Logicomix: Logic and Madness Reviewed

By Ralph Dumain


Logicomix by Apostolos Doxiades & Christos H. Papademetriou; art by Alekos Papadatos, color by Annie Di Donna. New York: Bloomsbury, 2009.

This is a story of the development of modern logic and mathematical logic as a graphic novel, or rather a graphic novelized biography. The story is framed by a lecture (real or imaginary?) given by Bertrand Russell in 1939 on logic and life. Russell is invited by pacifists to argue for keeping Britain out of another world war. His hosts demand that he again take a pacifist position. He will not do so. Instead, he tells the story of his quest for absolute certainty and the role of logic in life.

The story is also framed by the authors who interrupt at various points, discuss it, and argue among themselves. Was Russell’s quest a success or failure? Is this a story of people or a story of ideas?

It is a story of both, with possible implications about the relation between the two, especially as most of the logicians and mathematicians are psychologically unsound, or their offspring become mentally ill. But to leave it at that would be a banality. The question is raised whether these obsessively logical minds are too rigid for the messiness of the real world. But this isn’t too deep an observation either. The authors are not this superficial, but if there’s a moral to this dialectic, it is not clearly drawn in the realm of philosophy.

This is the history of the revolution in mathematical logic, centered on Bertrand Russell, showing the dialectic of logic and insanity. This adds a dimension to Russell hitherto unfamiliar to me. Russell himself is worried from childhood on about the problem of lapsing into madness. And he sees this problem in the mathematical logicians he admires most—Cantor, Frege, Wittgenstein, and eventually Gödel, who are barking mad. At stake is judging the inevitability of a relationship between madness/passion and logic/certainty.

Russell finds mathematics shaky and disorderly. Philosophy is lost in idealist speculation. The synthesis of mathematics and philosophy is to found in... logic. Russell is inspired by Euclid. Then, emerging from the rejection of Hegel—in effect neo-Hegelianism, British idealism—Russell is influenced by G. E. Moore. The progression continues: Leibniz —> Boole —> Whitehead. This takes us through the first two sections.

The third section is Russell’s sojourn in Germany, where he meets his idols. . . and finds that they’re nuts.

But what is also particularly interesting is the treatment of the evolution of Russell’s ideas, involving interaction with the ideas of Peano, Frege, Cantor; how Russell struggles with the theory of types, in collaboration with Whitehead. The relationship with Whitehead is stormy, not made any easier by Russell’s love jones for Mrs. Whitehead. Nevertheless, out of this collaboration comes the publication of Principia Mathematica.

At this point there is a lengthy Entracte in which the authors debate the argument of their book—their conflicting perspectives on the prioritizing of life (Apostolis) or logic (Christos, the computer scientist) and the interpretation of the relationship between the two, while their female friend is preoccupied with the theatre. Must the personalities of these logicians have been so extreme and distorted in order to enable their profound discoveries?  (Christos prefers algorithms that yield methods rather than trying to prove logically and abstractly simple addition.) Later, Christos has an epiphany as a result of traversing the city with a female friend, which he relates in a letter to Apostolis. Christos likens logicians to map-makers. He wants to revisit his past, but finds that all the landmarks have changed, but his mental map of the area has not. He and his friend separate and proceed down different paths. Christos is mugged, Afterwards, the two reunite and visit the theatre to see a Greek tragedy, which triggers a thought. Logicians reject contradictions, but life, which is tragic, contains them. The logicians were excellent map-makers, but confused their maps with reality, yielding logic from madness. This is what insanity is, concludes Apostolis. Now back to the historical narrative (section 5: Logico-Philosophical Wars).

Enter Wittgenstein, whom we see from his first encounter with Russell to his work on his groundbreaking opus while fighting in the trenches in World War I, while Russell agitates against the war. World War I is a turning point in the book, for politics as well as mathematical logic, particularly in the divergent paths taken by Russell, Whitehead, and Wittgenstein. Just to see what a delusional wanker Wittgenstein was makes this worth reading. (There is one acerbic comment on the auto-martyrdom of the overprivileged.) Russell opposed the war and was jailed for it. Whitehead supported the British side and his naïve son died in combat. Wittgenstein volunteered not only to join the army, but also for the most dangerous missions. Russell worked on his ideas in jail. Wittgenstein’s inspiration for the Tractatus was worked out in the trenches.

One also learns here of Wittgenstein’s peculiar view of reality and the relation or lack of such of language to reality, the picture theory of logic/language, etc., and of the philosophical tug-of-war between Wittgenstein and Russell. How Wittgenstein could be taken seriously is a mystery to me, but the comic book history of this development puts it all in proper perspective. Maybe all history of philosophy should be written in comic book form. Actually it has, but often rather pointlessly except when it gives us occasion to laugh. I thought Introducing Heidegger was hilarious, just like like Colbert’s old show on Comedy Central.

