Influence On Philosophy
As Nicholas Griffin discusses in the introduction to The Cambridge Companion to Bertrand Russell, Russell had a major influence on modern philosophy, especially in the English-speaking world. While others were also influential, notably Frege, Moore, and Wittgenstein, Russell made analysis the dominant methodology of professional philosophy. The various analytic movements throughout the last century all owe something to Russell's earlier works. Even Ray Monk, no admirer of Russell's personal snobbery, characterized his work on the philosophy of mathematics as intense, august and incontestably great and acknowledged in the preface to the second volume of his biography that he is one of the indisputably great philosophers of the twentieth century.
Russell's influence on individual philosophers is singular, perhaps most notably in the case of Ludwig Wittgenstein, who was his student between 1911 and 1914.
Wittgenstein had an important influence on Russell as he himself discusses in his My Philosophical Development. He led him, for example, to conclude, much to his regret, that mathematical truths were purely tautological truths, however it is doubtful that Wittgenstein actually held this view, which he discussed in relation to logical truth, since it is not clear that he was a logicist when he wrote the Tractatus. What is certain is that in 1901 Russell's own reflections on the issues raised by the paradox that takes his name Russell's Paradox, led him to doubt the intuitive certainty of mathematics. This doubt was perhaps Russell's most important 'influence' on mathematics, and was spread throughout the European universities, even as Russell himself laboured (with Alfred North Whitehead) in an attempt to solve the Paradox and related paradoxes, such as Burali-Forti. As Stewart Shapiro explains in his Thinking About Mathematics, Russell's attempts to solve the paradoxes led to the ramified theory of types, which, though it is highly complex and relies on the doubtful axiom of reducibility, actually manages to solve both syntactic and semantic paradoxes at the expense of rendering the logicist project suspect and introducing much complexity in the PM system. Philosopher and logician F.P. Ramsey would later simplify the theory of types arguing that there was no need to solve both semantic and syntactic paradoxes in order to provide a foundation for mathematics. The philosopher and logician George Boolos discusses the power of the PM system in the preface to his Logic, logic & logic, stating that it is powerful enough to derive most classical mathematics, equating the power of PM to that of Z, a weaker form of set theory than ZFC (Zermelo-Fraenkel Set theory with Choice). In fact, ZFC actually does circumvent Russell's paradox by restricting the comprehension axiom to already existing sets by the use of subset axioms.
Russell wrote (in Portraits from Memory, 1956) of his reaction to Gödel's 'Theorems of Undecidability':I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers wanted me to accept, were full of fallacies ... I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.
Evidence of Russell's influence on Wittgenstein can be seen throughout the Tractatus, which Russell was instrumental in having published. Russell also helped to secure Wittgenstein's doctorate and a faculty position at Cambridge, along with several fellowships along the way. However, as previously stated, he came to disagree with Wittgenstein's later linguistic and analytic approach to philosophy dismissing it as "trivial", while Wittgenstein came to think of Russell as "superficial and glib", particularly in his popular writings. However, Norman Malcolm tells us in his recollections of Wittgenstein that Wittgenstein showed a deference towards Russell such as he never saw him show towards any one, and even went so far as to reprimand students of his who criticized Russell. As Ray Monk relates in his biography of Wittgenstein, Wittgenstein used to say that Russell's books should be bound in two covers, those dealing with mathematical philosophy in blue, and every student of philosophy should read them, while those dealing with popular subjects should be bound in red and no one should be allowed to read them.
Russell's influence is also evident in the work of Alfred J. Ayer, Rudolf Carnap, Alonzo Church, Kurt Gödel, David Kaplan, Saul Kripke, Karl Popper, W. V. Quine, John R. Searle, and a number of other philosophers and logicians.
Some see Russell's influence as mostly negative, primarily those who have criticized Russell's emphasis on science and logic. Russell often characterized his moral and political writings as lying outside the scope of philosophy, but Russell's admirers and detractors are often more acquainted with his pronouncements on social and political matters, or what some (e.g., biographer Ray Monk) have called his "journalism," than they are with his technical, philosophical work. There is a marked tendency to conflate these matters, and to judge Russell the philosopher on what he himself would definitely consider to be his non-philosophical opinions. Russell often cautioned people to make this distinction. Beginning in the 1920s, Russell wrote frequently for The Nation on changing morals, disarmament and literature. In 1965, he wrote that the magazine "...has been one of the few voices which has been heard on behalf of individual liberty and social justice consistently throughout its existence."
Russell left a large assortment of writing. From his adolescent years, he wrote about 3,000 words a day, with relatively few corrections; his first draft nearly always was his last, even on the most complex, technical matters. His previously unpublished work is an immense treasure trove, and scholars continue to gain new insights into Russell's thought.
Read more about this topic: Bertrand Russell's Views On Philosophy