The Barber of Seville

Although it was not a real promise to write yet another time on Russell, nevertheless once I have said that I may return to him sooner or later I feel it as a kind of obligation to do so. And since there is a saying that you must never put off till tomorrow what you can do today, I think the best is to write about him now.

I reread the chapter “The Limits of Philosophical Knowledge” in Russell’s book The Problems of Philosophy, but when I asked myself what I should say about it, I realized that I had not so much to add to my criticism written a few weeks ago. For also in this chapter Russell’s view on philosophy (as treated here and in the whole book) is somewhat limited and moreover it is a bit outdated. When Russell thinks of philosophy he thinks of epistemological issues in the first place, so questions in the field of knowledge. But as I have written four weeks ago, there is so much more in philosophy. Now it is so that Russell himself writes in this chapter that “we have scarcely touched on many matters that occupy a great space in the writings of most philosophers. Most philosophers – or, at any rate, very many – profess to be able to prove, by a priori metaphysical reasoning, such things as the fundamental dogmas of religion, the essential rationality of the universe, the illusoriness of matter, the unreality of all evil, and so on.” (p. 82) And then he thinks of philosophers like Kant and Hegel. However, according to Russell, such problems cannot be solved by philosophy but only by science. That’s true, I think, but I doubt whether most, or otherwise very many philosophers spent their time in Russel’s days and before on the themes just mentioned and on related themes. I think that there were also quite a lot of philosophers who reflected on other themes, and they were not the least important. I guess that there were more of them than Russell thought. A case in point is Nietzsche. And when I was developing the ideas that led to my dissertation, I spent much time on studying the works of the German philosopher Wilhelm Dilthey (1833-1911), who transformed the method of explaining texts into a general method for the social sciences. By doing so he developed the method of Verstehen (understanding) and in this way he became one of the founders of the philosophy of action (still today one of the lively branches of philosophy). Dilthey was also an important contributor to the so-called Lebensphilosophie (philosophy of life). A few other philosophers I want to mention yet without further explanation are Montaigne, Rousseau and Karl Marx. All these philosophers (with the exception of Dilthey) are mentioned in Russell’s History of Western Philosophy.

But by writing in this way on Russell I tend to ignore his great contributions to philosophy. For example, his critique on set theory led to a shock in the world of mathematics around 1900. I am not a mathematician, so I can’t explain you the ins and outs in detail and in a accessible way, but who doesn’t know the story of the Barber of Seville? And then I don’t mean Rossini’s opera but the barber in this town who had written on the signboard of his shop “I shave all men who do not shave themselves” (implying: and only men who do not shave themselves). It’s a paradox, for what about the barber himself? The story has been told in another version by Lewis Carroll and has been used by Russell to criticize the set theory, for does or doesn’t the barber belong to the set of his clients? The set theory couldn’t tell and finally the problem was solved by changing the rules that define a set. It seems that there is nothing as easy as that: When you can’t solve it, ignore it. In a positive way we can say, of course, that a mistake in the set theory was eliminated in the sense of Popper’s error elimination. It’s the way science develops. Nevertheless, it looks a bit like a trick. Moreover, actually the entire paradox is based on the prejudice that the barber is not a woman.