Thursday, August 14, 2008

Grelling–Nelson paradox

An example of Russell's paradox.

“From Wikipedia, the free encyclopedia

“Suppose one interprets the adjectives 'autological' and 'heterological' as follows:

“An adjective is autological if and only if it describes itself. For example 'short' is autological, since the word 'short' is short. 'English,' 'unhyphenated' and 'pentasyllabic' are also autological.

“An adjective is heterological if and only if it does not describe itself. Hence 'long' is a heterological word, as are 'abbreviated' and 'monosyllabic.'

“All adjectives, it would seem, must be either autological or heterological, for each adjective either describes itself, or it doesn't. The Grelling–Nelson paradox arises when we consider the adjective 'heterological'....

“Is 'heterological' a heterological word? If the answer is 'yes', 'heterological' is autological (leading to a contradiction). If the answer is 'no', 'heterological' is heterological (again leading to a contradiction).”

No comments: