Abstract
Kurt Gödel said of the discovery of his famous incompleteness theorem that he substituted “unprovable” for “false” in the paradoxical statement This sentence is false. Thereby he obtained something that states its own unprovability, so that if the statement is true, it should indeed be unprovable. The big methodical obstacle that Gödel solved so brilliantly was to code such a self-referential statement in terms of arithmetic. The shorthand notes on incompleteness that Gödel had meticulously kept are examined for the first time, with a picture of the emergence of incompleteness different from the one the received story of its discovery suggests.
| Original language | English |
|---|---|
| Title of host publication | Proceedings of the International Congress of Mathematicians 2018 |
| Editors | Boyan Sirakov, Paulo Ney de Souza, Marcelo Viana |
| Number of pages | 19 |
| Volume | 3 |
| Publisher | World Scientific |
| Publication date | 2018 |
| Pages | 4043-4061 |
| ISBN (Print) | 978-981-3272-87-3 |
| Publication status | Published - 2018 |
| MoE publication type | B3 Article in conference proceedings |
| Event | International Congress of Mathematics - Rio de Janeiro, Brazil Duration: 1 Aug 2018 → 9 Aug 2018 |
Fields of Science
- 111 Mathematics