Workshop on revisiting Gödel's Incompleteness Theorems (25th WCP, August 1-8, 2024, Rome, Italy)

General abstract

Journey to the Edge of Reason - The Life of Kurt Gödel by Stephen Budiansky in 2021 (Norton & Company) presents « The first major biography written for a general audience of the logician and mathematician whose Incompleteness Theorems helped launch a modern scientific revolution. Nearly a hundred years after its publication, Kurt Gödel’s famous proof that every mathematical system must contain propositions that are true—yet never provable—continues to unsettle mathematics, philosophy, and computer science. »

This is no exaggeration, so what is there in Gödel's incompleteness theorem that unsettles people until now? Taking a closer look, we find that there is a malaise implicit in Gödel's proof: Gödel claimed to have argued that a paradoxical proposition such as « saying of itself that it is unprovable" is an "undecidable proposition" in a formal system, and thus concluded the incompleteness of the formal system.

We can't help but ask:

When "Russell's paradox" appeared in set theory, it was regarded as a crisis, and experts tried hard to resolve it. Then, when this paradoxical proposition "saying of itself that it is unprovable" appeared in Gödel's proof, why didn't experts have the same alertness, instead of treating it as a normal proposition in a formal system?
Does Gödel's proof provide a reasonable explanation for the incompleteness of formal systems? In other words, is Gödel's proof logically valid?

To promote academic and public reflection on Gödel's Incompleteness Theorems, we propose to revisit these theorems from different perspectives such as philosophy, epistemology, psychology, logic, mathematics, algorithmic theory and artificial intelligence, to penetrate into the original proof of the theorems in Gödel's 1931 paper, to go beyond the limits of our thinking, and to confront the malaise involved in Gödel's proof together.

We believe that the aspiration for truth and the seeking of truth is the most fundamental way to dissolve malaise, a quality indispensable when caring for the future of our world, …

Organizing committee