On Formally Undecidable Propositions of Principia Mathematica and Related Systems

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 (1874–1948)

    If an angel were ever to tell us anything of his philosophy I believe many propositions would sound like 2 times 2 equals 13.
    —G.C. (Georg Christoph)

    Becoming responsible adults is no longer a matter of whether children hang up their pajamas or put dirty towels in the hamper, but whether they care about themselves and others—and whether they see everyday chores as related to how we treat this planet.
    Eda Le Shan (20th century)

    In all systems of theology the devil figures as a male person.... Yes, it is women who keep the church going.
    Don Marquis (1878–1937)