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Gödel's proof has also been questioned by Graham Oppy, [16] asking whether many other almost-gods would also be "proven" through Gödel's axioms. This counter-argument has been questioned by Gettings, [ 17 ] who agrees that the axioms might be questioned, but disagrees that Oppy's particular counter-example can be shown from Gödel's axioms.
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.
Kurt Gödel's achievement in modern logic is singular and monumental—indeed it is more than a monument, it is a landmark which will remain visible far in space and time. ... The subject of logic has certainly completely changed its nature and possibilities with Gödel's achievement.
During his lifetime three English translations of Gödel's paper were printed, but the process was not without difficulty. The first English translation was by Bernard Meltzer; it was published in 1963 as a standalone work by Basic Books and has since been reprinted by Dover and reprinted by Hawking (God Created the Integers, Running Press, 2005:1097ff).
Douglas Hofstadter, in his books Gödel, Escher, Bach and I Am a Strange Loop, cites Gödel's theorems as an example of what he calls a strange loop, a hierarchical, self-referential structure existing within an axiomatic formal system. He argues that this is the same kind of structure that gives rise to consciousness, the sense of "I", in the ...
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 (1925) The proof of Gödel's completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 (and a shorter version of the proof, published as an article in 1930, titled "The completeness of the axioms of the functional calculus of logic" (in German)) is not easy to read today; it uses concepts and formalisms that are no longer used and terminology that is often obscure.
The axiom of constructibility is a possible axiom for set theory in mathematics that asserts that every set is constructible.The axiom is usually written as V = L.The axiom, first investigated by Kurt Gödel, is inconsistent with the proposition that zero sharp exists and stronger large cardinal axioms (see list of large cardinal properties).