Pencil Shavings

Saturday, December 19, 2009

Logicomix: An Epic Search for Truth, by Apostolos Doxiadis and Christos Papadimitriou


This graphic novel is about the life and work of Bertrand Russell, a logician whose search for the foundations of Mathematics led to the formation of analytic philosophy. He is famous for the paradox he stumbled upon (known to us as Russell's paradox), which in layman terms goes something like this.
Of all the books in the world, there are those that are refer to themselves in the text (self-referential) and those that don't refer to themselves. If I were to compile a catalogue of all books that are NOT self-referential, would the catalogue contain an entry of itself?

Therein is the conundrum: if the catalogue were to list itself, then it is no longer not self-referential; but if it did not list itself, then it is not a catalogue of books that are not self-referential!
In Mathematical language, the catalogue is "the set of all the sets that are not members of themselves". Of course this seems kinda mind-boggling that a set could be a member of itself, but when you think of specific examples it is not so weird. For example, a set of all ideas is an idea and so the set would contain itself, but a set of all birds is not a bird and so it won't contain itself. (Of course the practical functions of sets in Mathematics befuddles me...)
This comic is thought-provoking. While this comic is about logic, philosophy and Mathematics, the authors are emphatic that it is not a "Dummy's guide to logic" in pictures; instead, they say that it is a story where logicians are the superheroes, or to be precise, a tragedy. This is a most interesting way of seeing itself because the book then becomes a reflection of the struggle of the protagonist — the struggle between reason and passion, logic and madness. It could be said that tragedy can only occur with paradox and conundrum, yet these are the very things that Bertrand spends his life's work trying to solve. Does he solve his own paradox? What is his personal resolution?
At the end, Russell felt like a failure. Ludwig Wittgenstein's clever sidestep of Russell's paradox in his "picture theory" (where the world is modeled by language), in addition to the Kurt Godel's devastating Incompleteness Theorems, which pretty much says that it is impossible to prove all arithmetic proofs, which was what Russell spent 20 years trying to do, meant the end of Russell's lifelong quest for the foundations.
Yet, there is transcendence. Russell doesn't succumb to his arch-enemy, madness (not for long, anyway), but he quotes his protege Ludwig Wittgenstein near the end of the comic: "All the facts of Science are not enough to understand the world's meaning". The comic ends with Athena's resolution of the dilemma in the old Greek myth "Oresteia", which is a grand way to end a paradoxical tragedy about logic.

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