It is difficult to get the ideas of logic and foundations of mathematics across in such a narrative form. I am as familiar with many of them as is any professional dilettante, though not so much with Wittgenstein. My philosophical instruction comes with the first meeting of Russell and Wittgenstein, and the implications of Wittgenstein’s Tractatus.

In their first meeting, Wittgenstein compares the Principia to Mozart. Wittgenstein is a fanatic, arguing against Russell’s view that truth has a relationship to empirical facts. Nevertheless, while Russell is too worn out to advance his project, Wittgenstein is eager to complete the project initiated by the Principia. They also argue about the relation of logic and mathematics to reality, where Wittgenstein, opposing Russell, maintains that mathematics is only a tool, not a foundation, and is purely subjective. Wittgenstein doesn’t like the intrusion of infinity, either.

Wittgenstein learned to fashion his picture theory of language and logic during the war, in which generals would make models of the terrain of combat in plotting their strategy. Russell wanted to find a way of proving the whole of mathematics, which got him caught up in the paradoxes of self-reference. Wittgenstein countered that is a misguided mission, that such metalogic cannot be formulated, or stated; logic can only be shown.

This all comes out in a discussion of the Tractatus, which Wittgenstein sends to Russell from the trenches, claiming to solve all of philosophy’s problems. The world is all that is the case, and language is a picture of reality. Russell argues that the picture theory yields truth only because of the higher language of logic. Wittgenstein counters: there is no higher language; picture language gives the facts; logic is just the form of language. Logic cannot be discussed logically; it can only be shown, which is why Russell’s project failed. The notion of the independent existence of mathematics, sets, and infinity is nonsense. Talk of the universe is nonsense. You can say there are three leaves on a tree, but not three leaves in the universe, because the universe cannot be pictured. Logic is empty form that cannot yield substance. All the real issues and the world’s meaning lie outside of what language can logically provide. So ends section 5.

As far as the logical concepts discussed in the book go, this for me is the most interesting part of it, inciting to further pursuit. There seems to be something constricting in the views of both Russell and Wittgenstein, the limitations of the latter arising out of the logic of the former.

Section 6 (Incompleteness) begins with the authors, discussing how the story is to be wrapped up. Christos finds the Tractatus hugely overrated, though it shook up Russell’s dream of certainty. Apostolis translates the struggle of reality vs. maps to the terms concrete vs. abstract.

Then we are back to the story, as the world is turned upside-down with the war, emblematized by the Dada movement. Russell cannot accept irrationality, but then he becomes a father. Wittgenstein has decided to become a teacher.

Contrary to Moore, Russell is unhappy that Wittgenstein sees logic as producing mere tautologies. Russell gets wind of the Vienna Circle, a propitious development for the extension of his project following the “failure” of his logic. Interruption in the narrative: Christos strongly objects to the word “failure,” but apparently Russell himself said it. Back to the narrative: Russell is feted in Vienna, and venerated as is Frege and Wittgenstein, for laying the foundations of a logical, scientific world view. Wittgenstein and Gödel are there. To Russell’s surprise, Gödel has read the whole of the Principia and wants to prove more than it attempted to do. Missing in the Principia is a clear statement that the truth value of every logical proposition can be proven. Russell assumes this to be true, but Gödel addresses this foundational missing piece. (Christos still bristles at Russell’s own claim that he failed.)

Russell pays a visit to Frege, but finds him a paranoid madman logically obsessed with the Jewish ‘menace’. Russell concludes that the only way to counter the fundamental human tendency toward irrationality is via education. Meanwhile, Wittgenstein berates and torments his students for not being able to grasp geometry, and is eventually expelled for beating them. Russell decides that educational reform is needed, so he sponsors a new form of schooling, the free school, Beacon Hill. This doesn’t work either, because the little brats are not geared toward self-discipline and self-directed learning. (Also, Russell ended up neglecting his own son.) Opposite approaches to education have both failed.

Russell’s son and Hilbert’s son both succumbed to insanity. Frege is depicted as being totally indifferent. (Apostolis interjects that maybe the fear of ambiguity and emotion were responsible for the inadequacy of these logicians as parents. Christos is again miffed that Russell claimed his Principia to be a failure.) 

Hilbert persists in pursuing his program. Russell is introduced to Von Neumann. Then Gödel springs on his audience his shocking Incompleteness Theorem. Von Neumann reacts: it’s all over. (Christos pipes up: No, it was a new beginning.)

