of the PRINCIPIA MATHEMATICA is fairly easily traced.

THE LOGIC OF RELATIONS was written in 1900 and published the following year. It was composed in Peano's notation, although it represents work contemporary with the writing of much of the PRINCIPLES OF MATHEMATICS in which Russell uses an early form of the notation developed fully in the PRINCIPIA MATHEMATICA. Those unfamiliar with Peano's symbols will find a concise and admirable discussion of the system in Jørgen Jørgensen's standard rok, A TREATISE OF FORMAL LOGIC, Copenhagen and London, 1931, Vol. I, p. 176 ff. The Peano notation is actually not difficult to read if one knows that of the PRINCIPIA MATHEMATICA, and the paper is therefore reproduced in its original form.

Russell's first publication was in 1895, the year following his first period of residence at Cambridge. It is of no particular interest, although his mathematical investigations during the following four years led to publications that repay examination. However it is with this paper that we see clearly the appearance in philosophy of a creative mind of the first order, and on its publication (in the year in which he was twenty-nine) Russell's eventual position as a 'thinker of reputation' seems to have been assured. Asked what idea in the paper he now feels to be the most important, Russell replied 'my definition of cardinal number'which here appeared in print for the first time.

It was largely on the basis of this paper and next but one in this collection that Russell was elected a Fellow of the Royal Society in1908.

*The Philosophy of Bertrand Russell, Evanston and Cambridge, 1944
et seq., p. 12.

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