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)
“If the propositions of this Discourse are tenable, the “state of progressive collapse” is precisely that state in which alone we are warranted in considering All Things.”
—Edgar Allan Poe (1809–1849)
“The content of a thought depends on its external relations; on the way that the thought is related to the world, not on the way that it is related to other thoughts.”
—Jerry Alan Fodor (b. 1935)
“Before anything else, we need a new age of Enlightenment. Our present political systems must relinquish their claims on truth, justice and freedom and have to replace them with the search for truth, justice, freedom and reason.”
—Friedrich Dürrenmatt (1921–1990)