The Vienna Circle presents Wittgenstein with its manifesto, dismissing everything outside of logic as nonsense. Wittgenstein retorts that his point was just the opposite: it is only what is outside logic that really matters.

Meanwhile, anti-Semitism is mushrooming in Austria and becoming more and more violent. Schlick is assassinated. His assassin is hailed as a hero by the Nazis. And meanwhile, Russell recognizes Beacon Hill and his marriage as failures.

We return to Russell’s ‘present’, i.e. his address in 1939 sponsored by pacifists. He finds Europe about to be enslaved by Nazis, and freedom also under assault by Stalin. His audience members argue from different vantage points the cause of this crisis.  Russell reminds them that his entire project was to realize Leibniz’s dream of total logical rationality, but the dream is dead, and certainty cannot be ascertained. Logic itself can become malignant. Even more so in life, certainty and logical consistency are impossible, and so Russell, despite his rationalist and pacifist inclinations, cannot positively counsel staying out of war. The Vienna Circle doesn’t have the answers. Formulas cannot decide all questions. It is your individual responsibility to decide what to do.

Thus ends section 6 and Russell’s narrative. The Finale takes us back to the authors and illustrators of this tome, as they embark on attending a performance of the Oresteia. Christos again objects to Apostolis’s interpretation of their narrative: Russell’s foundational quest was not a failure, and it was not a tragedy. As a story about people, many of them come to bad ends, but the happy ending is the creation of the computer, thanks not only to Von Neumann but to Alan Turing, who helped win the war against the Nazis in the process. Christos and Apostolis argue over whether the computer is an unmixed blessing. Christos finds an apt analogy in the Oresteia: a malignant order of murder and revenge ends with the intervention of Athena’s rationality and the creation of a new democratic state. One of the women chimes in, adding that in real life, however, the democratic state of Britain thanked Turing for his service by torturing him for his homosexuality and driving him to suicide. They cannot come to a happy conclusion so they allow the conclusion of the Oresteia to speak for them. Athena acquits Orestes, but assuages the Furies by giving them an honored place in the new order.

Thus ends the metanarrative. In an afterward the authors remind us that this is a partially fictionalized account of the history of the foundations of mathematics and its founders. They invent meetings for which there is no evidence or which definitely never occurred, but the views of the actors are accurately represented. Russell probably never met Frege or Cantor or attended Hilbert’s 1900 lecture. Russell did meet Peano. Russell probably did not attend Gödel’s talk on incompleteness, Hilbert certainly did not, but Von Neumann certainly did and said “it’s all over.” Russell could not have visited Frege afterwards, as Frege was dead, but Frege was a rabid anti-Semite.

In a final section there is a mini-encyclopedia of key ideas and persons presented in this narrative.

Commentary

This is a remarkable effort, in its intertwining of biography and its depiction of the logic behind the development of modern logic and foundations of mathematics. It may even be helpful in understanding the rationale motivating these developments all the way up to the Vienna Circle. It is definitely a worthwhile read.

However, one should also take note of what is not there. The conclusion, that both reason and the irrational must be taken into account, does not fully wrap up the narrative, as the fundamental assumption of the narrative’s actors is that reason = logic. If the logicians’ obsessions and aberrations also yield cautionary tales, then we should have a complete account of their views of reality, and not just logic in tandem with scattered facts about their relation to the rest of reality.

The written philosophical traditions of the world and the individual philosophers and schools of so-called “Western philosophy” have approached the nature of what we call philosophy in different ways, but as a specialized discipline, one ought to think that the core of philosophy as a specialized, abstract endeavor consists of ontology, logic, and epistemology and their linkages. Why in the first place would anyone think that the millennia-old (and new) problems of philosophy could be solved or dissolved via logic alone? The authors never address this larger abstract question in its fullness; rather, they rest at counterpoising logic and life, and the logician and madness.

My question implicates the Vienna Circle as well, which wedded logic to empiricism, but substituting logic for ontology. It also questions the Vienna Circle’s and Russell’s antagonist Wittgenstein, whose Tractatus, posing all the vital questions as lying outside of logic and the logical use of language, in the end offers… what? The same question applies to the later Wittgenstein, who is not part of this narrative. Christos has to face that the ‘happy ending’ of the invention of the computer doesn’t automatically solve the problems of life … he doesn’t mention the problems of ontology. As tp the question of the potential or limitation of artificial intelligence ... crickets. In the end, the duality of formalism and messy reality remains untouched by the resolution of the Oresteia.

And so... the contradictions of bourgeois philosophy and reality remain an enigma.

Written 18-19 September, 30-31 October, 1-2 December 2018


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