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Kurt Friedrich Gödel (/ ˈ ɡ ɜːr d əl / GUR-dəl; [2] German: [kʊʁt ˈɡøːdl̩] ⓘ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher.
Gödel's ontological proof is a formal argument by the mathematician Kurt Gödel (1906–1978) for the existence of God. The argument is in a line of development that goes back to Anselm of Canterbury (1033–1109).
From Frege to Gödel: A Source Book on Mathematical Logic 1879–1931. Harvard University Press. Bernard Meltzer (1962). On Formally Undecidable Propositions of Principia Mathematica and Related Systems. Translation of the German original by Kurt Gödel, 1931. Basic Books, 1962. Reprinted, Dover, 1992. ISBN 0-486-66980-7. Raymond Smullyan (1966).
Kurt Gödel in 1925. Gödel's Loophole is a supposed "inner contradiction" in the Constitution of the United States which Austrian-American logician, mathematician, and analytic philosopher Kurt Gödel postulated in 1947. The loophole would permit the American democracy to be legally turned into a dictatorship.
Gödel's incompleteness theorems cast unexpected light on these two related questions. Gödel's first incompleteness theorem showed that no recursive extension of Principia could be both consistent and complete for arithmetic statements. (As mentioned above, Principia itself was already known to be incomplete for some non-arithmetic statements.)
Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press. Hao Wang, 1996, A Logical Journey: From Gödel to Philosophy, The MIT Press, Cambridge MA, ISBN 0-262-23189-1. Zach, Richard (2007). "Hilbert's Program Then and Now". In Jacquette, Dale (ed.). Philosophy of logic. Handbook of the Philosophy of Science ...
In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by , is a particular class of sets that can be described entirely in terms of simpler sets. L {\displaystyle L} is the union of the constructible hierarchy L α {\displaystyle L_{\alpha }} .
Kurt Gödel developed the concept for the proof of his incompleteness theorems. (Gödel 1931) A Gödel numbering can be interpreted as an encoding in which a number is assigned to each symbol of a mathematical notation, after which a sequence of natural numbers can then represent a sequence of symbols. These sequences of natural numbers can ...