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...