Russell, Bertrand Arthur William (1872–1970)

Bertrand Russell divided his efforts between philosophy and political advocacy on behalf of a variety of radical causes. He did his most important philosophical work in logic and the philosophy of mathematics between 1900 and 1913, though later he also did important work in epistemology, metaphysics and the philosophy of mind, and continued to contribute to philosophy until the late 1950s. He wrote relatively little on ethics. His political work went on until his death.

In the philosophy of mathematics his position was logicism, the view that all of mathematics can be derived from logical premises, which he attempted to establish in detail by actual derivations, creating in the process what is essentially now the standard formulation of classical logic. Early in this work he discovered the self- referential paradoxes which posed the main difficulty for logicism and which he eventually overcame by the ramified theory of types.

Logic was central to Russell’s philosophy from 1900 onwards, and much of his fertility and importance as a philosopher came from his application of the new logic to old problems. Among his most important logical innovations were the modern theory of relations and the theory of descriptions. The latter enabled him to reparse sentences containing the phrase ‘the so-and-so’ into a form in which the phrase did not appear. The importance of this theory for subsequent philosophy was that it enabled one to recast sentences which apparently committed one to the existence of the so-and-so into sentences in which no such commitment was suggested. This laid the basis for a new method in metaphysics (widely pursued by Russell and others in the first half of the century) in which theories about items of a given kind are reformulated so as to avoid reference to items of that kind.

Logicism itself offers just such a treatment of mathematics and in his later work Russell used the method repeatedly, though the reformulations he suggested were rarely so explicit as the ones he had offered in mathematics. In 1914 he proposed a solution to the problem of the external world by constructing matter out of sensibilia. After 1918 he proposed to construct both mind and matter out of events. After 1940 he treated all particulars as bundles of qualities. In each case his motivation was to avoid postulating anything that could be constructed, thereby eliminating ontological commitments which had no independent evidential support. Outside mathematics, his starting-point was the empirically given and he attempted to make his constructions depend as little as possible upon items not given in experience. He was not, however, a strict empiricist, since he did not think that empirical evidence alone would be sufficient for the constructions and he was always prepared to supplement it in order to obtain them. He wanted to construct, not those items which were empirically warranted, but those which were required by the relevant scientific theories, for he regarded science as the best available, though by no means an infallible, source of truth. The task, in each case, was therefore to reveal the least amount of apparatus that would have to be assumed in addition to the empirical data in order for the constructions required by science to be possible. This methodology, which he pursued throughout his career, gives an underlying unity to what, more superficially, appears as a series of abrupt changes of position.