On Formally Undecidable Propositions Of Principia Mathematica And Related Systems
Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I ("On Formally Undecidable Propositions of Principia Mathematica and Related Systems I") is a paper in mathematical logic by Kurt Gödel. Dated November 17, 1930, it was originally published in German in the 1931 volume of Monatshefte für Mathematik. Several English translations have appeared in print, and the paper has been included in two collections of classic mathematical logic papers. The paper is famous for the theorems it contains, which have many implications for consistency proofs in mathematics, and for the techniques that Gödel invented to prove these theorems.
Read more about On Formally Undecidable Propositions Of Principia Mathematica And Related Systems: Outline and Key Results, Published English Translations
Famous quotes containing the words formally, propositions, related and/or systems:
“From a bed in this hotel Seargent S. Prentiss arose in the middle of the night and made a speech in defense of a bedbug that had bitten him. It was heard by a mock jury and judge, and the bedbug was formally acquitted.”
—Federal Writers’ Project Of The Wor, U.S. public relief program (1935-1943)
“All propositions are of equal value.”
—Ludwig Wittgenstein (1889–1951)
“Women stand related to beautiful nature around us, and the enamoured youth mixes their form with moon and stars, with woods and waters, and the pomp of summer. They heal us of awkwardness by their words and looks. We observe their intellectual influence on the most serious student. They refine and clear his mind: teach him to put a pleasing method into what is dry and difficult.”
—Ralph Waldo Emerson (1803–1882)
“The only people who treasure systems are those whom the whole truth evades, who want to catch it by the tail. A system is just like truth’s tail, but the truth is like a lizard. It will leave the tail in your hand and escape; it knows that it will soon grow another tail.”
—Ivan Sergeevich Turgenev (1818–1883)