In Pynchon’s Gravity’s Rainbow there are a couple of references to Gödel’s incompleteness theorem. Pynchon himself wisely doesn’t try to explain the theorem, he simply weaves it in as a humorous side-remark. However, in the wonderful A Gravity’s Rainbow Companion (2nd ed.), the author — Steven C. Weisenburger — comes to the reader’s rescue with the following elaboration:
Gödel’s theorem is named for German mathematician Kurt Gödel (1906-78), whose famous paper of 1931 addresses the long-standing problem of “axiomatic consistency”. Before Gödel, it appeared that Alfred North Whitehead and Bertrand Russell’s monumental Principia Mathematica (1910) had established the consistency of all axioms within the system of arithmetic. Whitehead and Russell had employed a method of “mapping,” or translating, arithmetical expressions onto sentences of formal logic. These sentences could then be verified and tested for consistency as purely logical statements. But the results would also be applicable, by reversing the mapping, to the system of arithmetical axioms: for example, the axioms governing multiplication. Principia Mathematica ran to three cumbersome volumes. Gödel’s relatively succinct paper, “On Formally undecidable Propositions in Principia Mathematica and Related Systems” (1931), overturned the work of Russell and Whitehead in just over thirty pages. Using the same methods of “mapping” as appear in Principia, Gödel was able to produce a sentence that demonstrated that Russell and Whitehead’s work, “or any related system,” was inherently incomplete. There would always exist, within the rules of the system, the possibility of a sentence or proposition the validity of which could not be decided by the rules themselves.
Would Pynchon be pleased with the level of accuracy? Of course not.
[...] Ole Thomassen Hjortland bloggt darüber, dass in Thomas Pynchons Buch “Gravity’s Rainbow” (dt. “Die Enden der Parabeln“, übersetzt von Elfriede Jelinek und Thomas Piltz) Kurt Gödels Unvollständigkeitstheorem eine Rolle spielt, und dass Steven C. Weisenburger in seinem Companion zu Gravity’s Rainbow eine Erläuterung des Unvollständigkeitstheorems gibt. [...]
Nice post. I just stumbled upon your blog after doing a Google search for Hogrebe! I’ve spent the last thirty minutes perusing the site’s content and find most of it very insightful. After reading this particular post I wanted to ask whether you’d address a certain topic about which I’ve always been curious. Because I’m equipped with a rather superficial understanding of Gödel’s incompleteness theorom I can’t speak with any authority here, but it appears to me as if those working within literary studies often employ Gödel’s incompleteness theorem as a metaphor in order to provoke their readers into the recognition that every system of totality ultimately fails to account for something and, thus, leaves a remainder. When you read the commentator’s claims regarding Gödel, and its relation to Pynchon in Gravity’s Rainbow, do you find that something essential is lost in translation when G is transposed within a literary context? Is there something ontological about Gödel’s proof? That is, most people reference the proof when they attempt to “prove” that only perspectives exist.
Thanks.
There is nothing wrong with using Gödel’s theorems metaphorically – in fact, I think Pynchon does it quite successfully. Other authors, like Foster Wallace, also applies the theorems with some literary effect. Neither, of course, pretends to talk about the actual content of the mathematical theorems. The theorems are not about perspectives, nor about systems of totality. They are simply limitative results about a certain type of formal theories.
The above quote from Weisenburger’s Companion (an otherwise great source book) is unfortunately pretty misleading. First, the passage appears to mix up the first and second incompleteness theorem; second, the opaque reference to ‘mappings’ could be thought to refer either to the very process of formalizing arithmetic, or to Gödel coding, a technique applied in Gödel’s proof.
On the other hand, I’ve seen much worse summaries of the theorems: the problem is typically not that something is lost when the theorems are discussed in a literary context, but that things are added that have nothing to do with what has actually been proved. Among the things that the theorems certainly don’t prove is the claim that only perspectives exist.
[...] Farbenindustrie AG). The name is immediately familiar to anyone who has read Pynchon’s Gravity’s Rainbow. (Apprently, Pynchon’s own source is Richard Sasuly’s 1947 book IG Farben.) A number [...]
He was Austrian! Not German! Back in the good old day of Austria-Hungary…
Of course he was! Funny I didn’t spot that.