Political Logic

POLITICAL LOGIC

Political logic is not a formal system in the sense that Hilbert and the mathematical logicians meant, but mathematicians with a formalist outlook couldn't help but approach politics with the same kind of methodological sympathies. They were encouraged in this by Hilbert himself, who in his 1918 lecture “Axiomatic Thought” advocated that the other sciences adopt the axiomatic approach that had been so successful in mathematics.

For example, Gödel, whose theorem ruled out the possibility of definitively banishing contradiction from arithmetic, was also worried about the Constitution, which he was studying in preparation for his 1948 U.S. citizenship test. In his view, the document contained a contradiction that could allow a Fascist dictatorship to take over the country in a perfectly constitutional manner. Gödel’s friends Albert Einstein and Oskar Morgenstern begged him to avoid this matter in his exam, but, as Morgenstern recalls it, the conversation ended up going like this:

The examiner: Now, Mr. Gödel, where do you come from?

Gödel: Where I come from? Austria.

The examiner: What kind of government did you have in Austria?

Gödel: It was a republic, but the constitution was such that it finally was changed into a dictatorship.

The examiner: Oh! This is very bad. This could not happen in this country.

Gödel: Oh, yes, I can prove it.

Fortunately, the examiner hurriedly changed the subject and Gödel’s citizenship was duly granted. As to the nature of the contradiction Gödel found in the Constitution, it seems to have been lost to mathematical history. Perhaps for the best!

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Hilbert’s commitment to logical principle and deduction often led him, like Condorcet, to adopt a surprisingly modern outlook in non-mathematical matters.* At some political cost to himself, he refused to sign the 1914 Declaration to the Cultural World, which defended the kaiser’s war in Europe with a long list of denials, each one starting “It is not true”: “It is not true that Germany violated the neutrality of Belgium,” and so on. Many of the greatest German scientists, like Felix Klein, Wilhelm Roentgen, and Max Planck, signed the declaration. Hilbert said, quite simply, that he was unable to verify to his exacting standards that the assertions in question were not true.

A year later, when the faculty at Göttingen balked at offering a position to the great algebraist Emmy Noether, arguing that students could not possibly be asked to learn mathematics from a woman, Hilbert responded: “I do not see how the sex of the candidate is an argument against her admission. We are a university, not a bathhouse.”

But reasoned analysis of politics has its limits. As an old man in the 1930s, Hilbert seemed quite unable to grasp what was happening to his home country as the Nazis consolidated their power. His first PhD student, Otto Blumenthal, visited Hilbert in Göttingen in 1938 to celebrate his seventy-sixth birthday. Blumenthal was a Christian but came from a Jewish family, and for that reason had been removed from his academic position at Aachen. (It was the same year that Abraham Wald, in German-occupied Austria, left for the United States.)

Constance Reid, in her biography of Hilbert, recounts the conversation at the birthday party:

“What subjects are you lecturing on this semester?” Hilbert asked.

“I do not lecture anymore,” Blumenthal gently reminded him.

“What do you mean, you do not lecture?”

“I am not allowed to lecture anymore.”

“But that is completely impossible! This cannot be done. Nobody has the right to dismiss a professor unless he has committed a crime. Why do you not apply for justice?”