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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.
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 ...
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.
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 ...
A notable exception to the above may be the Grelling–Nelson paradox, in which words and meaning are the elements of the scenario rather than people and hair-cutting. Though it is easy to refute the barber's paradox by saying that such a barber does not (and cannot) exist, it is impossible to say something similar about a meaningfully defined ...
Unlike more general concepts of autology and self-reference, this particular distinction and opposition of autological and heterological words is uncommon in linguistics for describing linguistic phenomena or classes of words, but is current in logic and philosophy where it was introduced by Kurt Grelling and Leonard Nelson for describing a ...
The "paradox of the binary tree" is a paradox of the author's own making; see the sci.math thread "Review of Muckenheim's Book". Wikipedia is not for original research. In summary: the article is poorly organized, lacks historical context, mixes together paradoxes of naive set theory with assertions of axiomatic set theory, makes incorrect or ...