Russell summed up his work, not always without some reconstructive hindsight, in My Philosophical Development (1959) and in his Autobiography (1967–9). In 1895 he formed a plan to ‘write one series of books on the philosophy of the sciences from pure mathematics to physiology, and another series of books on social questions. I hoped that the two series might ultimately meet in a synthesis at once scientific and practical’ (1967–9, vol. 1, p. 125). The first part of this project was achieved, but not the final synthesis: most commentators agree that there is an unbridgeable gap between his writings on metaphysical or mathematical philosophy on one side and his works on morality, education, politics and his polemics against religion on the other. This latter part of his output (see Ryan 1988 for a full discussion) has been far less highly valued by later academic critics, although the proportion of his writing remaining in print must be testimony to its continuing popularity.

His long philosophical career fell into several phases.

(1) Until 1898, he was a Hegelian idealist (see Griffin 1991), a period he repudiated entirely.

(2) Then, he wrote: ‘It was towards the end of 1898 that Moore and I rebelled against both Kant and Hegel. Moore led the way, but I followed closely in his footsteps’ (1959, p. 54). Until around 1911 he was deeply engaged in the philosophy and foundations of mathematics, espousing varying forms of strongly realist metaphysics and epistemology.

(3) In 1911 he met Wittgenstein, first as his teacher and soon as a colleague. He had a period of atomism allied to forms of neutral monist ontology, with an increasing interest in language.

(4) From about 1927 to 1938 he spent much time away from narrowly defined philosophy, lecturing and writing on a huge range of popular subjects.

(5) Between 1938 and about 1950 he returned to academic philosophical work, making contributions to the philosophy of science.

(6) From 1950 to his death at the age of 98 in 1970, most of his energies went on extremely active political campaigning.

Russell said that his original interest in philosophy had two sources:

It is impossible to summarize common or continuous views in his work; but there are some assumptions that do underlie it from 1898 onwards.

(1) He never moved away from an egocentric, Cartesian stance as the starting-point for philosophical questioning, and was therefore unable to shake off the set of traditional problems associated with the reliability of ‘our’ knowledge of ‘the external world’. Here, he ended in a familiar cul de sac: ‘the whole of what we perceive without inference belongs to our private world. In this respect, I agree with Berkeley. The starry heaven that we know in visual sensation is inside us. The external starry heaven that we believe in is inferred’ (ibid., p. 27).

(2) He always maintained a reasoned confidence in what he was happy to collect under the title of science, accepting its results as data for philosophy, and preferring to clothe his philosophical writing in scientistic terminology (‘analysis’, ‘atomism’, ‘incomplete symbols’). This preference may have been a reaction against the view of metaphysics as a consolatory branch of belles lettres which he castigated in his idealist predecessors.

(3) More important, he always maintained that philosophy, in analogy with ‘science’, could and should deliver substantive results: theories about what exists, what can be known, how we come to know it. This assumption in his work caused some of its most serious problems, and also set it apart in the most obvious way from both the early and the late thinking of Wittgenstein. Although he shared the early Wittgenstein’s use of a language of analysis, a work such as The Philosophy of Logical Atomism (1918; very unlike Wittgenstein’s Tractatus) was deeply ambiguous about the nature of the analytical enterprise, its objectives and the nature of its end-points. The status of his ‘logical atoms’ was entirely unclear. The whole project was presented as a ‘scientific’ investigation into what sort of things exist, and how the mechanism of perceptual knowledge is meant to work. Yet he understood that he was in what he himself believed to be the territories of physics and empirical psychology. Russell retained a desire for an edifice of philosophical theory which would somehow explain how the mechanism of perception related to what can be known (or, sometimes, said). Here, his roots in the traditions of British empiricism are evident (see Pears, 1967), overlaid with an apparatus of modern logic and dressed in quasi-scientific language.

Russell’s important contributions to philosophy began negatively, with his rejection of the idealism he had read in Bradley and heard from McTaggart (see Hylton 1990). His study of Leibniz (1900) gave an example for later analytical-historical studies in identifying a handful of crucial tenets in Leibniz, and then diagnosing the conflicts inherent in them. The same procedure was applied by Russell (and Moore) against idealism. There, the crucial tenet was claimed to be the ‘dogma of internal relations’: all individuals are necessarily related to each other, forming a single Whole. Russell argued for the existence of genuinely independent individuals and the entire truth of particular statements (see his Philosophical Essays, 1910). His leap from idealism to a world of separate facts raised problems about the ontological status of those facts, and the relations between a judging subject, a judgement and an object of judgement (see F.P. Ramsey, ‘Facts and propositions’, Aristotelian Society Supplementary Volume, 1927, for a clear discussion). Regardless of his difficulties, to him, pluralism was a necessary presupposition of ‘analysis’ (see The Philosophy of Logical Atomism, 1918, I).

Russell’s ontological speculations were never resolved. By the time of The Analysis of Mind (1927) he had reached this view:

Both physics and psychology were built upon ‘a neutral stuff’ (p. 287). The mind itself was construed along Humeian lines, with ‘a collection of events connected with each other by memorychains’ (p. 27) as a modernized version of Hume’s congeries of ideas. is golden and a mountain” is false for all values of x’.(1959, p. 84)

Existence was understood in terms of truth: ‘“The author of Waverley exists” means “there is a value of c for which the prepositional function ⁶x wrote Waverley’ is always equivalent to ‘x is c’ is true”’ (p. 85).

