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Grelling–Nelson paradox

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. It is closely related to several other well-known paradoxes, in particular, the barber paradox and Russell's paradox. It is an antinomy, or a semantic self-referential paradox.

Similarities with Russell's paradox[edit]

The Grelling–Nelson paradox can be translated into Russell's paradox in the following way. First, one must identify each adjective with the set of objects to which that adjective applies. So, for example, the adjective "red" is equated with the set of all red objects. In this way, the adjective "pronounceable" is equated with the set of all pronounceable things, one of which is the word "pronounceable" itself. Thus, an autological word is understood as a set, one of whose elements is the set itself. The question of whether the word "heterological" is heterological becomes the question of whether the set of all sets which do not contain themselves contains itself.

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Liar paradox

List of paradoxes

Metamagical Themas

Use–mention distinction

Grelling, K.; Nelson, L. (1908). "Bemerkungen zu den Paradoxien von Russell und Burali-Forti". Abhandlungen der Fries'schen Schule II. Göttingen. pp. 301–334.{{}}: CS1 maint: location missing publisher (link) Also in: Nelson, Leonard (1974). Gesammelte Schriften III. Die kritische Methode in ihrer Bedeutung für die Wissenschaften. Hamburg: Felix Meiner Verlag. pp. 95–127. ISBN 3787302220.

cite book

Ramsey, Frank P. (1926). "The Foundations of Mathematics". . 2. 25 (1): 338–384. doi:10.1112/plms/s2-25.1.338.

Proceedings of the London Mathematical Society

Peckhaus, Volker (2004). "Paradoxes in Göttingen". In Link, Godehard (ed.). One hundred years of Russell's paradox: mathematics, logic, philosophy. Berlin: Walter de Gruyter. pp. 501–516.  3110174383.

ISBN

Autological words

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