Ray Monk

Truth for beginners

A graphic novel about logic? The idea is not as far-fetched, or as innovative, as one might think.

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Apostolos Doxiadis and Christos H. Papadimitriou

Bloomsbury, pp. 352, £

A graphic novel about logic? The idea is not as far-fetched, or as innovative, as one might think. Back in the 1970s, the publishing company Writers and Readers began producing a series of comic books (as they were then called) which sought to provide entertaining and instructive introductions, both to individual philosophers (Marx for Beginners, Wittgenstein for Beginners) and to intellectual movements and disciplines (Postmodernism for Beginners, Economics for Beginners). The series was extremely successful and many of these books are still in print.

Like those earlier books, Logicomix is written with the earnest intention to make an important but difficult body of work accessible to ordinary readers and a conviction that the way to do that is through comic-book art. In this case, though, the artwork and its reproduction (in full colour, on quality shiny paper) are a considerable improvement on the black and white line drawings of the … for Beginners series. Logicomix is a delight to look at.

The story it seeks to tell is that of Bertrand Russell’s quest for certainty and how that quest shaped the development of logic and computer science in the 20th century. Whether this is a story with a happy ending or not is something about which the authors of the book appear to be divided. Doxiadis (a novelist with a training in mathematics) takes his view from Russell himself, who said repeatedly that his quest for certainty had been a failure. The ten years he spent working on Principia Mathematica, in which he presented a system of logic he hoped to use to demonstrate with absolute certainty the truths of mathematics, he came to think had been a waste of time. This is because, under the influence of Wittgenstein, he came to believe that the ‘truths’ of mathematics were not, as he had previously imagined them to be, eternal verities concerning immutable, abstract objects; they were, rather, mere tautologies. That two times two equals four is a ‘truth’ on a par with the tautology that a four- legged animal is an animal. In the wake of this change of mind, Russell lost interest in logic and turned his attention to other things, e.g., politics, psychology, education, raising a family and sex.

In 1931, the logician Kurt Gödel published an astonishing proof that what Russell had wanted to do — construct a theory of logic from which every true mathematical statement could be derived — cannot possibly be done. Gödel’s Incompleteness Theorem has attracted an enormous amount of attention, and Logicomix makes much of it, but, in truth, Russell showed little interest in it. By the time it was published, he had, more or less, lost interest in both logic and mathematics and he never even bothered to read Gödel’s work.

Doxiadis, it seems, believes that Gödel effectively destroyed Russell’s hopes for logic and that therefore the story of his quest for certainty should be seen as a ‘tragedy’. His co-author, Papadimitriou, a computer scientist, believes that the story ends in triumph. His odd and unconvincing reason for this is that the ‘real hero’ of the story should be seen as the computer, which was developed by two mathematicians, Alan Turing and John von Neumann, trained in Russellian logic. Thanks to the computer, Papadimitriou claims, ‘the tools of reason are today at everybody’s fingertips’ and therefore Russell did succeed in making the world a more rational place, after all. This would make sense if that had been Russell’s aim in developing logic, but, as the first part of Logicomix makes clear, it wasn’t; what drove him was the desire to know something without any possible doubt.

The authors are a little too interested in their own disagreement on the question of whether the story they are telling is a happy one or not, and, at key points — including, most strikingly, the finale to the book — they insert themselves and their debate into the narrative. The book ends with an argument between the two authors about the value of computers, which seems only distantly related to the story they had initially set out to tell. Before we get to this disappointing conclusion, however, a surprising amount about Russell, logic, mathematics and philosophy has been conveyed in the most accessible and entertaining way possible.

Ray Monk’s two-volume life of Bertrand Russell is published by Vintage.