‘On denoting’ showed how a logical form could differ from obvious forms of common language. But it was not until 1918, Russell claimed later, that he first become interested in the definition of ‘meaning’ and in the relation of language to fact. ‘Until then I had regarded language as “transparent” and had never examined what makes its relation to the non-linguistic world’ (1959, p. 145). Although in his final period, after 1950, he tended to play down his earlier work on language (perhaps as a result of his scorn for what he considered as trivial, ‘linguistic’ philosophy), some of that work had been well ahead of its time. From 1921, for example, there is a passage that could have come from Wittgenstein twenty years later:

…and more strongly still: ‘For my part, I believe that, partly by means of the study of syntax, we can arrive at considerable knowledge concerning the structure of the world’ (last words of An Inquiry into Meaning and Truth, 1940).

Russell’s reputation is most unshakeable in logic and the philosophy of mathematics. His early search for a solid base of certainty for mathematical truth led him to the view that it was grounded in logic. His logicism was developed independently from the earlier work of Frege, and was expressed in notation he had learned from Giuseppe Peano in 1900. The Principles of Mathematics (1903) and the three volumes of Principia Mathematica (1910–13, written with A. N.Whitehead) remain as treasure-stores of painstaking logical argument: the foundation for modern, systematic logic (see Kilmister 1984). But the cracks in Russell’s project began to show as early as 1901, putting an end to his ‘logical honeymoon’, as he said (1959, p. 75). His interpretation of numbers as classes of classes was underminded by paradox: consider a class that is not a member of itself—is it a member of itself?—if yes, then no—if no, then yes. The theorizing required to avert this paradox cost Russell years of thought, and led to the development of important parts of the technical apparatus in Principia Mathematica. Later, after 1911, discussions with Wittgenstein convinced Russell that the logicist project was flawed in principle. He came to accept the view of the Tractatus that mathematical statements are vacuous tautologies, not truths about a realm of logico-mathematical entities.

In 1938, aged 66 and temporarily tired by two decades of political polemics, Russell returned to the academic teaching of philosophy. The results—An Enquiry into Meaning and Truth (1940) and Human Knowledge (1948)—contained valuable work on scientific method. He came to the view that inductive inference cannot be enough for ‘science’, and moved towards a surprisingly Kantian position that some ‘principles of inference’ must be presupposed: ‘And whatever these principles of inference may be, they certainly cannot be logically deduced from facts of experience. Either, therefore, we know something independently of experience, or science is moonshine’ (1948, p. 524). He ended by expressing his deeply ingrained empiricism in the broadest, most general terms:

Nothing has been said here about Russell’s works on morality, politics and religion. These were copious, forceful, elegant and full of wit, but he himself rarely saw them as original. He never shook off the radical, aristocratic, Victorian liberalism inherited from his parents. His attitude to religion was essentially that of an eighteenth-century rationalist.

An interesting angle on the tensions between Russell’s many concerns is seen in his affection for Spinoza (see Blackwell 1985) and a Spinozistic strain that appears many times in his writing (most strikingly, at the end of The Problems of Philosophy, 1912). Passages such as this, on Spinoza, must have contained some element of would-be self-portraiture: The love of humanity is a background to all his thoughts, and prevents the coldness which his intellectualism might otherwise engender. It was through the union of the love of truth and the love of humanity, combined with an entire absence of self-seeking, that he achieved a nobility, both in life and in speculation, which has not been equalled by his predecessors or successors in the realm of philosophy’ (review of Hale White and Stirling’s translation of Spinoza’s Ethics, The Nation, 12 November 1910, in Collected Papers, vol. VI, p. 254). Russell’s repeated attempts at systematic philosophical theorizing maintain their interest more from the brilliance of his writing and the virtuosity of his logical talents than from the creation of any single positive set of views that could be encapsulated as Russell’s Philosophy. (Indeed, it seems to have been fairly early in his career that he realized he was fated to change his mind so often that a lasting synthesis was unlikely.)

Russell is still the most widely read philosopher in the analytical tradition, as he might have wished: ‘Philosophy proper deals with matters of interest to the general educated public, and loses much of its value if only a few professionals can understand what is said’ (1948, p. 5). His popularity has had one important consequence: his writings may have brought more people to an interest in philosophy than those of anyone else in the twentieth century, and this is not negligible. He himself came to judge his political campaigning against nuclear weapons as more valuable than theoretical philosophizing. Whatever one thinks of that, the example he set for the role of an intellectual in practical affairs has been hugely influential. (Here he resembles Noam Chomsky, who delivered the memorial lectures on Russell in Cambridge in 1970.)

The Principles of Mathematics (finished on the last day of the nineteenth century), written at great speed, with a passion of intellectual discovery, must remain a monument to Russell’s great logical gifts. His place, with Frege, as a founder and builder of modern logic, must be untouchable.

His influence as a philosopher is less clear. Versions of logical empiricism similar to Russell’s varied positions remained popular in academic philosophy in the USA for some time after the influence of Wittgenstein had obliterated them in Britain. Russell’s analytical, quasi-scientific approach remained the dominant style in philosophy (but regrettably without his elegance and wit).

His relationship with Wittgenstein has been much debated. From 1911 to 1913 Russell’s problems became Wittgenstein’s problems. The extent of his intellectual generosity towards Wittgenstein was poorly acknowledged and has not been adequately recognized.