In search of the sources of incompleteness

Tutkimustuotos: Artikkeli kirjassa/raportissa/konferenssijulkaisussaKonferenssiartikkeliTieteellinen

Abstrakti

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.
Alkuperäiskielienglanti
OtsikkoProceedings of the International Congress of Mathematicians 2018
ToimittajatBoyan Sirakov, Paulo Ney de Souza, Marcelo Viana
Sivumäärä19
Vuosikerta3
KustantajaWorld Scientific
Julkaisupäivä2018
Sivut4043-4061
ISBN (painettu)978-981-3272-87-3
TilaJulkaistu - 2018
OKM-julkaisutyyppiB3 Vertaisarvioimaton artikkeli konferenssijulkaisussa
TapahtumaInternational Congress of Mathematics - Rio de Janeiro, Brasilia
Kesto: 1 elok. 20189 elok. 2018

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