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The Grelling–Nelson paradox arises from the question of whether the term "non-self-descriptive" is self-descriptive. It was formulated in 1908 by Kurt Grelling and Leonard Nelson, and is sometimes mistakenly attributed to the German philosopher and mathematician Hermann Weyl [1] thus occasionally called Weyl's paradox or Grelling's paradox.
Grelling–Nelson paradox: Is the word "heterological", meaning "not applicable to itself", a heterological word? (A close relative of Russell's paradox .) Hilbert–Bernays paradox : If there was a name for a natural number that is identical to a name of the successor of that number, there would be a natural number equal to its successor.
The paradox is further increased by the significance of the removal sequence. If the balls are not removed in the sequence 1, 2, 3, ... but in the sequence 1, 11, 21, ... after one hour infinitely many balls populate the reservoir, although the same amount of material as before has been moved.
Kurt Grelling was born on 2 March 1886 in Berlin. His father, the Doctor of Jurisprudence Richard Grelling, and his mother, Margarethe (née Simon), were Jewish.Shortly after his arrival in 1905 at University of Göttingen, Grelling began a collaboration with philosopher Leonard Nelson, with whom he tried to solve Russell's paradox, which had shaken the foundations of mathematics when it was ...
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician, Bertrand Russell, in 1901. [1] [2] Russell's paradox shows that every set theory that contains an unrestricted comprehension principle leads to contradictions. [3]
In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in 1905. The paradox is ordinarily used to motivate the importance of distinguishing carefully between mathematics and metamathematics .
The paradox can be interpreted as an application of Cantor's diagonal argument. It inspired Kurt Gödel and Alan Turing to their famous works. Kurt Gödel considered his incompleteness theorem as analogous to Richard's paradox which, in the original version runs as follows: Let E be the set of real numbers that can be defined by a finite number ...
[1] [2] It involves a breakdown of group communication in which each member mistakenly believes that their own preferences are counter to the group's, and therefore does not raise objections. They even go so far as to state support for an outcome they do not want. A common phrase related to the Abilene paradox is a desire to not "rock the boat".