Day 2, Friday, was Gödel’s birthday. I showed up for the panel discussion on unknowability, which wasn’t particularly enlightening. Then Piergiorgio Odifreddi gave a very entertaining talk, in which he speculated on what philosophical writings may have served as inspiration for Gödel’s results. He focussed on three figures: Aristotle, Kant, and Leibniz and drew some vague analogies between things Aristotle wrote in the Metaphysics and intuitionistic logic, between the antinomies of reason in Kant’s first Critique and incompleteness, and Leibniz’s calculus universalis and Gödel numbering. The latter was the most specific and interesting, I thought. Odifreddi reported that Sacks once told him that he heard Gödel say that he got the idea of arithmetization from Leibniz. Odifreddi went back to Leibniz’ papers to see what was in there and said that the coding Leibniz used doesn’t work — the code of a string is just the product of the codes of the symbols in it. So this is an answer to the question prompted by Coffa I mentioned a while back, but at some point I should really figure out to what extent exactly Gödel coding was anticipated by Leibniz. Then Petr Hájek gave a survey of Gödel’s ontological proof for the existence of God and the literature surrounding it. Hilary Putnam’s talk was a follow-up to his paper “Reflexive Reflections” (Erkenntnis 22, 1985, 143-154). In that paper, he gave an argument that, if human language and scientific competence can be represented by a Turing machine, we can never know that this is so. It required an assumption, viz., that no mathematical falsehood can be justified by empirical evidence, and in this talk he attempted to get rid of that assumption.
I skipped the second panel discussion to get ready for the gala dinner that night in the Belvedere’s Marble Hall. It was a very opulent affair. Here’s a picture of the place setting, so you can see just how opulent:
The galleries were open, cocktails were served, Gary Kasparov spoke, we ate, then the Young Investigator Awards were presented:
- 1st prize: Justin Moore: The continuum and aleph-2
- 2nd prize: Mark van Atten: Gödel and German Idealism
- 3rd prize: Eli Ben-Sasson: Searching for a conditional answer to Gödel’s question
After dessert, the string quartet performed the Barcarole from Offenbach’s Tales of Hoffman, which was Gödel’s favorite piece of music, and Paul Cohen gave an emotional closing speech which ended with everyone singing Happy Birthday.