Logic Day

"[Alfred Tarski] once confided to me that he considered himself 'the greatest living sane logician'," thus not so subtly avoiding the problem of comparison with Kurt Gödel.

lfred Tarski was born on January 14, 1901; Kurt Gödel died on January 14, 1978. In 2019, UNESCO declared this date “World Logic Day”, but for the rest of us, it’s always been the twin feast-day of Tarskimas and Gödelnalia.¹

Which raises the question: which logic-based festival should you celebrate?

Well, why not both?

For those who can’t keep those logicians straight: Kurt Gödel was the introverted Lutheran Platonist hypochondriac who exposed the limits of formal mathematical systems. Tarski was the gregarious Jewish semanticist lecher – the one who spent his life expanding those limits by tying formal logic to external statements of truth.

For Tarskimas, you could invite all your friends for food and entertainment. Serve home-made plum slivovitz. For snacks, provide hearty Central European foods: Polish ham, bigos - a heavy hunters’ stew, and Viennese pastries. Continue late into the night, popping Kola Astier, the French caffeine pills Tarski favored², and, when necessary, pot and benzedrine.

In celebration of Gödelnalia, encourage some guests to carefully examine all of the food, drinks, and drugs for signs of poison. Reject all of them if necessary. Urge them not to talk to anyone at the party, and instruct them to leave early (they will be relieved). Take a sedative washed down with Gelusil and bicarbonate to help settle your nervous stomach, and sleep off the affair, safe for for a few hours from your fear that God is unprovably absent from the world.

For those who already must deal with these kinds of party-goer in their lives – perhaps both are trapped within your own body? – the best celebration of today’s anniversaries must surely be to successfully craft a hybrid event suitable for both.

This will require a minimum of two rooms, one full of the smell of booze, pork fat and dancing, the other with pillows and dim lighting.⁵

Fortunately, we can use the date as an excuse to pick an external location for the party. In celebration of the European roots of both logicians, seek out a nearby ethnic fraternal hall or cultural center – they are surprisingly cheap to hire, and are well-organized for a private event. Polish, Czech, Austrian or German halls would work best – and if run by a local Embassy, might even sponsor the event. If you are a student, faculty will be delighted that you express any interest in academic pursuits and shower you with budget.

Now you have your venue: what should the conversation be about? Gödel, to Tarski’s continual irritation³ was the better known logician, so a parlor game or two trying to construct Gödelian propositions like “The following sentence is true. The preceding sentence is false.” should be straightforward to arrange.

Tarski’s Indefinability Theorem (1933) isn’t such a pop science draw, but it provides something of a conversational out for conversations stuck in the despair of Gödel’s proof.

Where Gödel showed that sufficiently powerful formal systems cannot prove internally all truths about themselves, Tarski showed why: you can’t even define “X is true” within a language that just contains sentences like X — truth has to be defined from outside the system.

His work went on to sketch out what those meta-systems are like, revealing a potentially infinite hierarchy of languages, each capable of describing truth for those below it—not a ladder to universal truth, exactly, but an architecture that keeps the project of truth-seeking open rather than foreclosed.

This might be symbolised by frequent cigarette breaks to the outside of the party, to discuss what kind of bullshit those inside are spouting.

For conversational bon mots: if you find yourself drawn to Gödel, you may want to brush up on one of the many fields that blossomed from his work. Why not look at Reverse Mathematics, Harvey Friedman’s 1975⁶ project to discover what axioms are necessary to prove what parts of mathematics?

If your humors match Tarski’s, his own school, Model Theory, continues to this day: dive into Peter Smith’s Logic Study Guide to explore more.

Placing Tarski and Gödel at opposing ends of the 20th century mathematical zodiac, tempting as it is, hides how much they had in common. Tarski and Gödel both successfully escaped the Nazi regime, though under very different circumstances. Tarski was lucky enough to be attending a U.S. conference just as his homeland of Poland was invaded and its borders shut, leaving him stranded with a single suitcase while his family remained trapped in wartime Poland.

Gödel and his wife followed to the United States six months later but were forced to take a circuitous route to avoid the dangerous Atlantic crossing: they traveled east on the Trans-Siberian railway through Russia to Japan, finally crossing the Pacific to San Francisco just as the war began to escalate globally.

The vital element of your Tarskimas/Gödelnalia party, then, should be to capture that bracing, alienated feeling of a suddenly exiled and harrowed intellectual community, emerging blinking into continuing possibility and a new world.

The mood need not depend on the times: while Gödel himself was depressed by the war, politics and everything else, Gödel’s family survived largely unharmed. Tarski’s wife and children had to hide in the Polish countryside until they could be rescued at the end of the war, and thirty of his closest relatives died in the Nazi death camps. He remained angry at the fate of so many, but generally cheery and ebullient for the rest of his life.

A party that can fight the despair of absent friends with the sympathetic congeniality of those present should be a successful party by all accounts.

Like relations between Thomas Jefferson and John Adams, that other pair of frenemies bound by tribulations and a fateful date⁴, Tarski and Gödel became closer in their later years, as those shared experiences overwhelmed their difference in outlook and fame:

"In spite of their profound differences in character, outlook, and attitude toward life, they had a world of understanding in common — beginning with their condition of exile, their European heritage and culture, and above all the interconnectedness of their work and their commitment to it. The tension and excitement of the unspoken competitiveness between them in its own way heightened their closeness. In their later correspondence, Tarski was one of the very few people Gödel addressed by first name and with the familiar du."

However the arguments fly in your logic party, end the night with continued friendship.