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:
“We find the most terrible form of atheism, not in the militant and passionate struggle against the idea of God himself, but in the practical atheism of everyday living, in indifference and torpor. We often encounter these forms of atheism among those who are formally Christians.”
—Nicolai A. Berdyaev (18741948)
“In fact, of course, I hold that propositions that contemporary
philosophers would properly count as empirical can be necessary and be known to be such.”
—Saul Kripke (b. 1940)
“Just as a new scientific discovery manifests something that was already latent in the order of nature, and at the same time is logically related to the total structure of the existing science, so the new poem manifests something that was already latent in the order of words.”
—Northrop Frye (b. 1912)
“What is most original in a mans nature is often that which is most desperate. Thus new systems are forced on the world by men who simply cannot bear the pain of living with what is. Creators care nothing for their systems except that they be unique. If Hitler had been born in Nazi Germany he wouldnt have been content to enjoy the atmosphere.”
—Leonard Cohen (b. 1934)