logicomix

It's an ambitious idea, creating a graphic novel about mathematicians, logicians and philosophers arguing about absolute truth. But 'Logicomix: An Epic Search For Truth', by Apostolos Doxiadis and Christos Papadimitriou, pulls it off by finding the drama in this rather heady subject. With many of the story's protagonists plagued by insanity, it even has shades of tragedy.

In 'A Brief History of Time' Stephen Hawking recounts the anecdote ascribed to Bertrand Russell, who after a lecture on astronomy got a question from the audience:

...a little old lady at the back of the room got up and said: "What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise." The scientist gave a superior smile before replying, "What is the tortoise standing on?" "You're very clever, young man, very clever", said the old lady. "But it's turtles all the way down!"
Logicomix - 1

The turtles provide a nice metaphor for the elusive 'foundational quest' that Russell, along with other illustrious figures like Whitehead, Wittgenstein, Frege, Cantor and Gödel, embarked on in the early 20th century. Was it possible to find some absolute basis to mathematics - a way to prove Euclid's 2000 year old 'Elements' - and to construct a system of logic to underpin all human knowledge?

[As a side note: for some reason the Dutch translation adds an article to the title ('Een epische zoektocht naar de waarheid', 'An Epic Search For the Truth'), which seems to miss the point: the quest was not for a specific truth but for the concept of truth itself.]

The answer, as it turned out - and as Kant had already predicted with his a priori knowledge - was no. Ultimately, knowledge is a human construct, whether it's mathematical or philosophical, and only expressible in language, which is again a human construct. Thus any attempt at defining something absolutely ends up being circular, or as Russell put it, tautological.

Put differently, a system of knowledge can be internally coherent and produce 'true' statements, but there will never be a way of proving those statements against anything outside that system. There is no objective point of reference, unless you make that point of reference part of the system you began with - which leads to an infinite regress. In that sense it really is turtles all the way down...

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In retrospect the foundational quest was a thoroughly modernist undertaking, doomed to failure but with a tragic beauty. As Doxiadis says in this making of video:

Bertrand Russell soon became our tale's hero, and also its narrator. He was one of the quest's greatest stars, its most eloquent protagonist. Bertrand Russell is a quintessentially modern person, an atheist yearning for the absolute, a cynic masquerading as an idealist - or was it the other way around?
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