Bertie’s Dream

Today’s birthday boy is a mathematician but he is not from the Renaissance and anything but obscure, he is Betrand Arthur William 3rd Earl Russell known to the world of academia as Mr Russell and to his friends as Bertie. An intellectual giant who straddled the 20th century, he was born 18th May 1870 and died aged 97 2nd February 1970. His Wikipedia article lists him as philosopher, logician, mathematician, historian, socialist, pacifist and social critic missing out popular author and educationalist; Russell left an intellectual heritage that touched almost areas of human existence. To produce a potted biography of Russell here would be literally impossible and I don’t intend to try I will just make a few remarks about Russell the logician.

I paid my dues as a historian of science working in a research project on the history of formal logic and Russell, of course, loomed large on the horizon no matter in which direction one looked as a logic historian. A mathematical graduate of Cambridge University Russell was inspired by a meeting with the Italian mathematician Giuseppe Peano at the International Philosophy Conference in Paris in 1900 and set out deduce the whole of mathematics from the axiom of formal logic in order to avoid the foundational crises into which mathematics had been plunged by the set theoretical antinomies generated by Cantorian set theory. Unbeknown to Russell at that point the German mathematician Gottlob Frege was already engaged in the same project. Unfortunately Russell torpedoed both his own and Frege’s efforts with the discovery of the so-called Russell’s paradox in 1901. Russell’s own presentation of the paradox in simple language is the question, ‘in a village where the barber shaves all of those who do not shave themselves who shaves the barber?’ If the barber shaves himself then he doesn’t shave himself however if he doesn’t shave himself then he as the barber must shave himself. Applied to infinite set theory the paradox torpedoes all attempts to define numbers in terms of sets, the basis of both Russell’s and Frege’s work. Russell’s solution to the problem was type theory just one of the monuments that he raised to himself in his long and fruitful life.

Russell presented his logically founded mathematics together with Alfred North Whitehead, who was actually the principle author, in the three volume Principia Mathematica (1910, 1912, 1913). The Cambridge University Press was convinced that the book would be a financial flop and set the price accordingly and only printed 750 copies. However the first edition sold out and they actually made a profit on what is probably the most unreadable ‘best seller’ of all times. A second edition was issued in 1925. Although probably inferior to Frege’s own Grundgesetze der Arithmetik PM set the standard for symbolic mathematical logic because Frege’s two-dimensional Begriffschrift was regarded as incomprehensible by most readers.

Somewhere in his autobiographical writings Russell tells the following story about PM. He has a recurring dream that takes place at some undefined point in the future. He is in a library and a librarian is walking along the stacks selecting books from the selves that are to be deleted and throwing them into a bucket. As Russell watches he reaches the last copy of PM in the world and stops, at this point Russell wakes from his dream…

All fame is transitory.

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1 Comment

Filed under History of Logic, History of Mathematics, Uncategorized

One response to “Bertie’s Dream

  1. Markk

    Good entry! “Bertie” is the star of one of the most interesting and odd comic books ever created. Logicomix is a wonderful self-referential paradox of a read, that makes up history but tells it too.

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